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["7.505", "7.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{508}{1{,}500}, \\dfrac{523}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{544}{1{,}500}, \\dfrac{563}{1{,}500}, \\dfrac{564}{1{,}500}, \\text{ and } \\dfrac{571}{1{,}500}", "__seed__": "0004"}}, {"seed": 5, "data": {"p1_how_many": "12", "p1_a": "7.01", "p1_b": "7.02", "p1_numbers": "7.0105, 7.011, 7.0115, 7.012, 7.0125, 7.013, 7.014, 7.015, 7.016, 7.017, 7.018, and 7.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.011", "7.012", "7.013", "7.013999999999999", "7.015", "7.016", "7.0169999999999995", "7.018", "7.019"], "p1_2_xs": ["7.0104999999999995", "7.0115", "7.012499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}412}{35{,}000}, \\dfrac{21{,}074}{35{,}000}, \\dfrac{21{,}811}{35{,}000}, \\dfrac{23{,}332}{35{,}000}, \\dfrac{24{,}310}{35{,}000}, \\dfrac{24{,}819}{35{,}000}, \\dfrac{25{,}142}{35{,}000}, \\dfrac{25{,}819}{35{,}000}, \\dfrac{26{,}255}{35{,}000}, \\dfrac{27{,}779}{35{,}000}, \\text{ and } \\dfrac{27{,}860}{35{,}000}", "__seed__": "0005"}}, {"seed": 6, "data": {"p1_how_many": "13", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": 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"p2_numbers": "\\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0007"}}, {"seed": 8, "data": {"p1_how_many": "14", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.235, 8.24, 8.245, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225", "8.235", "8.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{310}{1{,}200}, \\dfrac{318}{1{,}200}, \\dfrac{323}{1{,}200}, \\dfrac{335}{1{,}200}, \\dfrac{365}{1{,}200}, \\dfrac{387}{1{,}200}, \\dfrac{391}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0008"}}, {"seed": 9, "data": {"p1_how_many": "12", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.725, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999", "1.7249999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}280}{63{,}000}, \\dfrac{28{,}666}{63{,}000}, \\dfrac{29{,}987}{63{,}000}, \\dfrac{31{,}758}{63{,}000}, \\dfrac{32{,}086}{63{,}000}, \\dfrac{33{,}361}{63{,}000}, \\dfrac{33{,}400}{63{,}000}, \\dfrac{34{,}314}{63{,}000}, \\dfrac{34{,}409}{63{,}000}, \\dfrac{35{,}562}{63{,}000}, \\dfrac{35{,}764}{63{,}000}, \\text{ and } \\dfrac{35{,}819}{63{,}000}", 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["9.0405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{662}{1{,}500}, \\dfrac{688}{1{,}500}, \\dfrac{704}{1{,}500}, \\dfrac{772}{1{,}500}, \\dfrac{791}{1{,}500}, \\dfrac{839}{1{,}500}, \\dfrac{847}{1{,}500}, \\dfrac{853}{1{,}500}, \\dfrac{929}{1{,}500}, \\text{ and } \\dfrac{999}{1{,}500}", "__seed__": "0013"}}, {"seed": 14, "data": {"p1_how_many": "14", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.335, 7.34, 7.345, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999", "7.335", "7.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}265}{12{,}000}, \\dfrac{8{,}267}{12{,}000}, \\dfrac{8{,}276}{12{,}000}, \\dfrac{8{,}441}{12{,}000}, \\dfrac{8{,}755}{12{,}000}, \\dfrac{8{,}806}{12{,}000}, \\dfrac{8{,}933}{12{,}000}, \\text{ and } \\dfrac{8{,}996}{12{,}000}", "__seed__": "0014"}}, {"seed": 15, "data": {"p1_how_many": "14", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.645, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635", "1.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}032}{3{,}500}, \\dfrac{1{,}070}{3{,}500}, \\dfrac{1{,}077}{3{,}500}, \\dfrac{1{,}087}{3{,}500}, \\dfrac{1{,}165}{3{,}500}, \\dfrac{1{,}167}{3{,}500}, \\dfrac{1{,}249}{3{,}500}, \\dfrac{1{,}265}{3{,}500}, \\dfrac{1{,}321}{3{,}500}, \\dfrac{1{,}363}{3{,}500}, \\dfrac{1{,}387}{3{,}500}, \\text{ and } \\dfrac{1{,}399}{3{,}500}", "__seed__": "0015"}}, {"seed": 16, "data": {"p1_how_many": "13", "p1_a": "2.13", "p1_b": "2.14", "p1_numbers": "2.1305, 2.131, 2.1315, 2.132, 2.1325, 2.133, 2.1335, 2.134, 2.135, 2.136, 2.137, 2.138, and 2.139", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.131", "2.1319999999999997", "2.133", "2.134", "2.135", "2.1359999999999997", "2.137", "2.138", "2.139"], "p1_2_xs": ["2.1305", "2.1315", "2.1325", "2.1335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{812}{1{,}200}, \\dfrac{825}{1{,}200}, \\dfrac{843}{1{,}200}, \\dfrac{846}{1{,}200}, \\dfrac{847}{1{,}200}, \\dfrac{854}{1{,}200}, \\text{ and } \\dfrac{868}{1{,}200}", "__seed__": "0016"}}, {"seed": 17, "data": {"p1_how_many": "10", "p1_a": "9.46", "p1_b": "9.47", "p1_numbers": "9.4605, 9.461, 9.462, 9.463, 9.464, 9.465, 9.466, 9.467, 9.468, and 9.469", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.461", "9.462000000000002", "9.463000000000001", "9.464", "9.465000000000002", "9.466000000000001", "9.467", "9.468", "9.469000000000001"], "p1_2_xs": ["9.460500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}072}{3{,}500}, \\dfrac{2{,}130}{3{,}500}, \\dfrac{2{,}135}{3{,}500}, \\dfrac{2{,}257}{3{,}500}, \\dfrac{2{,}260}{3{,}500}, \\dfrac{2{,}371}{3{,}500}, \\dfrac{2{,}379}{3{,}500}, \\dfrac{2{,}636}{3{,}500}, \\dfrac{2{,}763}{3{,}500}, \\dfrac{2{,}778}{3{,}500}, \\text{ and } \\dfrac{2{,}786}{3{,}500}", "__seed__": "0017"}}, {"seed": 18, "data": {"p1_how_many": "11", "p1_a": "9.63", "p1_b": "9.64", "p1_numbers": "9.6305, 9.631, 9.6315, 9.632, 9.633, 9.634, 9.635, 9.636, 9.637, 9.638, and 9.639", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.631", "9.632000000000001", "9.633000000000001", "9.634", "9.635000000000002", "9.636000000000001", "9.637", "9.638", "9.639000000000001"], "p1_2_xs": ["9.630500000000001", "9.6315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}097}{12{,}000}, \\dfrac{8{,}252}{12{,}000}, \\dfrac{8{,}327}{12{,}000}, \\dfrac{8{,}525}{12{,}000}, \\dfrac{8{,}645}{12{,}000}, \\dfrac{8{,}760}{12{,}000}, \\dfrac{8{,}772}{12{,}000}, \\text{ and } \\dfrac{8{,}815}{12{,}000}", "__seed__": "0018"}}, {"seed": 19, "data": {"p1_how_many": "12", "p1_a": "9.34", "p1_b": "9.35", "p1_numbers": "9.3405, 9.341, 9.3415, 9.342, 9.3425, 9.343, 9.344, 9.345, 9.346, 9.347, 9.348, and 9.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.341", "9.342", "9.343", "9.344", "9.345", "9.346", "9.347", "9.347999999999999", "9.349"], "p1_2_xs": ["9.3405", "9.3415", "9.342500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{7{,}002}{56{,}000}, \\dfrac{7{,}021}{56{,}000}, \\dfrac{7{,}096}{56{,}000}, \\dfrac{7{,}159}{56{,}000}, \\dfrac{7{,}220}{56{,}000}, \\dfrac{7{,}321}{56{,}000}, \\dfrac{7{,}407}{56{,}000}, \\dfrac{7{,}408}{56{,}000}, \\dfrac{7{,}512}{56{,}000}, \\dfrac{7{,}689}{56{,}000}, \\dfrac{7{,}702}{56{,}000}, \\text{ and } \\dfrac{7{,}883}{56{,}000}", "__seed__": "0019"}}, {"seed": 20, "data": {"p1_how_many": "13", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{86}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0020"}}, {"seed": 21, "data": {"p1_how_many": "13", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.635, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999", "6.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}397}{20{,}000}, \\dfrac{12{,}749}{20{,}000}, \\dfrac{12{,}842}{20{,}000}, \\dfrac{12{,}851}{20{,}000}, \\dfrac{12{,}910}{20{,}000}, \\dfrac{12{,}936}{20{,}000}, \\dfrac{13{,}440}{20{,}000}, \\dfrac{13{,}549}{20{,}000}, \\dfrac{13{,}897}{20{,}000}, \\dfrac{13{,}941}{20{,}000}, \\dfrac{14{,}010}{20{,}000}, \\text{ and } \\dfrac{14{,}812}{20{,}000}", "__seed__": "0021"}}, {"seed": 22, "data": {"p1_how_many": "10", "p1_a": "9.61", "p1_b": "9.62", "p1_numbers": "9.6105, 9.611, 9.612, 9.613, 9.614, 9.615, 9.616, 9.617, 9.618, and 9.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.610999999999999", "9.612", "9.613", "9.613999999999999", "9.615", "9.616", "9.616999999999999", "9.617999999999999", "9.619"], "p1_2_xs": ["9.6105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}524}{42{,}000}, \\dfrac{30{,}556}{42{,}000}, \\dfrac{31{,}791}{42{,}000}, \\dfrac{32{,}491}{42{,}000}, \\dfrac{32{,}574}{42{,}000}, \\dfrac{33{,}445}{42{,}000}, \\dfrac{33{,}516}{42{,}000}, \\dfrac{33{,}549}{42{,}000}, \\dfrac{33{,}558}{42{,}000}, \\dfrac{34{,}268}{42{,}000}, \\text{ and } \\dfrac{34{,}794}{42{,}000}", "__seed__": "0022"}}, {"seed": 23, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}160}{35{,}000}, \\dfrac{7{,}670}{35{,}000}, \\dfrac{8{,}044}{35{,}000}, \\dfrac{8{,}205}{35{,}000}, \\dfrac{8{,}310}{35{,}000}, \\dfrac{8{,}410}{35{,}000}, \\dfrac{8{,}872}{35{,}000}, \\dfrac{9{,}095}{35{,}000}, \\text{ and } \\dfrac{9{,}911}{35{,}000}", "__seed__": "0023"}}, {"seed": 24, "data": {"p1_how_many": "10", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.52, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{92}{630}, \\dfrac{95}{630}, \\dfrac{108}{630}, \\dfrac{113}{630}, \\dfrac{118}{630}, \\dfrac{130}{630}, \\text{ and } \\dfrac{134}{630}", "__seed__": "0024"}}, {"seed": 25, "data": {"p1_how_many": "12", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}362}{20{,}000}, \\dfrac{4{,}521}{20{,}000}, \\dfrac{4{,}546}{20{,}000}, \\dfrac{4{,}628}{20{,}000}, \\dfrac{4{,}767}{20{,}000}, \\dfrac{4{,}889}{20{,}000}, \\text{ and } \\dfrac{4{,}927}{20{,}000}", "__seed__": "0025"}}, {"seed": 26, "data": {"p1_how_many": "12", "p1_a": "6.83", "p1_b": "6.84", "p1_numbers": "6.8305, 6.831, 6.8315, 6.832, 6.8325, 6.833, 6.834, 6.835, 6.836, 6.837, 6.838, and 6.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.831", "6.832", "6.833", "6.834", "6.835", "6.836", "6.837", "6.838", "6.839"], "p1_2_xs": ["6.8305", "6.8315", "6.8325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0026"}}, {"seed": 27, "data": {"p1_how_many": "12", "p1_a": "2.74", "p1_b": "2.75", "p1_numbers": "2.7405, 2.741, 2.7415, 2.742, 2.7425, 2.743, 2.744, 2.745, 2.746, 2.747, 2.748, and 2.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.741", "2.742", "2.7430000000000003", "2.744", "2.745", "2.746", "2.7470000000000003", "2.748", "2.749"], "p1_2_xs": ["2.7405000000000004", "2.7415000000000003", "2.7425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{501}{2{,}000}, \\dfrac{506}{2{,}000}, \\dfrac{527}{2{,}000}, \\dfrac{592}{2{,}000}, \\dfrac{605}{2{,}000}, \\dfrac{613}{2{,}000}, \\dfrac{671}{2{,}000}, \\dfrac{686}{2{,}000}, \\text{ and } \\dfrac{743}{2{,}000}", "__seed__": "0027"}}, {"seed": 28, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", "2.4349999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}210}{5{,}600}, \\dfrac{3{,}260}{5{,}600}, \\dfrac{3{,}269}{5{,}600}, \\dfrac{3{,}297}{5{,}600}, \\dfrac{3{,}334}{5{,}600}, \\dfrac{3{,}338}{5{,}600}, \\dfrac{3{,}412}{5{,}600}, \\dfrac{3{,}425}{5{,}600}, \\dfrac{3{,}426}{5{,}600}, \\text{ and } \\dfrac{3{,}445}{5{,}600}", "__seed__": "0028"}}, {"seed": 29, "data": {"p1_how_many": "11", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}098}{42{,}000}, \\dfrac{35{,}154}{42{,}000}, \\dfrac{35{,}216}{42{,}000}, \\dfrac{35{,}289}{42{,}000}, \\dfrac{35{,}374}{42{,}000}, \\dfrac{35{,}414}{42{,}000}, \\dfrac{35{,}728}{42{,}000}, \\dfrac{35{,}779}{42{,}000}, \\text{ and } \\dfrac{35{,}852}{42{,}000}", "__seed__": "0029"}}, {"seed": 30, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.5005, 7.501, 7.502, 7.503, 7.504, 7.505, 7.506, 7.507, 7.508, and 7.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.501", "7.502", "7.503", "7.504", "7.505", "7.506", "7.507", "7.508", "7.509"], "p1_2_xs": ["7.5005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}100}{30{,}000}, \\dfrac{5{,}412}{30{,}000}, \\dfrac{5{,}422}{30{,}000}, \\dfrac{5{,}455}{30{,}000}, \\dfrac{5{,}505}{30{,}000}, \\dfrac{5{,}602}{30{,}000}, \\dfrac{5{,}655}{30{,}000}, \\dfrac{5{,}842}{30{,}000}, \\text{ and } \\dfrac{5{,}858}{30{,}000}", "__seed__": "0030"}}, {"seed": 31, "data": {"p1_how_many": "12", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.0005, 7.001, 7.0015, 7.002, 7.0025, 7.003, 7.004, 7.005, 7.006, 7.007, 7.008, and 7.009", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.001", "7.002", "7.003", "7.004", "7.005", "7.006", "7.007", "7.008", "7.009"], "p1_2_xs": ["7.0005", "7.0015", "7.0024999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\dfrac{48}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0031"}}, {"seed": 32, "data": {"p1_how_many": "13", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.135, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125", "8.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}404}{15{,}000}, \\dfrac{7{,}976}{15{,}000}, \\dfrac{8{,}803}{15{,}000}, \\dfrac{9{,}397}{15{,}000}, \\dfrac{9{,}425}{15{,}000}, \\dfrac{9{,}637}{15{,}000}, \\dfrac{9{,}680}{15{,}000}, \\dfrac{9{,}685}{15{,}000}, \\text{ and } \\dfrac{9{,}786}{15{,}000}", "__seed__": "0032"}}, {"seed": 33, "data": {"p1_how_many": "11", "p1_a": "1.23", "p1_b": "1.24", "p1_numbers": "1.2305, 1.231, 1.2315, 1.232, 1.233, 1.234, 1.235, 1.236, 1.237, 1.238, and 1.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.2309999999999999", "1.232", "1.2329999999999999", "1.234", "1.2349999999999999", "1.236", "1.2369999999999999", "1.238", "1.2389999999999999"], "p1_2_xs": ["1.2305", "1.2314999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}016}{56{,}000}, \\dfrac{48{,}038}{56{,}000}, \\dfrac{48{,}193}{56{,}000}, \\dfrac{48{,}332}{56{,}000}, \\dfrac{48{,}431}{56{,}000}, \\dfrac{48{,}644}{56{,}000}, \\dfrac{48{,}711}{56{,}000}, \\dfrac{48{,}752}{56{,}000}, \\text{ and } \\dfrac{48{,}813}{56{,}000}", "__seed__": "0033"}}, {"seed": 34, "data": {"p1_how_many": "11", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0034"}}, {"seed": 35, "data": {"p1_how_many": "12", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.025, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015", "6.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{62}{150}, \\dfrac{68}{150}, \\dfrac{75}{150}, \\dfrac{76}{150}, \\dfrac{89}{150}, \\dfrac{94}{150}, \\text{ and } \\dfrac{96}{150}", "__seed__": "0035"}}, {"seed": 36, "data": {"p1_how_many": "11", "p1_a": "9.87", "p1_b": "9.88", "p1_numbers": "9.8705, 9.871, 9.8715, 9.872, 9.873, 9.874, 9.875, 9.876, 9.877, 9.878, and 9.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.870999999999999", "9.872", "9.873", "9.873999999999999", "9.875", "9.876", "9.876999999999999", "9.877999999999998", "9.879"], "p1_2_xs": ["9.8705", "9.8715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}046}{42{,}000}, \\dfrac{35{,}130}{42{,}000}, \\dfrac{35{,}275}{42{,}000}, \\dfrac{35{,}322}{42{,}000}, \\dfrac{35{,}331}{42{,}000}, \\dfrac{35{,}406}{42{,}000}, \\dfrac{35{,}471}{42{,}000}, \\dfrac{35{,}574}{42{,}000}, \\dfrac{35{,}845}{42{,}000}, \\dfrac{35{,}896}{42{,}000}, \\dfrac{35{,}917}{42{,}000}, \\text{ and } \\dfrac{35{,}969}{42{,}000}", "__seed__": "0036"}}, {"seed": 37, "data": {"p1_how_many": "10", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.12, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}725}{5{,}600}, \\dfrac{1{,}757}{5{,}600}, \\dfrac{1{,}811}{5{,}600}, \\dfrac{1{,}844}{5{,}600}, \\dfrac{1{,}901}{5{,}600}, \\dfrac{1{,}936}{5{,}600}, \\dfrac{1{,}945}{5{,}600}, \\dfrac{2{,}044}{5{,}600}, \\dfrac{2{,}075}{5{,}600}, \\text{ and } \\dfrac{2{,}091}{5{,}600}", "__seed__": "0037"}}, {"seed": 38, "data": {"p1_how_many": "14", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.535, 1.54, 1.545, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525", "1.535", "1.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{163}{350}, \\dfrac{173}{350}, \\dfrac{189}{350}, \\dfrac{193}{350}, \\dfrac{195}{350}, \\dfrac{198}{350}, \\dfrac{202}{350}, \\text{ and } \\dfrac{208}{350}", "__seed__": "0038"}}, {"seed": 39, "data": {"p1_how_many": "11", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{402}{2{,}000}, \\dfrac{412}{2{,}000}, \\dfrac{416}{2{,}000}, \\dfrac{429}{2{,}000}, \\dfrac{436}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{467}{2{,}000}, \\dfrac{473}{2{,}000}, \\dfrac{490}{2{,}000}, \\dfrac{491}{2{,}000}, \\text{ and } \\dfrac{492}{2{,}000}", "__seed__": "0039"}}, {"seed": 40, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}002}{42{,}000}, \\dfrac{6{,}142}{42{,}000}, \\dfrac{6{,}165}{42{,}000}, \\dfrac{6{,}275}{42{,}000}, \\dfrac{6{,}397}{42{,}000}, \\dfrac{6{,}408}{42{,}000}, \\dfrac{6{,}532}{42{,}000}, \\dfrac{6{,}971}{42{,}000}, \\text{ and } \\dfrac{6{,}989}{42{,}000}", "__seed__": "0040"}}, {"seed": 41, "data": {"p1_how_many": "12", "p1_a": "5.45", "p1_b": "5.46", "p1_numbers": "5.4505, 5.451, 5.4515, 5.452, 5.4525, 5.453, 5.454, 5.455, 5.456, 5.457, 5.458, and 5.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.4510000000000005", "5.452", "5.453", "5.454", "5.455", "5.456", "5.457", "5.458", "5.4590000000000005"], "p1_2_xs": ["5.4505", "5.4515", "5.4525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}016}{35{,}000}, \\dfrac{20{,}316}{35{,}000}, \\dfrac{20{,}375}{35{,}000}, \\dfrac{20{,}429}{35{,}000}, \\dfrac{20{,}494}{35{,}000}, \\dfrac{20{,}507}{35{,}000}, \\dfrac{20{,}544}{35{,}000}, \\dfrac{20{,}580}{35{,}000}, \\dfrac{20{,}601}{35{,}000}, \\dfrac{20{,}637}{35{,}000}, \\dfrac{20{,}651}{35{,}000}, \\text{ and } \\dfrac{20{,}830}{35{,}000}", "__seed__": "0041"}}, {"seed": 42, "data": {"p1_how_many": "14", "p1_a": "3.07", "p1_b": "3.08", "p1_numbers": "3.0705, 3.071, 3.0715, 3.072, 3.0725, 3.073, 3.0735, 3.074, 3.0745, 3.075, 3.076, 3.077, 3.078, and 3.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.0709999999999997", "3.0719999999999996", "3.073", "3.074", "3.0749999999999997", "3.0759999999999996", "3.077", "3.078", "3.0789999999999997"], "p1_2_xs": ["3.0705", "3.0715", "3.0725", "3.0735", "3.0745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{318}{1{,}200}, \\dfrac{354}{1{,}200}, \\dfrac{369}{1{,}200}, \\dfrac{372}{1{,}200}, \\dfrac{383}{1{,}200}, \\dfrac{387}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0042"}}, {"seed": 43, "data": {"p1_how_many": "13", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.735, 3.74, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725", "3.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}230}{2{,}000}, \\dfrac{1{,}237}{2{,}000}, \\dfrac{1{,}299}{2{,}000}, \\dfrac{1{,}354}{2{,}000}, \\dfrac{1{,}362}{2{,}000}, \\dfrac{1{,}371}{2{,}000}, \\dfrac{1{,}388}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\text{ and } \\dfrac{1{,}443}{2{,}000}", "__seed__": "0043"}}, {"seed": 44, "data": {"p1_how_many": "13", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315", "1.325", "1.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}509}{3{,}500}, \\dfrac{1{,}553}{3{,}500}, \\dfrac{1{,}665}{3{,}500}, \\dfrac{1{,}698}{3{,}500}, \\dfrac{1{,}710}{3{,}500}, \\dfrac{1{,}733}{3{,}500}, \\dfrac{1{,}754}{3{,}500}, \\dfrac{1{,}823}{3{,}500}, \\dfrac{1{,}859}{3{,}500}, \\text{ and } \\dfrac{1{,}876}{3{,}500}", "__seed__": "0044"}}, {"seed": 45, "data": {"p1_how_many": "13", "p1_a": "1.35", "p1_b": "1.36", "p1_numbers": "1.3505, 1.351, 1.3515, 1.352, 1.3525, 1.353, 1.3535, 1.354, 1.355, 1.356, 1.357, 1.358, and 1.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.351", "1.352", "1.353", "1.354", "1.355", "1.356", "1.357", "1.358", "1.359"], "p1_2_xs": ["1.3505", "1.3515", "1.3525", "1.3535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{67}{150}, \\dfrac{70}{150}, \\dfrac{71}{150}, \\dfrac{72}{150}, \\dfrac{74}{150}, \\dfrac{80}{150}, \\dfrac{82}{150}, \\dfrac{83}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0045"}}, {"seed": 46, "data": {"p1_how_many": "12", "p1_a": "6.4", "p1_b": "6.5", "p1_numbers": "6.405, 6.41, 6.415, 6.42, 6.425, 6.43, 6.44, 6.45, 6.46, 6.47, 6.48, and 6.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.41", "6.42", "6.430000000000001", "6.44", "6.45", "6.46", "6.470000000000001", "6.48", "6.49"], "p1_2_xs": ["6.405", "6.415", "6.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}362}{2{,}000}, \\dfrac{1{,}381}{2{,}000}, \\dfrac{1{,}412}{2{,}000}, \\dfrac{1{,}419}{2{,}000}, \\dfrac{1{,}424}{2{,}000}, \\dfrac{1{,}467}{2{,}000}, \\text{ and } \\dfrac{1{,}471}{2{,}000}", "__seed__": "0046"}}, {"seed": 47, "data": {"p1_how_many": "10", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.22, 9.23, 9.24, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}008}{15{,}000}, \\dfrac{6{,}681}{15{,}000}, \\dfrac{8{,}230}{15{,}000}, \\dfrac{8{,}890}{15{,}000}, \\dfrac{9{,}096}{15{,}000}, \\dfrac{9{,}265}{15{,}000}, \\text{ and } \\dfrac{9{,}940}{15{,}000}", "__seed__": "0047"}}, {"seed": 48, "data": {"p1_how_many": "13", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.125, 9.13, 9.135, 9.14, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125", "9.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{99}{630}, \\dfrac{102}{630}, \\dfrac{112}{630}, \\dfrac{116}{630}, \\dfrac{122}{630}, \\dfrac{127}{630}, \\dfrac{130}{630}, \\dfrac{135}{630}, \\text{ and } \\dfrac{139}{630}", "__seed__": "0048"}}, {"seed": 49, "data": {"p1_how_many": "11", "p1_a": "2.14", "p1_b": "2.15", "p1_numbers": "2.1405, 2.141, 2.1415, 2.142, 2.143, 2.144, 2.145, 2.146, 2.147, 2.148, and 2.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.141", "2.142", "2.1430000000000002", "2.144", "2.145", "2.146", "2.1470000000000002", "2.148", "2.149"], "p1_2_xs": ["2.1405000000000003", "2.1415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}012}{15{,}000}, \\dfrac{5{,}026}{15{,}000}, \\dfrac{5{,}159}{15{,}000}, \\dfrac{5{,}212}{15{,}000}, \\dfrac{5{,}441}{15{,}000}, \\dfrac{5{,}513}{15{,}000}, \\dfrac{5{,}543}{15{,}000}, \\dfrac{5{,}769}{15{,}000}, \\dfrac{5{,}854}{15{,}000}, \\dfrac{5{,}953}{15{,}000}, \\dfrac{5{,}979}{15{,}000}, \\text{ and } \\dfrac{5{,}995}{15{,}000}", "__seed__": "0049"}}, {"seed": 50, "data": {"p1_how_many": "10", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}227}{2{,}000}, \\dfrac{1{,}283}{2{,}000}, \\dfrac{1{,}332}{2{,}000}, \\dfrac{1{,}369}{2{,}000}, \\dfrac{1{,}398}{2{,}000}, \\dfrac{1{,}412}{2{,}000}, \\dfrac{1{,}458}{2{,}000}, \\dfrac{1{,}482}{2{,}000}, \\text{ and } \\dfrac{1{,}487}{2{,}000}", "__seed__": "0050"}}, {"seed": 51, "data": {"p1_how_many": "13", "p1_a": "7.75", "p1_b": "7.76", "p1_numbers": "7.7505, 7.751, 7.7515, 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"5.8325", "5.8335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}724}{6{,}300}, \\dfrac{2{,}731}{6{,}300}, \\dfrac{2{,}735}{6{,}300}, \\dfrac{2{,}760}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}790}{6{,}300}, \\text{ and } \\dfrac{2{,}793}{6{,}300}", "__seed__": "0054"}}, {"seed": 55, "data": {"p1_how_many": "11", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.63, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}202}{5{,}600}, \\dfrac{3{,}207}{5{,}600}, \\dfrac{3{,}264}{5{,}600}, \\dfrac{3{,}287}{5{,}600}, \\dfrac{3{,}338}{5{,}600}, \\dfrac{3{,}346}{5{,}600}, \\dfrac{3{,}422}{5{,}600}, \\dfrac{3{,}442}{5{,}600}, \\text{ and } \\dfrac{3{,}479}{5{,}600}", "__seed__": "0055"}}, {"seed": 56, "data": {"p1_how_many": "14", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.745, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735", "2.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}096}{12{,}000}, \\dfrac{3{,}121}{12{,}000}, \\dfrac{3{,}129}{12{,}000}, \\dfrac{3{,}182}{12{,}000}, \\dfrac{3{,}185}{12{,}000}, \\dfrac{3{,}299}{12{,}000}, \\dfrac{3{,}377}{12{,}000}, \\dfrac{3{,}440}{12{,}000}, \\dfrac{3{,}514}{12{,}000}, \\dfrac{3{,}697}{12{,}000}, \\dfrac{3{,}989}{12{,}000}, \\text{ and } \\dfrac{3{,}991}{12{,}000}", "__seed__": "0056"}}, {"seed": 57, "data": {"p1_how_many": "14", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.445, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435", "9.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}010}{63{,}000}, \\dfrac{27{,}035}{63{,}000}, \\dfrac{27{,}081}{63{,}000}, \\dfrac{27{,}371}{63{,}000}, \\dfrac{27{,}396}{63{,}000}, \\dfrac{27{,}611}{63{,}000}, \\dfrac{27{,}677}{63{,}000}, \\dfrac{27{,}785}{63{,}000}, \\text{ and } \\dfrac{27{,}888}{63{,}000}", "__seed__": "0057"}}, {"seed": 58, "data": {"p1_how_many": "11", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}139}{15{,}000}, \\dfrac{6{,}251}{15{,}000}, \\dfrac{7{,}090}{15{,}000}, \\dfrac{7{,}387}{15{,}000}, \\dfrac{8{,}199}{15{,}000}, \\dfrac{8{,}257}{15{,}000}, \\dfrac{8{,}737}{15{,}000}, \\dfrac{8{,}972}{15{,}000}, \\dfrac{9{,}488}{15{,}000}, \\dfrac{9{,}505}{15{,}000}, \\dfrac{9{,}609}{15{,}000}, \\text{ and } \\dfrac{9{,}781}{15{,}000}", "__seed__": "0058"}}, {"seed": 59, "data": {"p1_how_many": "12", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.625, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998", "2.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}607}{42{,}000}, \\dfrac{8{,}347}{42{,}000}, \\dfrac{8{,}898}{42{,}000}, \\dfrac{8{,}948}{42{,}000}, \\dfrac{10{,}129}{42{,}000}, \\dfrac{10{,}164}{42{,}000}, \\dfrac{11{,}063}{42{,}000}, \\dfrac{11{,}867}{42{,}000}, \\text{ and } \\dfrac{11{,}989}{42{,}000}", "__seed__": 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7.25, 7.26, 7.27, 7.28, and 7.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.21", "7.22", "7.23", "7.24", "7.25", "7.26", "7.2700000000000005", "7.28", "7.29"], "p1_2_xs": ["7.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{811}{1{,}200}, \\dfrac{824}{1{,}200}, \\dfrac{827}{1{,}200}, \\dfrac{829}{1{,}200}, \\dfrac{850}{1{,}200}, \\dfrac{860}{1{,}200}, \\dfrac{866}{1{,}200}, \\dfrac{868}{1{,}200}, \\dfrac{872}{1{,}200}, \\dfrac{873}{1{,}200}, \\dfrac{875}{1{,}200}, \\text{ and } \\dfrac{892}{1{,}200}", "__seed__": "0061"}}, {"seed": 62, "data": {"p1_how_many": "12", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.425, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", 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"9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}502}{2{,}000}, \\dfrac{1{,}516}{2{,}000}, \\dfrac{1{,}527}{2{,}000}, \\dfrac{1{,}529}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}551}{2{,}000}, \\dfrac{1{,}554}{2{,}000}, \\dfrac{1{,}569}{2{,}000}, \\text{ and } \\dfrac{1{,}586}{2{,}000}", "__seed__": "0063"}}, {"seed": 64, "data": {"p1_how_many": "14", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.645, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635", "1.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}170}{35{,}000}, \\dfrac{21{,}438}{35{,}000}, \\dfrac{22{,}800}{35{,}000}, \\dfrac{22{,}932}{35{,}000}, \\dfrac{23{,}416}{35{,}000}, \\dfrac{24{,}133}{35{,}000}, \\dfrac{25{,}067}{35{,}000}, \\dfrac{25{,}967}{35{,}000}, \\dfrac{26{,}570}{35{,}000}, \\text{ and } \\dfrac{26{,}586}{35{,}000}", "__seed__": "0064"}}, {"seed": 65, "data": {"p1_how_many": "11", "p1_a": "5.25", "p1_b": "5.26", "p1_numbers": "5.2505, 5.251, 5.2515, 5.252, 5.253, 5.254, 5.255, 5.256, 5.257, 5.258, and 5.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.251", "5.252", "5.253", "5.254", "5.255", "5.256", "5.257", "5.258", "5.259"], "p1_2_xs": ["5.2505", "5.2515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}509}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}524}{4{,}200}, \\dfrac{3{,}526}{4{,}200}, \\dfrac{3{,}534}{4{,}200}, \\dfrac{3{,}540}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\dfrac{3{,}588}{4{,}200}, \\text{ and } \\dfrac{3{,}599}{4{,}200}", "__seed__": "0065"}}, {"seed": 66, "data": {"p1_how_many": "12", "p1_a": "4.44", "p1_b": "4.45", "p1_numbers": "4.4405, 4.441, 4.4415, 4.442, 4.4425, 4.443, 4.444, 4.445, 4.446, 4.447, 4.448, and 4.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.441000000000001", "4.442", "4.4430000000000005", "4.444", "4.445", "4.446000000000001", "4.447", "4.448", "4.449000000000001"], "p1_2_xs": ["4.4405", "4.4415000000000004", "4.4425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{604}{1{,}500}, \\dfrac{662}{1{,}500}, \\dfrac{669}{1{,}500}, \\dfrac{771}{1{,}500}, \\dfrac{794}{1{,}500}, \\dfrac{807}{1{,}500}, \\dfrac{860}{1{,}500}, \\dfrac{875}{1{,}500}, \\dfrac{927}{1{,}500}, \\text{ and } \\dfrac{991}{1{,}500}", "__seed__": "0066"}}, {"seed": 67, "data": {"p1_how_many": "11", "p1_a": "4.02", "p1_b": "4.03", "p1_numbers": "4.0205, 4.021, 4.0215, 4.022, 4.023, 4.024, 4.025, 4.026, 4.027, 4.028, and 4.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.021", "4.021999999999999", "4.023", "4.023999999999999", "4.0249999999999995", "4.026", "4.026999999999999", "4.028", "4.029"], "p1_2_xs": ["4.020499999999999", "4.0215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}531}{5{,}600}, \\dfrac{3{,}604}{5{,}600}, \\dfrac{3{,}626}{5{,}600}, \\dfrac{3{,}708}{5{,}600}, \\dfrac{3{,}763}{5{,}600}, \\dfrac{3{,}815}{5{,}600}, \\dfrac{3{,}829}{5{,}600}, \\dfrac{3{,}868}{5{,}600}, \\dfrac{3{,}874}{5{,}600}, \\dfrac{3{,}884}{5{,}600}, \\text{ and } \\dfrac{3{,}951}{5{,}600}", "__seed__": "0067"}}, {"seed": 68, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}096}{30{,}000}, \\dfrac{24{,}225}{30{,}000}, \\dfrac{24{,}249}{30{,}000}, \\dfrac{24{,}451}{30{,}000}, \\dfrac{24{,}458}{30{,}000}, \\dfrac{24{,}464}{30{,}000}, \\dfrac{24{,}497}{30{,}000}, \\dfrac{24{,}535}{30{,}000}, \\dfrac{24{,}629}{30{,}000}, \\dfrac{24{,}735}{30{,}000}, \\text{ and } \\dfrac{24{,}998}{30{,}000}", "__seed__": "0068"}}, {"seed": 69, "data": {"p1_how_many": "10", "p1_a": "9.72", "p1_b": "9.73", "p1_numbers": "9.7205, 9.721, 9.722, 9.723, 9.724, 9.725, 9.726, 9.727, 9.728, and 9.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.721", "9.722000000000001", "9.723", "9.724", "9.725000000000001", "9.726", "9.727", "9.728", "9.729000000000001"], "p1_2_xs": ["9.720500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}219}{2{,}000}, \\dfrac{1{,}244}{2{,}000}, \\dfrac{1{,}291}{2{,}000}, \\dfrac{1{,}303}{2{,}000}, \\dfrac{1{,}368}{2{,}000}, \\dfrac{1{,}393}{2{,}000}, \\dfrac{1{,}425}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\dfrac{1{,}453}{2{,}000}, \\text{ and } \\dfrac{1{,}496}{2{,}000}", "__seed__": "0069"}}, {"seed": 70, "data": {"p1_how_many": "13", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}501}{4{,}200}, \\dfrac{3{,}505}{4{,}200}, \\dfrac{3{,}512}{4{,}200}, \\dfrac{3{,}532}{4{,}200}, \\dfrac{3{,}544}{4{,}200}, \\dfrac{3{,}546}{4{,}200}, \\text{ and } \\dfrac{3{,}593}{4{,}200}", "__seed__": "0070"}}, {"seed": 71, "data": {"p1_how_many": "14", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.545, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535", "7.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}005}{30{,}000}, \\dfrac{5{,}014}{30{,}000}, \\dfrac{5{,}075}{30{,}000}, \\dfrac{5{,}109}{30{,}000}, \\dfrac{5{,}231}{30{,}000}, \\dfrac{5{,}295}{30{,}000}, \\dfrac{5{,}352}{30{,}000}, \\dfrac{5{,}408}{30{,}000}, \\dfrac{5{,}589}{30{,}000}, \\dfrac{5{,}809}{30{,}000}, \\dfrac{5{,}908}{30{,}000}, \\text{ and } \\dfrac{5{,}966}{30{,}000}", "__seed__": "0071"}}, {"seed": 72, "data": {"p1_how_many": "10", "p1_a": "3.33", "p1_b": "3.34", "p1_numbers": "3.3305, 3.331, 3.332, 3.333, 3.334, 3.335, 3.336, 3.337, 3.338, and 3.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.331", "3.332", "3.333", "3.334", "3.335", "3.336", "3.337", "3.338", "3.339"], "p1_2_xs": ["3.3305000000000002"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}154}{20{,}000}, \\dfrac{4{,}171}{20{,}000}, \\dfrac{4{,}205}{20{,}000}, \\dfrac{4{,}251}{20{,}000}, \\dfrac{4{,}341}{20{,}000}, \\dfrac{4{,}693}{20{,}000}, \\dfrac{4{,}717}{20{,}000}, \\dfrac{4{,}802}{20{,}000}, \\text{ and } \\dfrac{4{,}962}{20{,}000}", "__seed__": "0072"}}, {"seed": 73, "data": {"p1_how_many": "10", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}381}{56{,}000}, \\dfrac{17{,}260}{56{,}000}, \\dfrac{17{,}752}{56{,}000}, \\dfrac{19{,}208}{56{,}000}, \\dfrac{20{,}611}{56{,}000}, \\dfrac{20{,}659}{56{,}000}, \\dfrac{20{,}679}{56{,}000}, \\text{ and } \\dfrac{20{,}826}{56{,}000}", "__seed__": "0073"}}, {"seed": 74, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{911}{6{,}300}, \\dfrac{938}{6{,}300}, \\dfrac{1{,}019}{6{,}300}, \\dfrac{1{,}052}{6{,}300}, \\dfrac{1{,}097}{6{,}300}, \\dfrac{1{,}137}{6{,}300}, \\dfrac{1{,}180}{6{,}300}, \\dfrac{1{,}224}{6{,}300}, \\dfrac{1{,}226}{6{,}300}, \\dfrac{1{,}264}{6{,}300}, \\dfrac{1{,}322}{6{,}300}, \\text{ and } \\dfrac{1{,}323}{6{,}300}", "__seed__": "0074"}}, {"seed": 75, "data": {"p1_how_many": "11", "p1_a": "6.03", "p1_b": "6.04", "p1_numbers": "6.0305, 6.031, 6.0315, 6.032, 6.033, 6.034, 6.035, 6.036, 6.037, 6.038, and 6.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.031000000000001", "6.032", "6.033", "6.034", "6.035", "6.0360000000000005", "6.037", "6.038", "6.039000000000001"], "p1_2_xs": ["6.0305", "6.0315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}400}{56{,}000}, \\dfrac{35{,}794}{56{,}000}, \\dfrac{36{,}842}{56{,}000}, \\dfrac{36{,}969}{56{,}000}, \\dfrac{37{,}025}{56{,}000}, \\dfrac{37{,}171}{56{,}000}, \\dfrac{38{,}336}{56{,}000}, \\dfrac{38{,}610}{56{,}000}, \\dfrac{38{,}915}{56{,}000}, \\dfrac{39{,}451}{56{,}000}, \\dfrac{39{,}631}{56{,}000}, \\text{ and } \\dfrac{39{,}775}{56{,}000}", "__seed__": "0075"}}, {"seed": 76, "data": {"p1_how_many": "12", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}094}{42{,}000}, \\dfrac{30{,}326}{42{,}000}, \\dfrac{30{,}504}{42{,}000}, \\dfrac{31{,}340}{42{,}000}, \\dfrac{31{,}374}{42{,}000}, \\dfrac{31{,}765}{42{,}000}, \\dfrac{32{,}079}{42{,}000}, \\dfrac{32{,}206}{42{,}000}, \\dfrac{32{,}417}{42{,}000}, \\dfrac{32{,}733}{42{,}000}, \\dfrac{33{,}990}{42{,}000}, \\text{ and } \\dfrac{34{,}154}{42{,}000}", "__seed__": "0076"}}, {"seed": 77, "data": {"p1_how_many": "11", "p1_a": "9.33", "p1_b": "9.34", "p1_numbers": "9.3305, 9.331, 9.3315, 9.332, 9.333, 9.334, 9.335, 9.336, 9.337, 9.338, and 9.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.331", "9.332", "9.333", "9.334", "9.335", "9.336", "9.337", "9.338", "9.339"], "p1_2_xs": ["9.3305", "9.3315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}001}{42{,}000}, \\dfrac{35{,}087}{42{,}000}, \\dfrac{35{,}099}{42{,}000}, \\dfrac{35{,}105}{42{,}000}, \\dfrac{35{,}185}{42{,}000}, \\dfrac{35{,}211}{42{,}000}, \\dfrac{35{,}658}{42{,}000}, \\dfrac{35{,}698}{42{,}000}, \\dfrac{35{,}769}{42{,}000}, \\dfrac{35{,}838}{42{,}000}, \\dfrac{35{,}896}{42{,}000}, \\text{ and } \\dfrac{35{,}988}{42{,}000}", "__seed__": "0077"}}, {"seed": 78, "data": {"p1_how_many": "14", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.345, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335", "5.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}645}{42{,}000}, \\dfrac{8{,}108}{42{,}000}, \\dfrac{8{,}231}{42{,}000}, \\dfrac{10{,}099}{42{,}000}, \\dfrac{10{,}474}{42{,}000}, \\dfrac{11{,}030}{42{,}000}, \\dfrac{11{,}118}{42{,}000}, \\dfrac{11{,}320}{42{,}000}, \\dfrac{11{,}354}{42{,}000}, \\dfrac{11{,}373}{42{,}000}, \\dfrac{11{,}631}{42{,}000}, \\text{ and } \\dfrac{11{,}680}{42{,}000}", "__seed__": "0078"}}, {"seed": 79, "data": {"p1_how_many": "14", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.735, 3.74, 3.745, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725", "3.735", "3.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}056}{12{,}000}, \\dfrac{3{,}068}{12{,}000}, \\dfrac{3{,}205}{12{,}000}, \\dfrac{3{,}260}{12{,}000}, \\dfrac{3{,}401}{12{,}000}, \\dfrac{3{,}479}{12{,}000}, \\dfrac{3{,}525}{12{,}000}, \\dfrac{3{,}606}{12{,}000}, \\dfrac{3{,}626}{12{,}000}, \\dfrac{3{,}816}{12{,}000}, \\dfrac{3{,}829}{12{,}000}, \\text{ and } \\dfrac{3{,}927}{12{,}000}", "__seed__": "0079"}}, {"seed": 80, "data": {"p1_how_many": "14", "p1_a": "8.56", "p1_b": "8.57", "p1_numbers": "8.5605, 8.561, 8.5615, 8.562, 8.5625, 8.563, 8.5635, 8.564, 8.5645, 8.565, 8.566, 8.567, 8.568, and 8.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.561", "8.562000000000001", "8.563", "8.564", "8.565000000000001", "8.566", "8.567", "8.568", "8.569"], "p1_2_xs": ["8.560500000000001", "8.5615", "8.562500000000002", "8.563500000000001", "8.5645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}600}{63{,}000}, \\dfrac{14{,}690}{63{,}000}, \\dfrac{14{,}767}{63{,}000}, \\dfrac{14{,}896}{63{,}000}, \\dfrac{15{,}153}{63{,}000}, \\dfrac{15{,}208}{63{,}000}, \\dfrac{15{,}435}{63{,}000}, \\dfrac{15{,}443}{63{,}000}, \\dfrac{15{,}480}{63{,}000}, \\dfrac{16{,}665}{63{,}000}, \\text{ and } \\dfrac{17{,}677}{63{,}000}", "__seed__": "0080"}}, {"seed": 81, "data": {"p1_how_many": "12", "p1_a": "6.25", "p1_b": "6.26", "p1_numbers": "6.2505, 6.251, 6.2515, 6.252, 6.2525, 6.253, 6.254, 6.255, 6.256, 6.257, 6.258, and 6.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.251", "6.252", "6.253", "6.254", "6.255", "6.256", "6.257", "6.258", "6.259"], "p1_2_xs": ["6.2505", "6.2515", "6.2524999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}209}{2{,}000}, \\dfrac{1{,}238}{2{,}000}, \\dfrac{1{,}305}{2{,}000}, \\dfrac{1{,}326}{2{,}000}, \\dfrac{1{,}328}{2{,}000}, \\dfrac{1{,}338}{2{,}000}, \\dfrac{1{,}426}{2{,}000}, \\dfrac{1{,}469}{2{,}000}, \\dfrac{1{,}489}{2{,}000}, \\text{ and } \\dfrac{1{,}493}{2{,}000}", "__seed__": "0081"}}, {"seed": 82, "data": {"p1_how_many": "12", "p1_a": "3.82", "p1_b": "3.83", "p1_numbers": "3.8205, 3.821, 3.8215, 3.822, 3.8225, 3.823, 3.824, 3.825, 3.826, 3.827, 3.828, and 3.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.8209999999999997", "3.8219999999999996", "3.823", "3.824", "3.8249999999999997", "3.8259999999999996", "3.827", "3.828", "3.8289999999999997"], "p1_2_xs": ["3.8205", "3.8215", "3.8225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{32{,}442}{42{,}000}, \\dfrac{32{,}593}{42{,}000}, \\dfrac{33{,}170}{42{,}000}, \\dfrac{33{,}298}{42{,}000}, \\dfrac{33{,}949}{42{,}000}, \\dfrac{34{,}283}{42{,}000}, \\text{ and } \\dfrac{34{,}909}{42{,}000}", "__seed__": "0082"}}, {"seed": 83, "data": {"p1_how_many": "12", "p1_a": "8.61", "p1_b": "8.62", "p1_numbers": "8.6105, 8.611, 8.6115, 8.612, 8.6125, 8.613, 8.614, 8.615, 8.616, 8.617, 8.618, and 8.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.610999999999999", "8.612", "8.613", "8.613999999999999", "8.615", "8.616", "8.616999999999999", "8.617999999999999", "8.619"], "p1_2_xs": ["8.6105", "8.6115", "8.6125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}268}{63{,}000}, \\dfrac{9{,}663}{63{,}000}, \\dfrac{10{,}499}{63{,}000}, \\dfrac{10{,}866}{63{,}000}, \\dfrac{11{,}114}{63{,}000}, \\dfrac{11{,}794}{63{,}000}, \\dfrac{11{,}983}{63{,}000}, \\dfrac{12{,}514}{63{,}000}, \\dfrac{12{,}650}{63{,}000}, \\dfrac{13{,}152}{63{,}000}, \\text{ and } \\dfrac{13{,}611}{63{,}000}", "__seed__": "0083"}}, {"seed": 84, "data": {"p1_how_many": "11", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}403}{42{,}000}, \\dfrac{8{,}219}{42{,}000}, \\dfrac{8{,}828}{42{,}000}, \\dfrac{9{,}621}{42{,}000}, \\dfrac{10{,}638}{42{,}000}, \\dfrac{10{,}897}{42{,}000}, \\dfrac{11{,}323}{42{,}000}, \\text{ and } \\dfrac{11{,}674}{42{,}000}", "__seed__": "0084"}}, {"seed": 85, "data": {"p1_how_many": "13", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.435, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425", "4.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}018}{3{,}500}, \\dfrac{1{,}049}{3{,}500}, \\dfrac{1{,}201}{3{,}500}, \\dfrac{1{,}208}{3{,}500}, \\dfrac{1{,}251}{3{,}500}, \\dfrac{1{,}281}{3{,}500}, \\dfrac{1{,}328}{3{,}500}, \\text{ and } \\dfrac{1{,}363}{3{,}500}", "__seed__": "0085"}}, {"seed": 86, "data": {"p1_how_many": "10", "p1_a": "5.03", "p1_b": "5.04", "p1_numbers": "5.0305, 5.031, 5.032, 5.033, 5.034, 5.035, 5.036, 5.037, 5.038, and 5.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.031000000000001", "5.032", "5.033", "5.034", "5.035", "5.0360000000000005", "5.037", "5.038", "5.039000000000001"], "p1_2_xs": ["5.0305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}464}{6{,}300}, \\dfrac{1{,}505}{6{,}300}, \\dfrac{1{,}530}{6{,}300}, \\dfrac{1{,}599}{6{,}300}, \\dfrac{1{,}717}{6{,}300}, \\dfrac{1{,}735}{6{,}300}, \\dfrac{1{,}740}{6{,}300}, \\dfrac{1{,}764}{6{,}300}, \\text{ and } \\dfrac{1{,}793}{6{,}300}", "__seed__": "0086"}}, {"seed": 87, "data": {"p1_how_many": "13", "p1_a": "4.25", "p1_b": "4.26", "p1_numbers": "4.2505, 4.251, 4.2515, 4.252, 4.2525, 4.253, 4.2535, 4.254, 4.255, 4.256, 4.257, 4.258, and 4.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.251", "4.252", "4.253", "4.254", "4.255", "4.256", "4.257", "4.258", "4.259"], "p1_2_xs": ["4.2505", "4.2515", "4.2524999999999995", "4.2535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}007}{56{,}000}, \\dfrac{32{,}332}{56{,}000}, \\dfrac{32{,}705}{56{,}000}, \\dfrac{33{,}022}{56{,}000}, \\dfrac{33{,}156}{56{,}000}, \\dfrac{33{,}494}{56{,}000}, \\dfrac{34{,}694}{56{,}000}, \\dfrac{34{,}881}{56{,}000}, \\text{ and } \\dfrac{34{,}909}{56{,}000}", "__seed__": "0087"}}, {"seed": 88, "data": {"p1_how_many": "14", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.635, 6.64, 6.645, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999", "6.635", "6.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}143}{20{,}000}, \\dfrac{4{,}244}{20{,}000}, \\dfrac{4{,}272}{20{,}000}, \\dfrac{4{,}370}{20{,}000}, \\dfrac{4{,}386}{20{,}000}, \\dfrac{4{,}483}{20{,}000}, \\text{ and } \\dfrac{4{,}903}{20{,}000}", "__seed__": "0088"}}, {"seed": 89, "data": {"p1_how_many": "14", "p1_a": "8.32", "p1_b": "8.33", "p1_numbers": "8.3205, 8.321, 8.3215, 8.322, 8.3225, 8.323, 8.3235, 8.324, 8.3245, 8.325, 8.326, 8.327, 8.328, and 8.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.321", "8.322000000000001", "8.323", "8.324", "8.325000000000001", "8.326", "8.327", "8.328", "8.329"], "p1_2_xs": ["8.320500000000001", "8.3215", "8.322500000000002", "8.323500000000001", "8.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{165}{350}, \\dfrac{167}{350}, \\dfrac{170}{350}, \\dfrac{174}{350}, \\dfrac{189}{350}, \\dfrac{191}{350}, \\text{ and } \\dfrac{193}{350}", "__seed__": "0089"}}, {"seed": 90, "data": {"p1_how_many": "13", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.435, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425", "4.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{61}{150}, \\dfrac{68}{150}, \\dfrac{72}{150}, \\dfrac{80}{150}, \\dfrac{85}{150}, \\dfrac{86}{150}, \\dfrac{94}{150}, \\dfrac{97}{150}, \\text{ and } \\dfrac{99}{150}", "__seed__": "0090"}}, {"seed": 91, "data": {"p1_how_many": "13", "p1_a": "7.04", "p1_b": "7.05", "p1_numbers": "7.0405, 7.041, 7.0415, 7.042, 7.0425, 7.043, 7.0435, 7.044, 7.045, 7.046, 7.047, 7.048, and 7.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.041", "7.042", "7.043", "7.044", "7.045", "7.046", "7.047", "7.048", "7.049"], "p1_2_xs": ["7.0405", "7.0415", "7.0424999999999995", "7.0435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0091"}}, {"seed": 92, "data": {"p1_how_many": "13", "p1_a": "8.15", "p1_b": "8.16", "p1_numbers": "8.1505, 8.151, 8.1515, 8.152, 8.1525, 8.153, 8.1535, 8.154, 8.155, 8.156, 8.157, 8.158, and 8.159", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.151", "8.152000000000001", "8.153", "8.154", "8.155000000000001", "8.156", "8.157", "8.158", "8.159"], "p1_2_xs": ["8.150500000000001", "8.1515", "8.152500000000002", "8.153500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}603}{5{,}600}, \\dfrac{3{,}700}{5{,}600}, \\dfrac{3{,}737}{5{,}600}, \\dfrac{3{,}825}{5{,}600}, \\dfrac{3{,}830}{5{,}600}, \\dfrac{3{,}902}{5{,}600}, \\dfrac{3{,}919}{5{,}600}, \\dfrac{3{,}921}{5{,}600}, \\text{ and } \\dfrac{3{,}978}{5{,}600}", "__seed__": "0092"}}, {"seed": 93, "data": {"p1_how_many": "10", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.52, 8.53, 8.54, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{704}{4{,}200}, \\dfrac{712}{4{,}200}, \\dfrac{727}{4{,}200}, \\dfrac{831}{4{,}200}, \\dfrac{857}{4{,}200}, \\dfrac{860}{4{,}200}, \\dfrac{960}{4{,}200}, \\text{ and } \\dfrac{1{,}086}{4{,}200}", "__seed__": "0093"}}, {"seed": 94, "data": {"p1_how_many": "12", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.6005, 1.601, 1.6015, 1.602, 1.6025, 1.603, 1.604, 1.605, 1.606, 1.607, 1.608, and 1.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.601", "1.602", "1.603", "1.604", "1.605", "1.606", "1.607", "1.608", "1.609"], "p1_2_xs": ["1.6005", "1.6015", "1.6025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}115}{12{,}000}, \\dfrac{3{,}171}{12{,}000}, \\dfrac{3{,}301}{12{,}000}, \\dfrac{3{,}364}{12{,}000}, \\dfrac{3{,}438}{12{,}000}, \\dfrac{3{,}471}{12{,}000}, \\dfrac{3{,}506}{12{,}000}, \\dfrac{3{,}546}{12{,}000}, \\dfrac{3{,}660}{12{,}000}, \\dfrac{3{,}914}{12{,}000}, \\text{ and } \\dfrac{3{,}942}{12{,}000}", "__seed__": "0094"}}, {"seed": 95, "data": {"p1_how_many": "14", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.735, 9.74, 9.745, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725", "9.735", "9.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{208}{350}, \\dfrac{244}{350}, \\dfrac{245}{350}, \\dfrac{249}{350}, \\dfrac{250}{350}, \\dfrac{252}{350}, \\dfrac{263}{350}, \\text{ and } \\dfrac{268}{350}", "__seed__": "0095"}}, {"seed": 96, "data": {"p1_how_many": "14", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.7005, 1.701, 1.7015, 1.702, 1.7025, 1.703, 1.7035, 1.704, 1.7045, 1.705, 1.706, 1.707, 1.708, and 1.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.7009999999999998", "1.702", "1.7029999999999998", "1.704", "1.7049999999999998", "1.706", "1.7069999999999999", "1.708", "1.7089999999999999"], "p1_2_xs": ["1.7005", "1.7014999999999998", "1.7025", "1.7034999999999998", "1.7045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}396}{7{,}700}, \\dfrac{4{,}464}{7{,}700}, \\dfrac{4{,}607}{7{,}700}, \\dfrac{4{,}639}{7{,}700}, \\dfrac{4{,}968}{7{,}700}, \\dfrac{5{,}083}{7{,}700}, \\dfrac{5{,}224}{7{,}700}, \\text{ and } \\dfrac{5{,}487}{7{,}700}", "__seed__": "0096"}}, {"seed": 97, "data": {"p1_how_many": "13", "p1_a": "7.83", "p1_b": "7.84", "p1_numbers": "7.8305, 7.831, 7.8315, 7.832, 7.8325, 7.833, 7.8335, 7.834, 7.835, 7.836, 7.837, 7.838, and 7.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.831", "7.832", "7.833", "7.834", "7.835", "7.836", "7.837", "7.838", "7.839"], "p1_2_xs": ["7.8305", "7.8315", "7.8325", "7.8335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{56}{200}, \\dfrac{61}{200}, \\dfrac{64}{200}, \\dfrac{67}{200}, \\dfrac{70}{200}, \\dfrac{76}{200}, \\text{ and } \\dfrac{78}{200}", "__seed__": "0097"}}, {"seed": 98, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}164}{15{,}000}, \\dfrac{5{,}313}{15{,}000}, \\dfrac{5{,}356}{15{,}000}, \\dfrac{5{,}388}{15{,}000}, \\dfrac{5{,}403}{15{,}000}, \\dfrac{5{,}528}{15{,}000}, \\dfrac{5{,}748}{15{,}000}, \\dfrac{5{,}802}{15{,}000}, \\dfrac{5{,}838}{15{,}000}, \\text{ and } \\dfrac{5{,}941}{15{,}000}", "__seed__": "0098"}}, {"seed": 99, "data": {"p1_how_many": "14", "p1_a": "8.45", "p1_b": "8.46", "p1_numbers": "8.4505, 8.451, 8.4515, 8.452, 8.4525, 8.453, 8.4535, 8.454, 8.4545, 8.455, 8.456, 8.457, 8.458, and 8.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.450999999999999", "8.452", "8.453", "8.453999999999999", "8.455", "8.456", "8.456999999999999", "8.457999999999998", "8.459"], "p1_2_xs": ["8.4505", "8.4515", "8.4525", "8.4535", "8.4545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}203}{15{,}000}, \\dfrac{5{,}235}{15{,}000}, \\dfrac{5{,}241}{15{,}000}, \\dfrac{5{,}450}{15{,}000}, \\dfrac{5{,}520}{15{,}000}, \\dfrac{5{,}659}{15{,}000}, \\dfrac{5{,}692}{15{,}000}, \\dfrac{5{,}832}{15{,}000}, \\dfrac{5{,}878}{15{,}000}, \\dfrac{5{,}883}{15{,}000}, \\text{ and } \\dfrac{5{,}894}{15{,}000}", "__seed__": "0099"}}, {"seed": 100, "data": {"p1_how_many": "14", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.635, 8.64, 8.645, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625", "8.635", "8.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}146}{35{,}000}, \\dfrac{21{,}115}{35{,}000}, \\dfrac{22{,}226}{35{,}000}, \\dfrac{24{,}946}{35{,}000}, \\dfrac{26{,}221}{35{,}000}, \\dfrac{26{,}916}{35{,}000}, \\text{ and } \\dfrac{27{,}392}{35{,}000}", "__seed__": "0100"}}, {"seed": 101, "data": {"p1_how_many": "10", "p1_a": "4.06", "p1_b": "4.07", "p1_numbers": "4.0605, 4.061, 4.062, 4.063, 4.064, 4.065, 4.066, 4.067, 4.068, and 4.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.061", "4.061999999999999", "4.063", "4.063999999999999", "4.0649999999999995", "4.066", "4.066999999999999", "4.068", "4.069"], "p1_2_xs": ["4.060499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}082}{30{,}000}, \\dfrac{5{,}122}{30{,}000}, \\dfrac{5{,}226}{30{,}000}, \\dfrac{5{,}340}{30{,}000}, \\dfrac{5{,}426}{30{,}000}, \\dfrac{5{,}632}{30{,}000}, \\text{ and } \\dfrac{5{,}719}{30{,}000}", "__seed__": "0101"}}, {"seed": 102, "data": {"p1_how_many": "13", "p1_a": "3.87", "p1_b": "3.88", "p1_numbers": "3.8705, 3.871, 3.8715, 3.872, 3.8725, 3.873, 3.8735, 3.874, 3.875, 3.876, 3.877, 3.878, and 3.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.871", "3.872", "3.873", "3.874", "3.875", "3.876", "3.8770000000000002", "3.878", "3.879"], "p1_2_xs": ["3.8705000000000003", "3.8715", "3.8725", "3.8735000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}443}{42{,}000}, \\dfrac{7{,}823}{42{,}000}, \\dfrac{8{,}453}{42{,}000}, \\dfrac{8{,}720}{42{,}000}, \\dfrac{9{,}435}{42{,}000}, \\dfrac{11{,}288}{42{,}000}, \\text{ and } \\dfrac{11{,}698}{42{,}000}", "__seed__": "0102"}}, {"seed": 103, "data": {"p1_how_many": "11", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}034}{35{,}000}, \\dfrac{7{,}554}{35{,}000}, \\dfrac{7{,}656}{35{,}000}, \\dfrac{7{,}946}{35{,}000}, \\dfrac{8{,}007}{35{,}000}, \\dfrac{8{,}132}{35{,}000}, \\dfrac{8{,}373}{35{,}000}, \\dfrac{9{,}373}{35{,}000}, \\dfrac{9{,}466}{35{,}000}, \\dfrac{9{,}523}{35{,}000}, \\dfrac{9{,}633}{35{,}000}, \\text{ and } \\dfrac{9{,}942}{35{,}000}", "__seed__": "0103"}}, {"seed": 104, "data": {"p1_how_many": "14", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.145, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135", "4.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}152}{63{,}000}, \\dfrac{27{,}269}{63{,}000}, \\dfrac{27{,}284}{63{,}000}, \\dfrac{27{,}298}{63{,}000}, \\dfrac{27{,}446}{63{,}000}, \\dfrac{27{,}519}{63{,}000}, \\dfrac{27{,}642}{63{,}000}, \\dfrac{27{,}650}{63{,}000}, \\dfrac{27{,}653}{63{,}000}, \\text{ and } \\dfrac{27{,}911}{63{,}000}", "__seed__": "0104"}}, {"seed": 105, "data": {"p1_how_many": "10", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}022}{20{,}000}, \\dfrac{4{,}111}{20{,}000}, \\dfrac{4{,}227}{20{,}000}, \\dfrac{4{,}520}{20{,}000}, \\dfrac{4{,}581}{20{,}000}, \\dfrac{4{,}774}{20{,}000}, \\dfrac{4{,}835}{20{,}000}, \\text{ and } \\dfrac{4{,}988}{20{,}000}", "__seed__": "0105"}}, {"seed": 106, "data": {"p1_how_many": "14", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.235, 9.24, 9.245, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225", "9.235", "9.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{52}{200}, \\dfrac{60}{200}, \\dfrac{61}{200}, \\dfrac{62}{200}, \\dfrac{63}{200}, \\dfrac{66}{200}, \\dfrac{68}{200}, \\dfrac{72}{200}, \\text{ and } \\dfrac{76}{200}", "__seed__": "0106"}}, {"seed": 107, "data": {"p1_how_many": "10", "p1_a": "4.52", "p1_b": "4.53", "p1_numbers": "4.5205, 4.521, 4.522, 4.523, 4.524, 4.525, 4.526, 4.527, 4.528, and 4.529", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.521", "4.521999999999999", "4.523", "4.523999999999999", "4.5249999999999995", "4.526", "4.526999999999999", "4.528", "4.529"], "p1_2_xs": ["4.520499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}715}{15{,}000}, \\dfrac{7{,}510}{15{,}000}, \\dfrac{7{,}725}{15{,}000}, \\dfrac{7{,}752}{15{,}000}, \\dfrac{7{,}867}{15{,}000}, \\dfrac{8{,}208}{15{,}000}, \\dfrac{8{,}698}{15{,}000}, \\dfrac{8{,}783}{15{,}000}, \\dfrac{9{,}309}{15{,}000}, \\dfrac{9{,}477}{15{,}000}, \\text{ and } \\dfrac{9{,}575}{15{,}000}", "__seed__": "0107"}}, {"seed": 108, "data": {"p1_how_many": "14", "p1_a": "8.57", "p1_b": "8.58", "p1_numbers": "8.5705, 8.571, 8.5715, 8.572, 8.5725, 8.573, 8.5735, 8.574, 8.5745, 8.575, 8.576, 8.577, 8.578, and 8.579", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.571", "8.572000000000001", "8.573", "8.574", "8.575000000000001", "8.576", "8.577", "8.578", "8.579"], "p1_2_xs": ["8.570500000000001", "8.5715", "8.572500000000002", "8.573500000000001", "8.5745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{123}{200}, \\dfrac{127}{200}, \\dfrac{134}{200}, \\dfrac{138}{200}, \\dfrac{139}{200}, \\dfrac{146}{200}, \\text{ and } \\dfrac{147}{200}", "__seed__": "0108"}}, {"seed": 109, "data": {"p1_how_many": "12", "p1_a": "1.16", "p1_b": "1.17", "p1_numbers": "1.1605, 1.161, 1.1615, 1.162, 1.1625, 1.163, 1.164, 1.165, 1.166, 1.167, 1.168, and 1.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.1609999999999998", "1.162", "1.1629999999999998", "1.164", "1.1649999999999998", "1.166", "1.1669999999999998", "1.168", "1.1689999999999998"], "p1_2_xs": ["1.1604999999999999", "1.1614999999999998", "1.1624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{78}{420}, \\dfrac{82}{420}, \\dfrac{88}{420}, \\dfrac{89}{420}, \\dfrac{95}{420}, \\dfrac{97}{420}, \\dfrac{101}{420}, \\dfrac{111}{420}, \\text{ and } \\dfrac{116}{420}", "__seed__": "0109"}}, {"seed": 110, "data": {"p1_how_many": "10", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.42, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}255}{2{,}000}, \\dfrac{1{,}284}{2{,}000}, \\dfrac{1{,}308}{2{,}000}, \\dfrac{1{,}346}{2{,}000}, \\dfrac{1{,}415}{2{,}000}, \\dfrac{1{,}427}{2{,}000}, \\text{ and } \\dfrac{1{,}478}{2{,}000}", "__seed__": "0110"}}, {"seed": 111, "data": {"p1_how_many": "12", "p1_a": "7.95", "p1_b": "7.96", "p1_numbers": "7.9505, 7.951, 7.9515, 7.952, 7.9525, 7.953, 7.954, 7.955, 7.956, 7.957, 7.958, and 7.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.9510000000000005", "7.952", "7.953", "7.954", "7.955", "7.956", "7.957", "7.958", "7.9590000000000005"], "p1_2_xs": ["7.9505", "7.9515", "7.9525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\dfrac{48}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0111"}}, {"seed": 112, "data": {"p1_how_many": "13", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.025, 1.03, 1.035, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015", "1.025", "1.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{505}{3{,}000}, \\dfrac{513}{3{,}000}, \\dfrac{521}{3{,}000}, \\dfrac{522}{3{,}000}, \\dfrac{530}{3{,}000}, \\dfrac{533}{3{,}000}, \\dfrac{539}{3{,}000}, \\dfrac{546}{3{,}000}, \\dfrac{566}{3{,}000}, \\text{ and } \\dfrac{580}{3{,}000}", "__seed__": "0112"}}, {"seed": 113, "data": {"p1_how_many": "11", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.6005, 5.601, 5.6015, 5.602, 5.603, 5.604, 5.605, 5.606, 5.607, 5.608, and 5.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.601", "5.601999999999999", "5.603", "5.603999999999999", "5.6049999999999995", "5.606", "5.606999999999999", "5.608", "5.609"], "p1_2_xs": ["5.600499999999999", "5.6015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}339}{56{,}000}, \\dfrac{32{,}540}{56{,}000}, \\dfrac{32{,}571}{56{,}000}, \\dfrac{32{,}891}{56{,}000}, \\dfrac{32{,}943}{56{,}000}, \\dfrac{33{,}193}{56{,}000}, \\dfrac{33{,}250}{56{,}000}, \\dfrac{33{,}444}{56{,}000}, \\dfrac{33{,}925}{56{,}000}, \\dfrac{34{,}082}{56{,}000}, \\text{ and } \\dfrac{34{,}122}{56{,}000}", "__seed__": "0113"}}, {"seed": 114, "data": {"p1_how_many": "10", "p1_a": "8.53", "p1_b": "8.54", "p1_numbers": "8.5305, 8.531, 8.532, 8.533, 8.534, 8.535, 8.536, 8.537, 8.538, and 8.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.530999999999999", "8.532", "8.533", "8.533999999999999", "8.535", "8.536", "8.536999999999999", "8.537999999999998", "8.539"], "p1_2_xs": ["8.5305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}042}{12{,}000}, \\dfrac{8{,}153}{12{,}000}, \\dfrac{8{,}265}{12{,}000}, \\dfrac{8{,}293}{12{,}000}, \\dfrac{8{,}341}{12{,}000}, \\dfrac{8{,}517}{12{,}000}, \\dfrac{8{,}761}{12{,}000}, \\dfrac{8{,}774}{12{,}000}, \\text{ and } \\dfrac{8{,}984}{12{,}000}", "__seed__": "0114"}}, {"seed": 115, "data": {"p1_how_many": "11", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.215, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205", "4.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{353}{560}, \\dfrac{361}{560}, \\dfrac{362}{560}, \\dfrac{365}{560}, \\dfrac{368}{560}, \\dfrac{372}{560}, \\dfrac{381}{560}, \\dfrac{384}{560}, \\text{ and } \\dfrac{393}{560}", "__seed__": "0115"}}, {"seed": 116, "data": {"p1_how_many": "10", "p1_a": "5.04", "p1_b": "5.05", "p1_numbers": "5.0405, 5.041, 5.042, 5.043, 5.044, 5.045, 5.046, 5.047, 5.048, and 5.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.041", "5.042", "5.043", "5.044", "5.045", "5.046", "5.047", "5.048", "5.049"], "p1_2_xs": ["5.0405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}730}{20{,}000}, \\dfrac{12{,}794}{20{,}000}, \\dfrac{13{,}303}{20{,}000}, \\dfrac{13{,}726}{20{,}000}, \\dfrac{13{,}843}{20{,}000}, \\dfrac{13{,}921}{20{,}000}, \\dfrac{14{,}165}{20{,}000}, \\text{ and } \\dfrac{14{,}819}{20{,}000}", "__seed__": "0116"}}, {"seed": 117, "data": {"p1_how_many": "10", "p1_a": "9.55", "p1_b": "9.56", "p1_numbers": "9.5505, 9.551, 9.552, 9.553, 9.554, 9.555, 9.556, 9.557, 9.558, and 9.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.551", "9.552000000000001", "9.553", "9.554", "9.555000000000001", "9.556000000000001", "9.557", "9.558", "9.559000000000001"], "p1_2_xs": ["9.550500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{729}{3{,}500}, \\dfrac{731}{3{,}500}, \\dfrac{794}{3{,}500}, \\dfrac{812}{3{,}500}, \\dfrac{814}{3{,}500}, \\dfrac{850}{3{,}500}, \\dfrac{854}{3{,}500}, \\dfrac{911}{3{,}500}, \\dfrac{938}{3{,}500}, \\dfrac{994}{3{,}500}, \\text{ and } \\dfrac{998}{3{,}500}", "__seed__": "0117"}}, {"seed": 118, "data": {"p1_how_many": "10", "p1_a": "2.55", "p1_b": "2.56", "p1_numbers": "2.5505, 2.551, 2.552, 2.553, 2.554, 2.555, 2.556, 2.557, 2.558, and 2.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5509999999999997", "2.5519999999999996", "2.553", "2.554", "2.5549999999999997", "2.5559999999999996", "2.557", "2.558", "2.5589999999999997"], "p1_2_xs": ["2.5505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}033}{42{,}000}, \\dfrac{35{,}037}{42{,}000}, \\dfrac{35{,}120}{42{,}000}, \\dfrac{35{,}232}{42{,}000}, \\dfrac{35{,}235}{42{,}000}, \\dfrac{35{,}680}{42{,}000}, \\dfrac{35{,}837}{42{,}000}, \\dfrac{35{,}844}{42{,}000}, \\dfrac{35{,}860}{42{,}000}, \\dfrac{35{,}914}{42{,}000}, \\text{ and } \\dfrac{35{,}983}{42{,}000}", "__seed__": "0118"}}, {"seed": 119, "data": {"p1_how_many": "11", "p1_a": "2.53", "p1_b": "2.54", "p1_numbers": "2.5305, 2.531, 2.5315, 2.532, 2.533, 2.534, 2.535, 2.536, 2.537, 2.538, and 2.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5309999999999997", "2.5319999999999996", "2.533", "2.534", "2.5349999999999997", "2.5359999999999996", "2.537", "2.538", "2.5389999999999997"], "p1_2_xs": ["2.5305", "2.5315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": 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\\dfrac{851}{1{,}200}, \\dfrac{855}{1{,}200}, \\text{ and } \\dfrac{895}{1{,}200}", "__seed__": "0121"}}, {"seed": 122, "data": {"p1_how_many": "10", "p1_a": "3.22", "p1_b": "3.23", "p1_numbers": "3.2205, 3.221, 3.222, 3.223, 3.224, 3.225, 3.226, 3.227, 3.228, and 3.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.221", "3.222", "3.2230000000000003", "3.224", "3.225", "3.226", "3.2270000000000003", "3.228", "3.229"], "p1_2_xs": ["3.2205000000000004"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}504}{4{,}200}, \\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}520}{4{,}200}, \\dfrac{3{,}529}{4{,}200}, \\dfrac{3{,}532}{4{,}200}, \\dfrac{3{,}537}{4{,}200}, \\text{ and } \\dfrac{3{,}549}{4{,}200}", "__seed__": "0122"}}, {"seed": 123, "data": {"p1_how_many": "11", "p1_a": "2.85", "p1_b": "2.86", "p1_numbers": "2.8505, 2.851, 2.8515, 2.852, 2.853, 2.854, 2.855, 2.856, 2.857, 2.858, and 2.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.851", "2.852", "2.853", "2.854", "2.855", "2.856", "2.857", "2.858", "2.859"], "p1_2_xs": ["2.8505000000000003", "2.8515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}625}{5{,}600}, \\dfrac{1{,}642}{5{,}600}, \\dfrac{1{,}659}{5{,}600}, \\dfrac{1{,}678}{5{,}600}, \\dfrac{1{,}991}{5{,}600}, \\dfrac{1{,}996}{5{,}600}, \\text{ and } \\dfrac{2{,}006}{5{,}600}", "__seed__": "0123"}}, {"seed": 124, "data": {"p1_how_many": "13", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.735, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725", "6.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}164}{42{,}000}, \\dfrac{6{,}272}{42{,}000}, \\dfrac{6{,}301}{42{,}000}, \\dfrac{6{,}305}{42{,}000}, \\dfrac{6{,}342}{42{,}000}, \\dfrac{6{,}498}{42{,}000}, \\text{ and } \\dfrac{6{,}710}{42{,}000}", "__seed__": "0124"}}, {"seed": 125, "data": {"p1_how_many": "14", "p1_a": "9.07", "p1_b": "9.08", "p1_numbers": "9.0705, 9.071, 9.0715, 9.072, 9.0725, 9.073, 9.0735, 9.074, 9.0745, 9.075, 9.076, 9.077, 9.078, and 9.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.071", "9.072000000000001", "9.073", "9.074", "9.075000000000001", "9.076", "9.077", "9.078", "9.079"], "p1_2_xs": ["9.070500000000001", "9.0715", "9.072500000000002", "9.073500000000001", "9.0745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{512}{1{,}500}, \\dfrac{516}{1{,}500}, \\dfrac{525}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{536}{1{,}500}, \\dfrac{543}{1{,}500}, \\dfrac{572}{1{,}500}, \\dfrac{575}{1{,}500}, \\dfrac{580}{1{,}500}, \\dfrac{590}{1{,}500}, \\text{ and } \\dfrac{591}{1{,}500}", "__seed__": "0125"}}, {"seed": 126, "data": {"p1_how_many": "14", "p1_a": "5.85", "p1_b": "5.86", "p1_numbers": "5.8505, 5.851, 5.8515, 5.852, 5.8525, 5.853, 5.8535, 5.854, 5.8545, 5.855, 5.856, 5.857, 5.858, and 5.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.851", "5.851999999999999", "5.853", "5.853999999999999", "5.8549999999999995", "5.856", "5.856999999999999", "5.858", "5.859"], "p1_2_xs": ["5.850499999999999", "5.8515", "5.852499999999999", "5.8534999999999995", "5.854499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}693}{35{,}000}, \\dfrac{8{,}192}{35{,}000}, \\dfrac{8{,}263}{35{,}000}, \\dfrac{8{,}376}{35{,}000}, \\dfrac{8{,}491}{35{,}000}, \\dfrac{8{,}503}{35{,}000}, \\dfrac{8{,}552}{35{,}000}, \\dfrac{8{,}635}{35{,}000}, \\dfrac{9{,}088}{35{,}000}, \\dfrac{9{,}659}{35{,}000}, \\dfrac{9{,}762}{35{,}000}, \\text{ and } \\dfrac{9{,}838}{35{,}000}", "__seed__": "0126"}}, {"seed": 127, "data": {"p1_how_many": "10", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}313}{63{,}000}, \\dfrac{9{,}327}{63{,}000}, \\dfrac{10{,}381}{63{,}000}, \\dfrac{10{,}629}{63{,}000}, \\dfrac{11{,}043}{63{,}000}, \\dfrac{11{,}281}{63{,}000}, \\dfrac{11{,}286}{63{,}000}, \\dfrac{12{,}328}{63{,}000}, \\dfrac{12{,}630}{63{,}000}, \\text{ and } \\dfrac{13{,}572}{63{,}000}", "__seed__": "0127"}}, {"seed": 128, "data": {"p1_how_many": "13", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.005, 5.01, 5.015, 5.02, 5.025, 5.03, 5.035, 5.04, 5.05, 5.06, 5.07, 5.08, and 5.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005", "5.015", "5.0249999999999995", "5.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{92}{630}, \\dfrac{102}{630}, \\dfrac{118}{630}, \\dfrac{120}{630}, \\dfrac{131}{630}, \\dfrac{132}{630}, \\dfrac{134}{630}, \\dfrac{137}{630}, \\text{ and } \\dfrac{138}{630}", "__seed__": "0128"}}, {"seed": 129, "data": {"p1_how_many": "10", "p1_a": "6.61", "p1_b": "6.62", "p1_numbers": "6.6105, 6.611, 6.612, 6.613, 6.614, 6.615, 6.616, 6.617, 6.618, and 6.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.611000000000001", "6.612", "6.613", "6.614", "6.615", "6.6160000000000005", "6.617", "6.618", "6.619000000000001"], "p1_2_xs": ["6.6105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}046}{20{,}000}, \\dfrac{4{,}338}{20{,}000}, \\dfrac{4{,}486}{20{,}000}, \\dfrac{4{,}527}{20{,}000}, \\dfrac{4{,}742}{20{,}000}, \\dfrac{4{,}774}{20{,}000}, \\dfrac{4{,}776}{20{,}000}, \\dfrac{4{,}891}{20{,}000}, \\text{ and } \\dfrac{4{,}918}{20{,}000}", "__seed__": "0129"}}, {"seed": 130, "data": {"p1_how_many": "11", "p1_a": "4.37", "p1_b": "4.38", "p1_numbers": "4.3705, 4.371, 4.3715, 4.372, 4.373, 4.374, 4.375, 4.376, 4.377, 4.378, and 4.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.371", "4.372", "4.373", "4.374", "4.375", "4.376", "4.377", "4.378", "4.3790000000000004"], "p1_2_xs": ["4.3705", "4.3715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}074}{12{,}000}, \\dfrac{8{,}158}{12{,}000}, \\dfrac{8{,}168}{12{,}000}, \\dfrac{8{,}596}{12{,}000}, \\dfrac{8{,}654}{12{,}000}, \\dfrac{8{,}681}{12{,}000}, \\text{ and } \\dfrac{8{,}855}{12{,}000}", "__seed__": "0130"}}, {"seed": 131, "data": {"p1_how_many": "13", "p1_a": "4.63", "p1_b": "4.64", "p1_numbers": "4.6305, 4.631, 4.6315, 4.632, 4.6325, 4.633, 4.6335, 4.634, 4.635, 4.636, 4.637, 4.638, and 4.639", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.631", "4.632", "4.633", "4.6339999999999995", "4.635", "4.636", "4.637", "4.638", "4.639"], "p1_2_xs": ["4.6305", "4.6315", "4.632499999999999", "4.6335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{510}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{535}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{567}{1{,}500}, \\dfrac{572}{1{,}500}, \\dfrac{581}{1{,}500}, \\text{ and } \\dfrac{584}{1{,}500}", "__seed__": "0131"}}, {"seed": 132, "data": {"p1_how_many": "11", "p1_a": "8.16", "p1_b": "8.17", "p1_numbers": "8.1605, 8.161, 8.1615, 8.162, 8.163, 8.164, 8.165, 8.166, 8.167, 8.168, and 8.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.161", "8.162", "8.163", "8.164", "8.165000000000001", "8.166", "8.167", "8.168", "8.169"], "p1_2_xs": ["8.1605", "8.1615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}047}{42{,}000}, \\dfrac{6{,}193}{42{,}000}, \\dfrac{6{,}200}{42{,}000}, \\dfrac{6{,}231}{42{,}000}, \\dfrac{6{,}305}{42{,}000}, \\dfrac{6{,}524}{42{,}000}, \\dfrac{6{,}590}{42{,}000}, \\dfrac{6{,}631}{42{,}000}, \\dfrac{6{,}671}{42{,}000}, \\text{ and } \\dfrac{6{,}947}{42{,}000}", "__seed__": "0132"}}, {"seed": 133, "data": {"p1_how_many": "13", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", 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accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{822}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{871}{1{,}200}, \\dfrac{872}{1{,}200}, \\dfrac{886}{1{,}200}, \\dfrac{887}{1{,}200}, \\text{ and } \\dfrac{890}{1{,}200}", "__seed__": "0134"}}, {"seed": 135, "data": {"p1_how_many": "10", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{604}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{646}{4{,}200}, \\dfrac{651}{4{,}200}, \\dfrac{669}{4{,}200}, \\text{ and } 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3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}244}{2{,}000}, \\dfrac{1{,}277}{2{,}000}, \\dfrac{1{,}313}{2{,}000}, \\dfrac{1{,}359}{2{,}000}, \\dfrac{1{,}379}{2{,}000}, \\dfrac{1{,}383}{2{,}000}, \\dfrac{1{,}405}{2{,}000}, \\dfrac{1{,}475}{2{,}000}, \\text{ and } \\dfrac{1{,}488}{2{,}000}", "__seed__": "0138"}}, {"seed": 139, "data": {"p1_how_many": "11", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.13, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}018}{15{,}000}, \\dfrac{5{,}101}{15{,}000}, \\dfrac{5{,}167}{15{,}000}, \\dfrac{5{,}301}{15{,}000}, \\dfrac{5{,}307}{15{,}000}, \\dfrac{5{,}384}{15{,}000}, \\dfrac{5{,}451}{15{,}000}, \\dfrac{5{,}533}{15{,}000}, \\dfrac{5{,}560}{15{,}000}, \\dfrac{5{,}645}{15{,}000}, \\text{ and } \\dfrac{5{,}781}{15{,}000}", "__seed__": "0139"}}, {"seed": 140, "data": {"p1_how_many": "10", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0140"}}, {"seed": 141, "data": {"p1_how_many": "12", "p1_a": "8.76", "p1_b": "8.77", "p1_numbers": "8.7605, 8.761, 8.7615, 8.762, 8.7625, 8.763, 8.764, 8.765, 8.766, 8.767, 8.768, and 8.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.761", "8.762", "8.763", "8.764", "8.765", "8.766", "8.767", "8.767999999999999", "8.769"], "p1_2_xs": ["8.7605", "8.7615", "8.762500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}886}{42{,}000}, \\dfrac{8{,}572}{42{,}000}, \\dfrac{8{,}617}{42{,}000}, \\dfrac{8{,}791}{42{,}000}, \\dfrac{9{,}367}{42{,}000}, \\dfrac{9{,}719}{42{,}000}, \\dfrac{9{,}808}{42{,}000}, \\dfrac{10{,}076}{42{,}000}, \\dfrac{10{,}592}{42{,}000}, \\dfrac{11{,}074}{42{,}000}, \\dfrac{11{,}403}{42{,}000}, \\text{ and } \\dfrac{11{,}407}{42{,}000}", "__seed__": "0141"}}, {"seed": 142, "data": {"p1_how_many": "12", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.325, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995", "3.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{107}{350}, \\dfrac{112}{350}, \\dfrac{113}{350}, \\dfrac{117}{350}, \\dfrac{120}{350}, \\dfrac{125}{350}, \\text{ and } \\dfrac{131}{350}", "__seed__": "0142"}}, {"seed": 143, "data": {"p1_how_many": "13", "p1_a": "1.95", "p1_b": "1.96", "p1_numbers": "1.9505, 1.951, 1.9515, 1.952, 1.9525, 1.953, 1.9535, 1.954, 1.955, 1.956, 1.957, 1.958, and 1.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9509999999999998", "1.952", "1.9529999999999998", "1.954", "1.9549999999999998", "1.956", "1.9569999999999999", "1.958", "1.9589999999999999"], "p1_2_xs": ["1.9505", "1.9514999999999998", "1.9525", "1.9534999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}812}{5{,}600}, \\dfrac{4{,}817}{5{,}600}, \\dfrac{4{,}819}{5{,}600}, \\dfrac{4{,}826}{5{,}600}, \\dfrac{4{,}831}{5{,}600}, \\dfrac{4{,}843}{5{,}600}, \\dfrac{4{,}847}{5{,}600}, \\dfrac{4{,}856}{5{,}600}, \\dfrac{4{,}862}{5{,}600}, \\text{ and } \\dfrac{4{,}880}{5{,}600}", "__seed__": "0143"}}, {"seed": 144, "data": {"p1_how_many": "11", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{504}{2{,}000}, \\dfrac{522}{2{,}000}, \\dfrac{546}{2{,}000}, \\dfrac{548}{2{,}000}, \\dfrac{564}{2{,}000}, \\dfrac{610}{2{,}000}, \\dfrac{667}{2{,}000}, \\dfrac{675}{2{,}000}, \\dfrac{714}{2{,}000}, \\dfrac{716}{2{,}000}, \\text{ and } \\dfrac{781}{2{,}000}", "__seed__": "0144"}}, {"seed": 145, "data": {"p1_how_many": "10", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, \\dfrac{243}{300}, \\dfrac{245}{300}, \\dfrac{247}{300}, \\dfrac{248}{300}, \\text{ and } \\dfrac{249}{300}", "__seed__": "0145"}}, {"seed": 146, "data": {"p1_how_many": "10", "p1_a": "1.07", "p1_b": "1.08", "p1_numbers": "1.0705, 1.071, 1.072, 1.073, 1.074, 1.075, 1.076, 1.077, 1.078, and 1.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.071", "1.072", "1.073", "1.074", "1.075", "1.076", "1.077", "1.078", "1.079"], "p1_2_xs": ["1.0705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{2{,}000}, \\dfrac{549}{2{,}000}, \\dfrac{566}{2{,}000}, \\dfrac{569}{2{,}000}, \\dfrac{607}{2{,}000}, \\dfrac{658}{2{,}000}, \\dfrac{715}{2{,}000}, \\text{ and } \\dfrac{751}{2{,}000}", "__seed__": "0146"}}, {"seed": 147, "data": {"p1_how_many": "13", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{506}{1{,}500}, \\dfrac{524}{1{,}500}, \\dfrac{534}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{564}{1{,}500}, \\dfrac{587}{1{,}500}, \\text{ and } \\dfrac{592}{1{,}500}", "__seed__": "0147"}}, {"seed": 148, "data": {"p1_how_many": "14", "p1_a": "7.26", "p1_b": "7.27", "p1_numbers": "7.2605, 7.261, 7.2615, 7.262, 7.2625, 7.263, 7.2635, 7.264, 7.2645, 7.265, 7.266, 7.267, 7.268, and 7.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.261", "7.262", "7.263", "7.263999999999999", "7.265", "7.266", "7.2669999999999995", "7.268", "7.269"], "p1_2_xs": ["7.2604999999999995", "7.2615", "7.262499999999999", "7.2635", "7.264499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}098}{15{,}000}, \\dfrac{5{,}258}{15{,}000}, \\dfrac{5{,}384}{15{,}000}, \\dfrac{5{,}435}{15{,}000}, \\dfrac{5{,}466}{15{,}000}, \\dfrac{5{,}477}{15{,}000}, \\dfrac{5{,}620}{15{,}000}, \\dfrac{5{,}738}{15{,}000}, \\text{ and } \\dfrac{5{,}868}{15{,}000}", "__seed__": "0148"}}, {"seed": 149, "data": {"p1_how_many": "11", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.215, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205", "4.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}491}{42{,}000}, \\dfrac{31{,}310}{42{,}000}, \\dfrac{32{,}240}{42{,}000}, \\dfrac{32{,}674}{42{,}000}, \\dfrac{33{,}363}{42{,}000}, \\dfrac{34{,}099}{42{,}000}, \\dfrac{34{,}441}{42{,}000}, \\dfrac{34{,}528}{42{,}000}, \\text{ and } \\dfrac{34{,}659}{42{,}000}", "__seed__": "0149"}}, {"seed": 150, "data": {"p1_how_many": "14", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.025, 1.03, 1.035, 1.04, 1.045, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015", "1.025", "1.035", "1.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}120}{20{,}000}, \\dfrac{4{,}422}{20{,}000}, \\dfrac{4{,}445}{20{,}000}, \\dfrac{4{,}466}{20{,}000}, \\dfrac{4{,}630}{20{,}000}, \\dfrac{4{,}671}{20{,}000}, \\dfrac{4{,}738}{20{,}000}, \\text{ and } \\dfrac{4{,}927}{20{,}000}", "__seed__": "0150"}}, {"seed": 151, "data": {"p1_how_many": "14", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.545, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535", "9.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}290}{7{,}700}, \\dfrac{4{,}386}{7{,}700}, \\dfrac{4{,}699}{7{,}700}, \\dfrac{5{,}119}{7{,}700}, \\dfrac{5{,}228}{7{,}700}, \\dfrac{5{,}439}{7{,}700}, \\dfrac{5{,}639}{7{,}700}, \\dfrac{5{,}698}{7{,}700}, \\dfrac{5{,}838}{7{,}700}, \\dfrac{6{,}019}{7{,}700}, \\dfrac{6{,}392}{7{,}700}, \\text{ and } \\dfrac{6{,}560}{7{,}700}", "__seed__": "0151"}}, {"seed": 152, "data": {"p1_how_many": "14", "p1_a": "3.67", "p1_b": "3.68", "p1_numbers": "3.6705, 3.671, 3.6715, 3.672, 3.6725, 3.673, 3.6735, 3.674, 3.6745, 3.675, 3.676, 3.677, 3.678, and 3.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.671", "3.6719999999999997", "3.673", "3.674", "3.675", "3.6759999999999997", "3.677", "3.678", "3.679"], "p1_2_xs": ["3.6705", "3.6715", "3.6725", "3.6735", "3.6745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0152"}}, {"seed": 153, "data": {"p1_how_many": "12", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{54}{200}, \\dfrac{55}{200}, \\dfrac{56}{200}, \\dfrac{61}{200}, \\dfrac{65}{200}, \\dfrac{67}{200}, \\dfrac{70}{200}, \\dfrac{76}{200}, \\text{ and } \\dfrac{78}{200}", "__seed__": "0153"}}, {"seed": 154, "data": {"p1_how_many": "14", "p1_a": "2.01", "p1_b": "2.02", "p1_numbers": "2.0105, 2.011, 2.0115, 2.012, 2.0125, 2.013, 2.0135, 2.014, 2.0145, 2.015, 2.016, 2.017, 2.018, and 2.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.0109999999999997", "2.0119999999999996", "2.013", "2.014", "2.0149999999999997", "2.0159999999999996", "2.017", "2.018", "2.0189999999999997"], "p1_2_xs": ["2.0105", "2.0115", "2.0124999999999997", "2.0135", "2.0145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{150}, \\dfrac{52}{150}, \\dfrac{53}{150}, \\dfrac{54}{150}, \\dfrac{55}{150}, \\dfrac{56}{150}, \\text{ and } \\dfrac{58}{150}", "__seed__": "0154"}}, {"seed": 155, "data": {"p1_how_many": "13", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.635, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625", "8.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}266}{7{,}700}, \\dfrac{4{,}652}{7{,}700}, \\dfrac{4{,}657}{7{,}700}, \\dfrac{4{,}700}{7{,}700}, \\dfrac{4{,}917}{7{,}700}, \\dfrac{5{,}017}{7{,}700}, \\dfrac{5{,}139}{7{,}700}, \\text{ and } \\dfrac{5{,}192}{7{,}700}", "__seed__": "0155"}}, {"seed": 156, "data": {"p1_how_many": "11", "p1_a": "4.17", "p1_b": "4.18", "p1_numbers": "4.1705, 4.171, 4.1715, 4.172, 4.173, 4.174, 4.175, 4.176, 4.177, 4.178, and 4.179", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.171", "4.172", "4.173", "4.1739999999999995", "4.175", "4.176", "4.177", "4.178", "4.179"], "p1_2_xs": ["4.1705", "4.1715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{544}{2{,}000}, \\dfrac{552}{2{,}000}, \\dfrac{559}{2{,}000}, \\dfrac{572}{2{,}000}, \\dfrac{585}{2{,}000}, \\dfrac{603}{2{,}000}, \\dfrac{626}{2{,}000}, \\dfrac{663}{2{,}000}, \\dfrac{685}{2{,}000}, \\dfrac{761}{2{,}000}, \\dfrac{762}{2{,}000}, \\text{ and } \\dfrac{794}{2{,}000}", "__seed__": "0156"}}, {"seed": 157, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{516}{1{,}500}, \\dfrac{521}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{536}{1{,}500}, \\dfrac{538}{1{,}500}, \\dfrac{559}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{563}{1{,}500}, \\dfrac{578}{1{,}500}, \\text{ and } \\dfrac{579}{1{,}500}", "__seed__": "0157"}}, {"seed": 158, "data": {"p1_how_many": "10", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}404}{3{,}000}, \\dfrac{2{,}407}{3{,}000}, \\dfrac{2{,}409}{3{,}000}, \\dfrac{2{,}432}{3{,}000}, \\dfrac{2{,}437}{3{,}000}, \\dfrac{2{,}452}{3{,}000}, \\dfrac{2{,}467}{3{,}000}, \\dfrac{2{,}478}{3{,}000}, \\dfrac{2{,}483}{3{,}000}, \\text{ and } \\dfrac{2{,}498}{3{,}000}", "__seed__": "0158"}}, {"seed": 159, "data": {"p1_how_many": "14", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.125, 1.13, 1.135, 1.14, 1.145, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115", "1.125", "1.135", "1.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}141}{5{,}600}, \\dfrac{2{,}151}{5{,}600}, \\dfrac{2{,}169}{5{,}600}, \\dfrac{2{,}210}{5{,}600}, \\dfrac{2{,}235}{5{,}600}, \\dfrac{2{,}304}{5{,}600}, \\text{ and } \\dfrac{2{,}326}{5{,}600}", "__seed__": "0159"}}, {"seed": 160, "data": {"p1_how_many": "14", "p1_a": "6.4", "p1_b": "6.5", "p1_numbers": "6.4005, 6.401, 6.4015, 6.402, 6.4025, 6.403, 6.4035, 6.404, 6.4045, 6.405, 6.406, 6.407, 6.408, and 6.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.401000000000001", "6.402", "6.4030000000000005", "6.404", "6.405", "6.406000000000001", "6.407", "6.408", "6.409000000000001"], "p1_2_xs": ["6.4005", "6.4015", "6.4025", "6.4035", "6.4045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}513}{4{,}200}, \\dfrac{3{,}527}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}543}{4{,}200}, \\dfrac{3{,}550}{4{,}200}, \\text{ and } \\dfrac{3{,}560}{4{,}200}", "__seed__": "0160"}}, {"seed": 161, "data": {"p1_how_many": "13", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.435, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425", "7.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{321}{560}, \\dfrac{324}{560}, \\dfrac{331}{560}, \\dfrac{332}{560}, \\dfrac{334}{560}, \\dfrac{337}{560}, \\dfrac{343}{560}, \\dfrac{344}{560}, \\text{ and } \\dfrac{346}{560}", "__seed__": "0161"}}, {"seed": 162, "data": {"p1_how_many": "11", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}870}{20{,}000}, \\dfrac{5{,}873}{20{,}000}, \\dfrac{5{,}900}{20{,}000}, \\dfrac{6{,}161}{20{,}000}, \\dfrac{6{,}443}{20{,}000}, \\dfrac{6{,}542}{20{,}000}, \\dfrac{6{,}640}{20{,}000}, \\dfrac{7{,}039}{20{,}000}, \\dfrac{7{,}611}{20{,}000}, \\dfrac{7{,}673}{20{,}000}, \\text{ and } \\dfrac{7{,}807}{20{,}000}", "__seed__": "0162"}}, {"seed": 163, "data": {"p1_how_many": "11", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}079}{3{,}500}, \\dfrac{1{,}116}{3{,}500}, \\dfrac{1{,}171}{3{,}500}, \\dfrac{1{,}189}{3{,}500}, \\dfrac{1{,}191}{3{,}500}, \\dfrac{1{,}258}{3{,}500}, \\dfrac{1{,}269}{3{,}500}, \\dfrac{1{,}316}{3{,}500}, \\dfrac{1{,}325}{3{,}500}, \\dfrac{1{,}353}{3{,}500}, \\text{ and } \\dfrac{1{,}354}{3{,}500}", "__seed__": "0163"}}, {"seed": 164, "data": {"p1_how_many": "10", "p1_a": "5.14", "p1_b": "5.15", "p1_numbers": "5.1405, 5.141, 5.142, 5.143, 5.144, 5.145, 5.146, 5.147, 5.148, and 5.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.141", "5.1419999999999995", "5.143", "5.143999999999999", "5.145", "5.146", "5.146999999999999", "5.148", "5.149"], "p1_2_xs": ["5.140499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{151}{350}, \\dfrac{168}{350}, \\dfrac{179}{350}, \\dfrac{181}{350}, \\dfrac{185}{350}, \\dfrac{187}{350}, \\dfrac{191}{350}, \\dfrac{205}{350}, \\text{ and } \\dfrac{207}{350}", "__seed__": "0164"}}, {"seed": 165, "data": {"p1_how_many": "13", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.535, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995", "4.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}266}{20{,}000}, \\dfrac{15{,}267}{20{,}000}, \\dfrac{15{,}457}{20{,}000}, \\dfrac{15{,}486}{20{,}000}, \\dfrac{15{,}581}{20{,}000}, \\dfrac{15{,}756}{20{,}000}, \\dfrac{15{,}857}{20{,}000}, \\dfrac{15{,}889}{20{,}000}, \\dfrac{15{,}906}{20{,}000}, \\text{ and } \\dfrac{15{,}988}{20{,}000}", "__seed__": "0165"}}, {"seed": 166, "data": {"p1_how_many": "14", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.3005, 2.301, 2.3015, 2.302, 2.3025, 2.303, 2.3035, 2.304, 2.3045, 2.305, 2.306, 2.307, 2.308, and 2.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3009999999999997", "2.3019999999999996", "2.303", "2.304", "2.3049999999999997", "2.3059999999999996", "2.307", "2.308", "2.3089999999999997"], "p1_2_xs": ["2.3005", "2.3015", "2.3024999999999998", "2.3035", "2.3045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{509}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{533}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{570}{1{,}500}, \\text{ and } \\dfrac{592}{1{,}500}", "__seed__": "0166"}}, {"seed": 167, "data": {"p1_how_many": "12", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{31}{120}, \\dfrac{32}{120}, \\dfrac{33}{120}, \\dfrac{34}{120}, \\dfrac{35}{120}, \\dfrac{36}{120}, \\dfrac{37}{120}, \\dfrac{38}{120}, \\text{ and } \\dfrac{39}{120}", "__seed__": "0167"}}, {"seed": 168, "data": {"p1_how_many": "12", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}127}{42{,}000}, \\dfrac{35{,}262}{42{,}000}, \\dfrac{35{,}272}{42{,}000}, \\dfrac{35{,}369}{42{,}000}, \\dfrac{35{,}433}{42{,}000}, \\dfrac{35{,}463}{42{,}000}, \\dfrac{35{,}912}{42{,}000}, \\text{ and } \\dfrac{35{,}915}{42{,}000}", "__seed__": "0168"}}, {"seed": 169, "data": {"p1_how_many": "10", "p1_a": "9.66", "p1_b": "9.67", "p1_numbers": "9.6605, 9.661, 9.662, 9.663, 9.664, 9.665, 9.666, 9.667, 9.668, and 9.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.661", "9.662", "9.663", "9.664", "9.665000000000001", "9.666", "9.667", "9.668", "9.669"], "p1_2_xs": ["9.6605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{656}{1{,}500}, \\dfrac{692}{1{,}500}, \\dfrac{721}{1{,}500}, \\dfrac{722}{1{,}500}, \\dfrac{728}{1{,}500}, \\dfrac{744}{1{,}500}, \\dfrac{777}{1{,}500}, \\dfrac{900}{1{,}500}, \\dfrac{972}{1{,}500}, \\text{ and } \\dfrac{982}{1{,}500}", "__seed__": "0169"}}, {"seed": 170, "data": {"p1_how_many": "11", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}145}{20{,}000}, \\dfrac{4{,}196}{20{,}000}, \\dfrac{4{,}242}{20{,}000}, \\dfrac{4{,}258}{20{,}000}, \\dfrac{4{,}412}{20{,}000}, \\dfrac{4{,}534}{20{,}000}, \\dfrac{4{,}590}{20{,}000}, \\dfrac{4{,}678}{20{,}000}, \\dfrac{4{,}741}{20{,}000}, \\dfrac{4{,}832}{20{,}000}, \\text{ and } \\dfrac{4{,}871}{20{,}000}", "__seed__": "0170"}}, {"seed": 171, "data": {"p1_how_many": "11", "p1_a": "5.03", "p1_b": "5.04", "p1_numbers": "5.0305, 5.031, 5.0315, 5.032, 5.033, 5.034, 5.035, 5.036, 5.037, 5.038, and 5.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.031000000000001", "5.032", "5.033", "5.034", "5.035", "5.0360000000000005", "5.037", "5.038", "5.039000000000001"], "p1_2_xs": ["5.0305", "5.0315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0171"}}, {"seed": 172, "data": {"p1_how_many": "12", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}505}{4{,}200}, \\dfrac{3{,}516}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}541}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}555}{4{,}200}, \\dfrac{3{,}559}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}573}{4{,}200}, \\text{ and } \\dfrac{3{,}595}{4{,}200}", "__seed__": "0172"}}, {"seed": 173, "data": {"p1_how_many": "10", "p1_a": "8.12", "p1_b": "8.13", "p1_numbers": "8.1205, 8.121, 8.122, 8.123, 8.124, 8.125, 8.126, 8.127, 8.128, and 8.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.120999999999999", "8.122", "8.123", "8.123999999999999", "8.125", "8.126", "8.126999999999999", "8.127999999999998", "8.129"], "p1_2_xs": ["8.1205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0173"}}, {"seed": 174, "data": {"p1_how_many": "11", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}514}{2{,}000}, \\dfrac{1{,}546}{2{,}000}, \\dfrac{1{,}557}{2{,}000}, \\dfrac{1{,}558}{2{,}000}, \\dfrac{1{,}567}{2{,}000}, \\dfrac{1{,}576}{2{,}000}, \\text{ and } \\dfrac{1{,}592}{2{,}000}", "__seed__": "0174"}}, {"seed": 175, "data": {"p1_how_many": "10", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.42, 5.43, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{602}{4{,}200}, \\dfrac{605}{4{,}200}, \\dfrac{617}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{656}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{682}{4{,}200}, \\dfrac{687}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0175"}}, {"seed": 176, "data": {"p1_how_many": "14", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.125, 5.13, 5.135, 5.14, 5.145, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999", "5.124999999999999", "5.135", "5.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}968}{35{,}000}, \\dfrac{8{,}071}{35{,}000}, \\dfrac{8{,}149}{35{,}000}, \\dfrac{8{,}243}{35{,}000}, \\dfrac{8{,}640}{35{,}000}, \\dfrac{8{,}710}{35{,}000}, \\dfrac{8{,}955}{35{,}000}, \\dfrac{9{,}075}{35{,}000}, \\dfrac{9{,}300}{35{,}000}, \\text{ and } \\dfrac{9{,}879}{35{,}000}", "__seed__": "0176"}}, {"seed": 177, "data": {"p1_how_many": "14", "p1_a": "4.43", "p1_b": "4.44", "p1_numbers": "4.4305, 4.431, 4.4315, 4.432, 4.4325, 4.433, 4.4335, 4.434, 4.4345, 4.435, 4.436, 4.437, 4.438, and 4.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.431", "4.4319999999999995", "4.433", "4.433999999999999", "4.435", "4.436", "4.436999999999999", "4.438", "4.439"], "p1_2_xs": ["4.430499999999999", "4.4315", "4.432499999999999", "4.4334999999999996", "4.434499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}057}{42{,}000}, \\dfrac{35{,}082}{42{,}000}, \\dfrac{35{,}254}{42{,}000}, \\dfrac{35{,}262}{42{,}000}, \\dfrac{35{,}319}{42{,}000}, \\dfrac{35{,}361}{42{,}000}, \\dfrac{35{,}374}{42{,}000}, \\dfrac{35{,}402}{42{,}000}, \\dfrac{35{,}738}{42{,}000}, \\dfrac{35{,}860}{42{,}000}, \\text{ and } \\dfrac{35{,}948}{42{,}000}", "__seed__": "0177"}}, {"seed": 178, "data": {"p1_how_many": "13", "p1_a": "4.65", "p1_b": "4.66", "p1_numbers": "4.6505, 4.651, 4.6515, 4.652, 4.6525, 4.653, 4.6535, 4.654, 4.655, 4.656, 4.657, 4.658, and 4.659", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.651000000000001", "4.652", "4.6530000000000005", "4.654", "4.655", "4.656000000000001", "4.657", "4.658", "4.659000000000001"], "p1_2_xs": ["4.6505", "4.6515", "4.6525", "4.6535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}215}{7{,}700}, \\dfrac{4{,}382}{7{,}700}, \\dfrac{4{,}460}{7{,}700}, \\dfrac{4{,}476}{7{,}700}, \\dfrac{4{,}630}{7{,}700}, \\dfrac{4{,}728}{7{,}700}, \\dfrac{4{,}799}{7{,}700}, \\dfrac{5{,}294}{7{,}700}, \\dfrac{5{,}307}{7{,}700}, \\text{ and } \\dfrac{5{,}337}{7{,}700}", "__seed__": "0178"}}, {"seed": 179, "data": {"p1_how_many": "14", "p1_a": "3.92", "p1_b": "3.93", "p1_numbers": "3.9205, 3.921, 3.9215, 3.922, 3.9225, 3.923, 3.9235, 3.924, 3.9245, 3.925, 3.926, 3.927, 3.928, and 3.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.921", "3.9219999999999997", "3.923", "3.924", "3.925", "3.9259999999999997", "3.927", "3.928", "3.929"], "p1_2_xs": ["3.9205", "3.9215", "3.9225", "3.9235", "3.9245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}219}{2{,}000}, \\dfrac{1{,}270}{2{,}000}, \\dfrac{1{,}272}{2{,}000}, \\dfrac{1{,}286}{2{,}000}, \\dfrac{1{,}325}{2{,}000}, \\dfrac{1{,}369}{2{,}000}, \\dfrac{1{,}398}{2{,}000}, \\dfrac{1{,}425}{2{,}000}, \\dfrac{1{,}429}{2{,}000}, \\dfrac{1{,}462}{2{,}000}, \\dfrac{1{,}483}{2{,}000}, \\text{ and } \\dfrac{1{,}494}{2{,}000}", "__seed__": "0179"}}, {"seed": 180, "data": {"p1_how_many": "14", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.635, 4.64, 4.645, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999", "4.635", "4.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{413}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{419}{2{,}000}, \\dfrac{441}{2{,}000}, \\dfrac{447}{2{,}000}, \\dfrac{458}{2{,}000}, \\dfrac{472}{2{,}000}, \\dfrac{483}{2{,}000}, \\dfrac{485}{2{,}000}, \\dfrac{486}{2{,}000}, \\dfrac{490}{2{,}000}, \\text{ and } \\dfrac{498}{2{,}000}", "__seed__": "0180"}}, {"seed": 181, "data": {"p1_how_many": "10", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}169}{30{,}000}, \\dfrac{24{,}351}{30{,}000}, \\dfrac{24{,}386}{30{,}000}, \\dfrac{24{,}408}{30{,}000}, \\dfrac{24{,}512}{30{,}000}, \\dfrac{24{,}569}{30{,}000}, \\dfrac{24{,}610}{30{,}000}, \\dfrac{24{,}754}{30{,}000}, \\text{ and } \\dfrac{24{,}816}{30{,}000}", "__seed__": "0181"}}, {"seed": 182, "data": {"p1_how_many": "11", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{603}{1{,}500}, \\dfrac{655}{1{,}500}, \\dfrac{672}{1{,}500}, \\dfrac{688}{1{,}500}, \\dfrac{691}{1{,}500}, \\dfrac{700}{1{,}500}, \\dfrac{771}{1{,}500}, \\dfrac{904}{1{,}500}, \\dfrac{917}{1{,}500}, \\dfrac{931}{1{,}500}, \\dfrac{942}{1{,}500}, \\text{ and } \\dfrac{962}{1{,}500}", "__seed__": "0182"}}, {"seed": 183, "data": {"p1_how_many": "10", "p1_a": "3.91", "p1_b": "3.92", "p1_numbers": "3.9105, 3.911, 3.912, 3.913, 3.914, 3.915, 3.916, 3.917, 3.918, and 3.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.911", "3.912", "3.9130000000000003", "3.914", "3.915", "3.916", "3.9170000000000003", "3.918", "3.919"], "p1_2_xs": ["3.9105000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}536}{5{,}600}, \\dfrac{3{,}556}{5{,}600}, \\dfrac{3{,}571}{5{,}600}, \\dfrac{3{,}578}{5{,}600}, \\dfrac{3{,}581}{5{,}600}, \\dfrac{3{,}718}{5{,}600}, \\dfrac{3{,}790}{5{,}600}, \\dfrac{3{,}831}{5{,}600}, \\dfrac{3{,}847}{5{,}600}, \\dfrac{3{,}961}{5{,}600}, \\text{ and } \\dfrac{3{,}983}{5{,}600}", "__seed__": "0183"}}, {"seed": 184, "data": {"p1_how_many": "10", "p1_a": "2.2", "p1_b": "2.3", "p1_numbers": "2.205, 2.21, 2.22, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, and 2.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.21", "2.22", "2.23", "2.24", "2.25", "2.2600000000000002", "2.27", "2.2800000000000002", "2.29"], "p1_2_xs": ["2.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{517}{2{,}000}, \\dfrac{536}{2{,}000}, \\dfrac{543}{2{,}000}, \\dfrac{598}{2{,}000}, \\dfrac{615}{2{,}000}, \\dfrac{681}{2{,}000}, \\dfrac{696}{2{,}000}, \\dfrac{726}{2{,}000}, \\dfrac{729}{2{,}000}, \\dfrac{739}{2{,}000}, \\text{ and } \\dfrac{782}{2{,}000}", "__seed__": "0184"}}, {"seed": 185, "data": {"p1_how_many": "10", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.32, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}029}{3{,}500}, \\dfrac{1{,}042}{3{,}500}, \\dfrac{1{,}085}{3{,}500}, \\dfrac{1{,}134}{3{,}500}, \\dfrac{1{,}141}{3{,}500}, \\dfrac{1{,}193}{3{,}500}, \\dfrac{1{,}199}{3{,}500}, \\dfrac{1{,}313}{3{,}500}, \\text{ and } \\dfrac{1{,}331}{3{,}500}", "__seed__": "0185"}}, {"seed": 186, "data": {"p1_how_many": "12", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}020}{15{,}000}, \\dfrac{6{,}659}{15{,}000}, \\dfrac{7{,}395}{15{,}000}, \\dfrac{7{,}514}{15{,}000}, \\dfrac{7{,}746}{15{,}000}, \\dfrac{8{,}297}{15{,}000}, \\dfrac{8{,}363}{15{,}000}, \\dfrac{8{,}440}{15{,}000}, \\dfrac{8{,}499}{15{,}000}, \\text{ and } \\dfrac{9{,}247}{15{,}000}", "__seed__": "0186"}}, {"seed": 187, "data": {"p1_how_many": "12", "p1_a": "3.93", "p1_b": "3.94", "p1_numbers": "3.9305, 3.931, 3.9315, 3.932, 3.9325, 3.933, 3.934, 3.935, 3.936, 3.937, 3.938, and 3.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.931", "3.932", "3.9330000000000003", "3.934", "3.935", "3.936", "3.9370000000000003", "3.938", "3.939"], "p1_2_xs": ["3.9305000000000003", "3.9315", "3.9325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}039}{42{,}000}, \\dfrac{6{,}044}{42{,}000}, \\dfrac{6{,}057}{42{,}000}, \\dfrac{6{,}377}{42{,}000}, \\dfrac{6{,}403}{42{,}000}, \\dfrac{6{,}427}{42{,}000}, \\dfrac{6{,}479}{42{,}000}, \\dfrac{6{,}638}{42{,}000}, \\dfrac{6{,}686}{42{,}000}, \\text{ and } \\dfrac{6{,}794}{42{,}000}", "__seed__": "0187"}}, {"seed": 188, "data": {"p1_how_many": "14", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.235, 9.24, 9.245, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225", "9.235", "9.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}257}{7{,}700}, \\dfrac{4{,}579}{7{,}700}, \\dfrac{4{,}764}{7{,}700}, \\dfrac{5{,}239}{7{,}700}, \\dfrac{5{,}393}{7{,}700}, \\dfrac{5{,}661}{7{,}700}, \\dfrac{5{,}778}{7{,}700}, \\dfrac{6{,}003}{7{,}700}, \\dfrac{6{,}009}{7{,}700}, \\dfrac{6{,}233}{7{,}700}, \\text{ and } \\dfrac{6{,}326}{7{,}700}", "__seed__": "0188"}}, {"seed": 189, "data": {"p1_how_many": "12", "p1_a": "8.25", "p1_b": "8.26", "p1_numbers": "8.2505, 8.251, 8.2515, 8.252, 8.2525, 8.253, 8.254, 8.255, 8.256, 8.257, 8.258, and 8.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.251", "8.252", "8.253", "8.254", "8.255", "8.256", "8.257", "8.258", "8.259"], "p1_2_xs": ["8.2505", "8.2515", "8.252500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0189"}}, {"seed": 190, "data": {"p1_how_many": "12", "p1_a": "8.67", "p1_b": "8.68", "p1_numbers": "8.6705, 8.671, 8.6715, 8.672, 8.6725, 8.673, 8.674, 8.675, 8.676, 8.677, 8.678, and 8.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.671", "8.672", "8.673", "8.674", "8.675", "8.676", "8.677", "8.677999999999999", "8.679"], "p1_2_xs": ["8.6705", "8.6715", "8.672500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}510}{2{,}000}, \\dfrac{1{,}512}{2{,}000}, \\dfrac{1{,}536}{2{,}000}, \\dfrac{1{,}539}{2{,}000}, \\dfrac{1{,}549}{2{,}000}, \\dfrac{1{,}572}{2{,}000}, \\dfrac{1{,}576}{2{,}000}, \\dfrac{1{,}585}{2{,}000}, \\dfrac{1{,}589}{2{,}000}, \\text{ and } \\dfrac{1{,}590}{2{,}000}", "__seed__": "0190"}}, {"seed": 191, "data": {"p1_how_many": "14", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.145, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135", "7.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}125}{20{,}000}, \\dfrac{4{,}137}{20{,}000}, \\dfrac{4{,}206}{20{,}000}, \\dfrac{4{,}289}{20{,}000}, \\dfrac{4{,}496}{20{,}000}, \\dfrac{4{,}511}{20{,}000}, \\dfrac{4{,}514}{20{,}000}, \\dfrac{4{,}524}{20{,}000}, \\dfrac{4{,}624}{20{,}000}, \\dfrac{4{,}727}{20{,}000}, \\text{ and } \\dfrac{4{,}949}{20{,}000}", "__seed__": "0191"}}, {"seed": 192, "data": {"p1_how_many": "10", "p1_a": "7.03", "p1_b": "7.04", "p1_numbers": "7.0305, 7.031, 7.032, 7.033, 7.034, 7.035, 7.036, 7.037, 7.038, and 7.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.031000000000001", "7.032", "7.033", "7.034", "7.035", "7.0360000000000005", "7.037", "7.038", "7.039000000000001"], "p1_2_xs": ["7.0305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}235}{7{,}700}, \\dfrac{4{,}281}{7{,}700}, \\dfrac{4{,}694}{7{,}700}, \\dfrac{4{,}940}{7{,}700}, \\dfrac{5{,}378}{7{,}700}, \\dfrac{5{,}419}{7{,}700}, \\dfrac{5{,}431}{7{,}700}, \\dfrac{5{,}493}{7{,}700}, \\dfrac{5{,}539}{7{,}700}, \\dfrac{5{,}816}{7{,}700}, \\text{ and } \\dfrac{6{,}088}{7{,}700}", "__seed__": "0192"}}, {"seed": 193, "data": {"p1_how_many": "12", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}014}{20{,}000}, \\dfrac{5{,}019}{20{,}000}, \\dfrac{5{,}608}{20{,}000}, \\dfrac{6{,}113}{20{,}000}, \\dfrac{6{,}129}{20{,}000}, \\dfrac{7{,}092}{20{,}000}, \\dfrac{7{,}643}{20{,}000}, \\dfrac{7{,}705}{20{,}000}, \\dfrac{7{,}768}{20{,}000}, \\dfrac{7{,}868}{20{,}000}, \\text{ and } \\dfrac{7{,}953}{20{,}000}", "__seed__": "0193"}}, {"seed": 194, "data": {"p1_how_many": "10", "p1_a": "3.87", "p1_b": "3.88", "p1_numbers": "3.8705, 3.871, 3.872, 3.873, 3.874, 3.875, 3.876, 3.877, 3.878, and 3.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.871", "3.872", "3.873", "3.874", "3.875", "3.876", "3.8770000000000002", "3.878", "3.879"], "p1_2_xs": ["3.8705000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{126}{200}, \\dfrac{127}{200}, \\dfrac{128}{200}, \\dfrac{131}{200}, \\dfrac{133}{200}, \\dfrac{140}{200}, \\dfrac{144}{200}, \\dfrac{145}{200}, \\text{ and } \\dfrac{146}{200}", "__seed__": "0194"}}, {"seed": 195, "data": 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"p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005", "5.015", "5.0249999999999995", "5.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}543}{3{,}500}, \\dfrac{1{,}588}{3{,}500}, \\dfrac{1{,}632}{3{,}500}, \\dfrac{1{,}634}{3{,}500}, \\dfrac{1{,}703}{3{,}500}, \\dfrac{1{,}806}{3{,}500}, \\dfrac{1{,}830}{3{,}500}, \\dfrac{1{,}992}{3{,}500}, \\text{ and } \\dfrac{2{,}086}{3{,}500}", "__seed__": "0196"}}, {"seed": 197, "data": {"p1_how_many": "12", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{747}{4{,}200}, \\dfrac{772}{4{,}200}, \\dfrac{784}{4{,}200}, \\dfrac{805}{4{,}200}, \\dfrac{862}{4{,}200}, \\dfrac{868}{4{,}200}, \\dfrac{881}{4{,}200}, \\dfrac{931}{4{,}200}, \\dfrac{935}{4{,}200}, \\dfrac{1{,}117}{4{,}200}, \\dfrac{1{,}135}{4{,}200}, \\text{ and } \\dfrac{1{,}188}{4{,}200}", "__seed__": "0197"}}, {"seed": 198, "data": {"p1_how_many": "10", "p1_a": "3.27", "p1_b": "3.28", "p1_numbers": "3.2705, 3.271, 3.272, 3.273, 3.274, 3.275, 3.276, 3.277, 3.278, and 3.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.271", "3.272", "3.273", "3.274", "3.275", "3.276", "3.277", "3.278", "3.279"], "p1_2_xs": ["3.2705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}663}{63{,}000}, \\dfrac{28{,}914}{63{,}000}, \\dfrac{29{,}229}{63{,}000}, \\dfrac{29{,}513}{63{,}000}, \\dfrac{29{,}855}{63{,}000}, \\dfrac{32{,}010}{63{,}000}, \\dfrac{33{,}570}{63{,}000}, \\dfrac{34{,}556}{63{,}000}, \\text{ and } \\dfrac{34{,}793}{63{,}000}", "__seed__": "0198"}}, {"seed": 199, "data": {"p1_how_many": "11", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.015, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{61}{420}, \\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0199"}}, {"seed": 200, "data": {"p1_how_many": "14", "p1_a": "4.06", "p1_b": "4.07", "p1_numbers": "4.0605, 4.061, 4.0615, 4.062, 4.0625, 4.063, 4.0635, 4.064, 4.0645, 4.065, 4.066, 4.067, 4.068, and 4.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.061", "4.061999999999999", "4.063", "4.063999999999999", "4.0649999999999995", "4.066", "4.066999999999999", "4.068", "4.069"], "p1_2_xs": ["4.060499999999999", "4.0615", "4.062499999999999", "4.0634999999999994", "4.064499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{67}{150}, \\dfrac{69}{150}, \\dfrac{74}{150}, \\dfrac{77}{150}, \\dfrac{84}{150}, \\dfrac{90}{150}, \\dfrac{95}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0200"}}, {"seed": 201, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}026}{35{,}000}, \\dfrac{7{,}989}{35{,}000}, \\dfrac{8{,}378}{35{,}000}, \\dfrac{8{,}670}{35{,}000}, \\dfrac{8{,}918}{35{,}000}, \\dfrac{8{,}967}{35{,}000}, \\dfrac{9{,}528}{35{,}000}, \\dfrac{9{,}530}{35{,}000}, \\dfrac{9{,}659}{35{,}000}, \\text{ and } \\dfrac{9{,}851}{35{,}000}", "__seed__": "0201"}}, {"seed": 202, "data": {"p1_how_many": "12", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.215, 1.22, 1.225, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998", "1.2149999999999999", "1.2249999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}111}{12{,}000}, \\dfrac{3{,}348}{12{,}000}, \\dfrac{3{,}402}{12{,}000}, \\dfrac{3{,}519}{12{,}000}, \\dfrac{3{,}548}{12{,}000}, \\dfrac{3{,}591}{12{,}000}, \\dfrac{3{,}735}{12{,}000}, \\dfrac{3{,}771}{12{,}000}, \\dfrac{3{,}809}{12{,}000}, \\dfrac{3{,}893}{12{,}000}, \\dfrac{3{,}949}{12{,}000}, \\text{ and } \\dfrac{3{,}956}{12{,}000}", "__seed__": "0202"}}, {"seed": 203, "data": {"p1_how_many": "14", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.025, 3.03, 3.035, 3.04, 3.045, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997", "3.025", "3.0349999999999997", "3.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{732}{3{,}500}, \\dfrac{740}{3{,}500}, \\dfrac{760}{3{,}500}, \\dfrac{794}{3{,}500}, \\dfrac{957}{3{,}500}, \\dfrac{963}{3{,}500}, \\dfrac{977}{3{,}500}, \\text{ and } \\dfrac{995}{3{,}500}", "__seed__": "0203"}}, {"seed": 204, "data": {"p1_how_many": "12", "p1_a": "2.91", "p1_b": "2.92", "p1_numbers": "2.9105, 2.911, 2.9115, 2.912, 2.9125, 2.913, 2.914, 2.915, 2.916, 2.917, 2.918, and 2.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.911", "2.912", "2.9130000000000003", "2.914", "2.915", "2.916", "2.9170000000000003", "2.918", "2.919"], "p1_2_xs": ["2.9105000000000003", "2.9115", "2.9125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}102}{20{,}000}, \\dfrac{4{,}108}{20{,}000}, \\dfrac{4{,}215}{20{,}000}, \\dfrac{4{,}220}{20{,}000}, \\dfrac{4{,}543}{20{,}000}, \\dfrac{4{,}545}{20{,}000}, \\text{ and } \\dfrac{4{,}728}{20{,}000}", "__seed__": "0204"}}, {"seed": 205, "data": {"p1_how_many": "10", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{1{,}099}{6{,}300}, \\dfrac{1{,}107}{6{,}300}, \\dfrac{1{,}127}{6{,}300}, \\dfrac{1{,}168}{6{,}300}, \\dfrac{1{,}177}{6{,}300}, \\dfrac{1{,}194}{6{,}300}, \\dfrac{1{,}200}{6{,}300}, \\text{ and } \\dfrac{1{,}395}{6{,}300}", "__seed__": "0205"}}, {"seed": 206, "data": {"p1_how_many": "11", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{518}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{538}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{557}{1{,}500}, \\dfrac{565}{1{,}500}, \\dfrac{585}{1{,}500}, \\text{ and } \\dfrac{596}{1{,}500}", "__seed__": "0206"}}, {"seed": 207, "data": {"p1_how_many": "11", "p1_a": "8.94", "p1_b": "8.95", "p1_numbers": "8.9405, 8.941, 8.9415, 8.942, 8.943, 8.944, 8.945, 8.946, 8.947, 8.948, and 8.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.940999999999999", "8.942", "8.943", "8.943999999999999", "8.945", "8.946", "8.947", "8.947999999999999", "8.949"], "p1_2_xs": ["8.9405", "8.9415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{202}{350}, \\dfrac{205}{350}, \\dfrac{218}{350}, \\dfrac{236}{350}, \\dfrac{248}{350}, \\dfrac{256}{350}, \\dfrac{263}{350}, \\text{ and } \\dfrac{275}{350}", "__seed__": 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numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}109}{4{,}200}, \\dfrac{3{,}148}{4{,}200}, \\dfrac{3{,}209}{4{,}200}, \\dfrac{3{,}248}{4{,}200}, \\dfrac{3{,}333}{4{,}200}, \\dfrac{3{,}461}{4{,}200}, \\text{ and } \\dfrac{3{,}463}{4{,}200}", "__seed__": "0210"}}, {"seed": 211, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}508}{2{,}000}, \\dfrac{1{,}514}{2{,}000}, \\dfrac{1{,}525}{2{,}000}, \\dfrac{1{,}538}{2{,}000}, \\dfrac{1{,}546}{2{,}000}, \\dfrac{1{,}575}{2{,}000}, \\text{ and } \\dfrac{1{,}581}{2{,}000}", "__seed__": "0211"}}, {"seed": 212, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}702}{6{,}300}, \\dfrac{2{,}707}{6{,}300}, \\dfrac{2{,}723}{6{,}300}, \\dfrac{2{,}724}{6{,}300}, \\dfrac{2{,}727}{6{,}300}, \\dfrac{2{,}728}{6{,}300}, \\dfrac{2{,}732}{6{,}300}, \\dfrac{2{,}754}{6{,}300}, \\dfrac{2{,}775}{6{,}300}, \\dfrac{2{,}788}{6{,}300}, \\text{ and } \\dfrac{2{,}791}{6{,}300}", "__seed__": "0212"}}, {"seed": 213, "data": {"p1_how_many": "11", "p1_a": "8.43", "p1_b": "8.44", "p1_numbers": "8.4305, 8.431, 8.4315, 8.432, 8.433, 8.434, 8.435, 8.436, 8.437, 8.438, and 8.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.431", "8.432", "8.433", "8.434", "8.435", "8.436", "8.437", "8.437999999999999", "8.439"], "p1_2_xs": ["8.4305", "8.4315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}128}{5{,}600}, \\dfrac{2{,}132}{5{,}600}, \\dfrac{2{,}149}{5{,}600}, \\dfrac{2{,}236}{5{,}600}, \\dfrac{2{,}252}{5{,}600}, \\dfrac{2{,}265}{5{,}600}, \\dfrac{2{,}289}{5{,}600}, \\dfrac{2{,}297}{5{,}600}, \\dfrac{2{,}302}{5{,}600}, \\text{ and } \\dfrac{2{,}379}{5{,}600}", "__seed__": "0213"}}, {"seed": 214, "data": {"p1_how_many": "12", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.015, 9.02, 9.025, 9.03, 9.04, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005", "9.015", "9.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{512}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{531}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{540}{1{,}500}, \\dfrac{571}{1{,}500}, \\dfrac{577}{1{,}500}, \\dfrac{581}{1{,}500}, \\dfrac{588}{1{,}500}, \\dfrac{590}{1{,}500}, \\text{ and } \\dfrac{598}{1{,}500}", "__seed__": "0214"}}, {"seed": 215, "data": {"p1_how_many": "14", "p1_a": "2.41", "p1_b": "2.42", "p1_numbers": "2.4105, 2.411, 2.4115, 2.412, 2.4125, 2.413, 2.4135, 2.414, 2.4145, 2.415, 2.416, 2.417, 2.418, and 2.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.411", "2.412", "2.4130000000000003", "2.414", "2.415", "2.416", "2.4170000000000003", "2.418", "2.419"], "p1_2_xs": ["2.4105000000000003", "2.4115", "2.4125", "2.4135000000000004", "2.4145000000000003"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}057}{12{,}000}, \\dfrac{3{,}243}{12{,}000}, \\dfrac{3{,}263}{12{,}000}, \\dfrac{3{,}405}{12{,}000}, \\dfrac{3{,}455}{12{,}000}, \\dfrac{3{,}494}{12{,}000}, \\dfrac{3{,}785}{12{,}000}, \\dfrac{3{,}854}{12{,}000}, \\dfrac{3{,}894}{12{,}000}, \\dfrac{3{,}915}{12{,}000}, \\text{ and } \\dfrac{3{,}929}{12{,}000}", "__seed__": "0215"}}, {"seed": 216, "data": {"p1_how_many": "11", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}021}{15{,}000}, \\dfrac{5{,}059}{15{,}000}, \\dfrac{5{,}225}{15{,}000}, \\dfrac{5{,}472}{15{,}000}, \\dfrac{5{,}517}{15{,}000}, \\dfrac{5{,}610}{15{,}000}, \\dfrac{5{,}654}{15{,}000}, \\dfrac{5{,}700}{15{,}000}, \\dfrac{5{,}728}{15{,}000}, \\dfrac{5{,}758}{15{,}000}, \\text{ and } \\dfrac{5{,}851}{15{,}000}", "__seed__": "0216"}}, {"seed": 217, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}097}{63{,}000}, \\dfrac{27{,}287}{63{,}000}, \\dfrac{27{,}479}{63{,}000}, \\dfrac{27{,}563}{63{,}000}, \\dfrac{27{,}649}{63{,}000}, \\dfrac{27{,}686}{63{,}000}, \\dfrac{27{,}768}{63{,}000}, \\dfrac{27{,}922}{63{,}000}, \\text{ and } \\dfrac{27{,}991}{63{,}000}", "__seed__": "0217"}}, {"seed": 218, "data": {"p1_how_many": "10", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.0005, 5.001, 5.002, 5.003, 5.004, 5.005, 5.006, 5.007, 5.008, and 5.009", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.001", "5.002", "5.003", "5.004", "5.005", "5.006", "5.007", "5.008", "5.009"], "p1_2_xs": ["5.0005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}049}{30{,}000}, \\dfrac{5{,}060}{30{,}000}, \\dfrac{5{,}080}{30{,}000}, \\dfrac{5{,}082}{30{,}000}, \\dfrac{5{,}131}{30{,}000}, \\dfrac{5{,}237}{30{,}000}, \\dfrac{5{,}294}{30{,}000}, \\dfrac{5{,}315}{30{,}000}, \\dfrac{5{,}383}{30{,}000}, \\dfrac{5{,}428}{30{,}000}, \\dfrac{5{,}816}{30{,}000}, \\text{ and } \\dfrac{5{,}996}{30{,}000}", "__seed__": "0218"}}, {"seed": 219, "data": {"p1_how_many": "13", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.2005, 8.201, 8.2015, 8.202, 8.2025, 8.203, 8.2035, 8.204, 8.205, 8.206, 8.207, 8.208, and 8.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.200999999999999", "8.202", "8.203", "8.203999999999999", "8.205", "8.206", "8.206999999999999", "8.207999999999998", "8.209"], "p1_2_xs": ["8.2005", "8.2015", "8.2025", "8.2035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}108}{63{,}000}, \\dfrac{14{,}109}{63{,}000}, \\dfrac{14{,}308}{63{,}000}, \\dfrac{15{,}114}{63{,}000}, \\dfrac{15{,}310}{63{,}000}, \\dfrac{15{,}672}{63{,}000}, \\dfrac{16{,}385}{63{,}000}, \\dfrac{17{,}037}{63{,}000}, \\dfrac{17{,}091}{63{,}000}, \\text{ and } \\dfrac{17{,}326}{63{,}000}", "__seed__": "0219"}}, {"seed": 220, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}413}{15{,}000}, \\dfrac{7{,}217}{15{,}000}, \\dfrac{7{,}264}{15{,}000}, \\dfrac{7{,}386}{15{,}000}, \\dfrac{7{,}581}{15{,}000}, \\dfrac{7{,}805}{15{,}000}, \\dfrac{8{,}031}{15{,}000}, \\dfrac{8{,}151}{15{,}000}, \\dfrac{8{,}828}{15{,}000}, \\dfrac{9{,}495}{15{,}000}, \\dfrac{9{,}837}{15{,}000}, \\text{ and } \\dfrac{9{,}893}{15{,}000}", "__seed__": "0220"}}, {"seed": 221, "data": {"p1_how_many": "10", "p1_a": "5.51", "p1_b": "5.52", "p1_numbers": "5.5105, 5.511, 5.512, 5.513, 5.514, 5.515, 5.516, 5.517, 5.518, and 5.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.511", "5.512", "5.513", "5.513999999999999", "5.515", "5.516", "5.5169999999999995", "5.518", "5.519"], "p1_2_xs": ["5.5104999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}054}{35{,}000}, \\dfrac{20{,}126}{35{,}000}, \\dfrac{20{,}219}{35{,}000}, \\dfrac{20{,}221}{35{,}000}, \\dfrac{20{,}407}{35{,}000}, \\dfrac{20{,}546}{35{,}000}, \\dfrac{20{,}564}{35{,}000}, \\dfrac{20{,}588}{35{,}000}, \\dfrac{20{,}641}{35{,}000}, \\dfrac{20{,}897}{35{,}000}, \\text{ and } \\dfrac{20{,}968}{35{,}000}", "__seed__": "0221"}}, {"seed": 222, "data": {"p1_how_many": "12", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0222"}}, {"seed": 223, "data": {"p1_how_many": "12", "p1_a": "7.13", "p1_b": "7.14", "p1_numbers": "7.1305, 7.131, 7.1315, 7.132, 7.1325, 7.133, 7.134, 7.135, 7.136, 7.137, 7.138, and 7.139", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.131", "7.132", "7.133", "7.1339999999999995", "7.135", "7.136", "7.137", "7.138", "7.139"], "p1_2_xs": ["7.1305", "7.1315", "7.132499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{731}{4{,}200}, \\dfrac{745}{4{,}200}, \\dfrac{780}{4{,}200}, \\dfrac{782}{4{,}200}, \\dfrac{823}{4{,}200}, \\dfrac{834}{4{,}200}, \\dfrac{910}{4{,}200}, \\dfrac{932}{4{,}200}, \\text{ and } \\dfrac{1{,}051}{4{,}200}", "__seed__": "0223"}}, {"seed": 224, "data": {"p1_how_many": "10", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.22, 6.23, 6.24, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{607}{4{,}200}, \\dfrac{613}{4{,}200}, \\dfrac{621}{4{,}200}, \\dfrac{629}{4{,}200}, \\dfrac{631}{4{,}200}, \\dfrac{635}{4{,}200}, \\dfrac{666}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{669}{4{,}200}, \\text{ and } \\dfrac{682}{4{,}200}", "__seed__": "0224"}}, {"seed": 225, "data": {"p1_how_many": "12", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}551}{35{,}000}, \\dfrac{7{,}671}{35{,}000}, \\dfrac{8{,}324}{35{,}000}, \\dfrac{8{,}859}{35{,}000}, \\dfrac{9{,}326}{35{,}000}, \\dfrac{9{,}399}{35{,}000}, \\text{ and } \\dfrac{9{,}856}{35{,}000}", "__seed__": "0225"}}, {"seed": 226, "data": {"p1_how_many": "12", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{723}{5{,}600}, \\dfrac{724}{5{,}600}, \\dfrac{725}{5{,}600}, \\dfrac{735}{5{,}600}, \\dfrac{737}{5{,}600}, \\dfrac{744}{5{,}600}, \\dfrac{746}{5{,}600}, \\dfrac{752}{5{,}600}, \\dfrac{781}{5{,}600}, \\text{ and } \\dfrac{789}{5{,}600}", "__seed__": "0226"}}, {"seed": 227, "data": {"p1_how_many": "14", "p1_a": "4.02", "p1_b": "4.03", "p1_numbers": "4.0205, 4.021, 4.0215, 4.022, 4.0225, 4.023, 4.0235, 4.024, 4.0245, 4.025, 4.026, 4.027, 4.028, and 4.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.021", "4.021999999999999", "4.023", "4.023999999999999", "4.0249999999999995", "4.026", "4.026999999999999", "4.028", "4.029"], "p1_2_xs": ["4.020499999999999", "4.0215", "4.022499999999999", "4.023499999999999", "4.024499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{501}{2{,}000}, \\dfrac{514}{2{,}000}, \\dfrac{597}{2{,}000}, \\dfrac{643}{2{,}000}, \\dfrac{644}{2{,}000}, \\dfrac{663}{2{,}000}, \\dfrac{722}{2{,}000}, \\dfrac{771}{2{,}000}, \\dfrac{779}{2{,}000}, \\text{ and } \\dfrac{797}{2{,}000}", "__seed__": "0227"}}, {"seed": 228, "data": {"p1_how_many": "14", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.425, 5.43, 5.435, 5.44, 5.445, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415", "5.425", "5.4350000000000005", "5.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{809}{1{,}200}, \\dfrac{811}{1{,}200}, \\dfrac{821}{1{,}200}, \\dfrac{840}{1{,}200}, \\dfrac{843}{1{,}200}, \\dfrac{849}{1{,}200}, \\dfrac{869}{1{,}200}, \\dfrac{878}{1{,}200}, \\text{ and } \\dfrac{891}{1{,}200}", "__seed__": "0228"}}, {"seed": 229, "data": {"p1_how_many": "14", "p1_a": "5.11", "p1_b": "5.12", "p1_numbers": "5.1105, 5.111, 5.1115, 5.112, 5.1125, 5.113, 5.1135, 5.114, 5.1145, 5.115, 5.116, 5.117, 5.118, and 5.119", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.111000000000001", "5.112", "5.113", "5.114", "5.115", "5.1160000000000005", "5.117", "5.118", "5.119000000000001"], "p1_2_xs": ["5.1105", "5.1115", "5.1125", "5.1135", "5.1145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}648}{15{,}000}, \\dfrac{6{,}872}{15{,}000}, \\dfrac{6{,}917}{15{,}000}, \\dfrac{6{,}930}{15{,}000}, \\dfrac{7{,}387}{15{,}000}, \\dfrac{7{,}564}{15{,}000}, \\dfrac{8{,}044}{15{,}000}, \\dfrac{8{,}219}{15{,}000}, \\dfrac{8{,}630}{15{,}000}, \\dfrac{8{,}679}{15{,}000}, \\dfrac{8{,}775}{15{,}000}, \\text{ and } \\dfrac{9{,}155}{15{,}000}", "__seed__": "0229"}}, {"seed": 230, "data": {"p1_how_many": "12", "p1_a": "1.8", "p1_b": "1.9", "p1_numbers": "1.8005, 1.801, 1.8015, 1.802, 1.8025, 1.803, 1.804, 1.805, 1.806, 1.807, 1.808, and 1.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.801", "1.802", "1.803", "1.804", "1.805", "1.806", "1.807", "1.808", "1.809"], "p1_2_xs": ["1.8005", "1.8014999999999999", "1.8025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}074}{4{,}200}, \\dfrac{3{,}126}{4{,}200}, \\dfrac{3{,}171}{4{,}200}, \\dfrac{3{,}173}{4{,}200}, \\dfrac{3{,}245}{4{,}200}, \\dfrac{3{,}259}{4{,}200}, \\dfrac{3{,}383}{4{,}200}, \\dfrac{3{,}391}{4{,}200}, \\dfrac{3{,}432}{4{,}200}, \\dfrac{3{,}442}{4{,}200}, \\dfrac{3{,}481}{4{,}200}, \\text{ and } \\dfrac{3{,}495}{4{,}200}", "__seed__": "0230"}}, {"seed": 231, "data": {"p1_how_many": "14", "p1_a": "7.57", "p1_b": "7.58", "p1_numbers": "7.5705, 7.571, 7.5715, 7.572, 7.5725, 7.573, 7.5735, 7.574, 7.5745, 7.575, 7.576, 7.577, 7.578, and 7.579", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.571000000000001", "7.572", "7.573", "7.574", "7.575", "7.5760000000000005", "7.577", "7.578", "7.579000000000001"], "p1_2_xs": ["7.5705", "7.5715", "7.5725", "7.5735", "7.5745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}223}{2{,}000}, \\dfrac{1{,}225}{2{,}000}, \\dfrac{1{,}256}{2{,}000}, \\dfrac{1{,}281}{2{,}000}, \\dfrac{1{,}290}{2{,}000}, \\dfrac{1{,}355}{2{,}000}, \\dfrac{1{,}384}{2{,}000}, \\dfrac{1{,}452}{2{,}000}, \\text{ and } \\dfrac{1{,}499}{2{,}000}", "__seed__": "0231"}}, {"seed": 232, "data": {"p1_how_many": "12", "p1_a": "9.27", "p1_b": "9.28", "p1_numbers": "9.2705, 9.271, 9.2715, 9.272, 9.2725, 9.273, 9.274, 9.275, 9.276, 9.277, 9.278, and 9.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.270999999999999", "9.272", "9.273", "9.274", "9.275", "9.276", "9.277", "9.277999999999999", "9.279"], "p1_2_xs": ["9.2705", "9.2715", "9.2725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}017}{35{,}000}, \\dfrac{14{,}250}{35{,}000}, \\dfrac{14{,}266}{35{,}000}, \\dfrac{14{,}439}{35{,}000}, \\dfrac{14{,}623}{35{,}000}, \\dfrac{14{,}664}{35{,}000}, \\dfrac{14{,}814}{35{,}000}, \\dfrac{14{,}869}{35{,}000}, \\dfrac{14{,}894}{35{,}000}, \\dfrac{14{,}976}{35{,}000}, \\text{ and } \\dfrac{14{,}989}{35{,}000}", "__seed__": "0232"}}, {"seed": 233, "data": {"p1_how_many": "10", "p1_a": "5.07", "p1_b": "5.08", "p1_numbers": "5.0705, 5.071, 5.072, 5.073, 5.074, 5.075, 5.076, 5.077, 5.078, and 5.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.071000000000001", "5.072", "5.073", "5.074", "5.075", "5.0760000000000005", "5.077", "5.078", "5.079000000000001"], "p1_2_xs": ["5.0705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}116}{35{,}000}, \\dfrac{8{,}306}{35{,}000}, \\dfrac{8{,}472}{35{,}000}, \\dfrac{8{,}634}{35{,}000}, \\dfrac{9{,}104}{35{,}000}, \\dfrac{9{,}621}{35{,}000}, \\text{ and } \\dfrac{9{,}685}{35{,}000}", "__seed__": "0233"}}, {"seed": 234, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}045}{35{,}000}, \\dfrac{20{,}193}{35{,}000}, \\dfrac{20{,}203}{35{,}000}, \\dfrac{20{,}368}{35{,}000}, \\dfrac{20{,}395}{35{,}000}, \\dfrac{20{,}479}{35{,}000}, \\dfrac{20{,}732}{35{,}000}, \\dfrac{20{,}757}{35{,}000}, \\dfrac{20{,}927}{35{,}000}, \\dfrac{20{,}970}{35{,}000}, \\text{ and } \\dfrac{20{,}996}{35{,}000}", "__seed__": "0234"}}, {"seed": 235, "data": {"p1_how_many": "13", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{315}{1{,}200}, \\dfrac{318}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{349}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{353}{1{,}200}, \\dfrac{356}{1{,}200}, \\dfrac{359}{1{,}200}, \\dfrac{388}{1{,}200}, \\text{ and } \\dfrac{396}{1{,}200}", "__seed__": "0235"}}, {"seed": 236, "data": {"p1_how_many": "14", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.235, 8.24, 8.245, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225", "8.235", "8.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}320}{20{,}000}, \\dfrac{12{,}476}{20{,}000}, \\dfrac{12{,}599}{20{,}000}, \\dfrac{12{,}781}{20{,}000}, \\dfrac{12{,}968}{20{,}000}, \\dfrac{13{,}463}{20{,}000}, \\dfrac{13{,}485}{20{,}000}, \\dfrac{13{,}672}{20{,}000}, \\dfrac{14{,}191}{20{,}000}, \\dfrac{14{,}586}{20{,}000}, \\text{ and } \\dfrac{14{,}998}{20{,}000}", "__seed__": "0236"}}, {"seed": 237, "data": {"p1_how_many": "14", "p1_a": "9.27", "p1_b": "9.28", "p1_numbers": "9.2705, 9.271, 9.2715, 9.272, 9.2725, 9.273, 9.2735, 9.274, 9.2745, 9.275, 9.276, 9.277, 9.278, and 9.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.270999999999999", "9.272", "9.273", "9.274", "9.275", "9.276", "9.277", "9.277999999999999", "9.279"], "p1_2_xs": ["9.2705", "9.2715", "9.2725", "9.2735", "9.2745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}146}{35{,}000}, \\dfrac{20{,}164}{35{,}000}, \\dfrac{20{,}175}{35{,}000}, \\dfrac{20{,}188}{35{,}000}, \\dfrac{20{,}307}{35{,}000}, \\dfrac{20{,}381}{35{,}000}, \\dfrac{20{,}395}{35{,}000}, \\dfrac{20{,}440}{35{,}000}, \\dfrac{20{,}631}{35{,}000}, \\text{ and } \\dfrac{20{,}998}{35{,}000}", "__seed__": "0237"}}, {"seed": 238, "data": {"p1_how_many": "10", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{424}{2{,}000}, \\dfrac{428}{2{,}000}, \\dfrac{448}{2{,}000}, \\dfrac{458}{2{,}000}, \\dfrac{463}{2{,}000}, \\dfrac{467}{2{,}000}, \\dfrac{469}{2{,}000}, \\dfrac{476}{2{,}000}, \\text{ and } \\dfrac{490}{2{,}000}", "__seed__": "0238"}}, {"seed": 239, "data": {"p1_how_many": "11", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.1005, 1.101, 1.1015, 1.102, 1.103, 1.104, 1.105, 1.106, 1.107, 1.108, and 1.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.101", "1.102", "1.103", "1.104", "1.105", "1.106", "1.107", "1.108", "1.109"], "p1_2_xs": ["1.1005", "1.1015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}523}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}531}{2{,}000}, \\dfrac{1{,}533}{2{,}000}, \\dfrac{1{,}563}{2{,}000}, \\dfrac{1{,}568}{2{,}000}, \\dfrac{1{,}569}{2{,}000}, \\dfrac{1{,}582}{2{,}000}, \\dfrac{1{,}589}{2{,}000}, \\text{ and } \\dfrac{1{,}593}{2{,}000}", "__seed__": "0239"}}, {"seed": 240, "data": {"p1_how_many": "10", "p1_a": "4.24", "p1_b": "4.25", "p1_numbers": "4.2405, 4.241, 4.242, 4.243, 4.244, 4.245, 4.246, 4.247, 4.248, and 4.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.2410000000000005", "4.242", "4.243", "4.244", "4.245", "4.246", "4.247", "4.248", "4.2490000000000006"], "p1_2_xs": ["4.2405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}406}{3{,}500}, \\dfrac{1{,}413}{3{,}500}, 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"p2_numbers": "\\dfrac{15{,}779}{35{,}000}, \\dfrac{16{,}776}{35{,}000}, \\dfrac{16{,}998}{35{,}000}, \\dfrac{17{,}362}{35{,}000}, \\dfrac{18{,}923}{35{,}000}, \\dfrac{20{,}483}{35{,}000}, \\dfrac{20{,}569}{35{,}000}, \\dfrac{20{,}625}{35{,}000}, \\text{ and } \\dfrac{20{,}908}{35{,}000}", "__seed__": "0248"}}, {"seed": 249, "data": {"p1_how_many": "10", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}197}{12{,}000}, \\dfrac{8{,}206}{12{,}000}, \\dfrac{8{,}208}{12{,}000}, \\dfrac{8{,}281}{12{,}000}, \\dfrac{8{,}757}{12{,}000}, \\dfrac{8{,}802}{12{,}000}, \\dfrac{8{,}828}{12{,}000}, \\dfrac{8{,}832}{12{,}000}, \\dfrac{8{,}844}{12{,}000}, \\text{ and } \\dfrac{8{,}904}{12{,}000}", "__seed__": "0249"}}, {"seed": 250, "data": {"p1_how_many": "11", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{762}{3{,}500}, \\dfrac{780}{3{,}500}, \\dfrac{789}{3{,}500}, \\dfrac{829}{3{,}500}, \\dfrac{887}{3{,}500}, \\dfrac{922}{3{,}500}, \\dfrac{929}{3{,}500}, \\text{ and } \\dfrac{945}{3{,}500}", "__seed__": "0250"}}, {"seed": 251, "data": {"p1_how_many": "13", "p1_a": "7.93", "p1_b": "7.94", "p1_numbers": "7.9305, 7.931, 7.9315, 7.932, 7.9325, 7.933, 7.9335, 7.934, 7.935, 7.936, 7.937, 7.938, and 7.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.931", "7.9319999999999995", "7.933", "7.933999999999999", "7.935", "7.936", "7.936999999999999", "7.938", "7.939"], "p1_2_xs": ["7.930499999999999", "7.9315", "7.932499999999999", "7.9334999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{2{,}008}{3{,}500}, \\dfrac{2{,}021}{3{,}500}, \\dfrac{2{,}023}{3{,}500}, \\dfrac{2{,}029}{3{,}500}, \\dfrac{2{,}039}{3{,}500}, \\dfrac{2{,}052}{3{,}500}, \\dfrac{2{,}053}{3{,}500}, \\dfrac{2{,}061}{3{,}500}, \\dfrac{2{,}077}{3{,}500}, \\text{ and } \\dfrac{2{,}095}{3{,}500}", "__seed__": "0251"}}, {"seed": 252, "data": {"p1_how_many": "14", "p1_a": "2.75", "p1_b": "2.76", "p1_numbers": "2.7505, 2.751, 2.7515, 2.752, 2.7525, 2.753, 2.7535, 2.754, 2.7545, 2.755, 2.756, 2.757, 2.758, and 2.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.751", "2.752", "2.753", "2.754", "2.755", "2.756", "2.757", "2.758", "2.759"], "p1_2_xs": ["2.7505", "2.7515", "2.7525", "2.7535000000000003", "2.7545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}705}{6{,}300}, \\dfrac{2{,}706}{6{,}300}, \\dfrac{2{,}745}{6{,}300}, \\dfrac{2{,}749}{6{,}300}, \\dfrac{2{,}760}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}785}{6{,}300}, \\dfrac{2{,}794}{6{,}300}, \\dfrac{2{,}795}{6{,}300}, \\text{ and } \\dfrac{2{,}797}{6{,}300}", "__seed__": "0252"}}, {"seed": 253, "data": {"p1_how_many": "13", "p1_a": "3.3", "p1_b": 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"\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0256"}}, {"seed": 257, "data": {"p1_how_many": "12", "p1_a": "4.3", "p1_b": "4.4", "p1_numbers": "4.3005, 4.301, 4.3015, 4.302, 4.3025, 4.303, 4.304, 4.305, 4.306, 4.307, 4.308, and 4.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.301", "4.302", "4.303", "4.303999999999999", "4.305", "4.306", "4.3069999999999995", "4.308", "4.309"], "p1_2_xs": ["4.3004999999999995", "4.3015", "4.302499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{622}{4{,}200}, \\dfrac{624}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{633}{4{,}200}, \\dfrac{646}{4{,}200}, \\dfrac{663}{4{,}200}, 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\\dfrac{2{,}499}{3{,}000}", "__seed__": "0258"}}, {"seed": 259, "data": {"p1_how_many": "14", "p1_a": "5.22", "p1_b": "5.23", "p1_numbers": "5.2205, 5.221, 5.2215, 5.222, 5.2225, 5.223, 5.2235, 5.224, 5.2245, 5.225, 5.226, 5.227, 5.228, and 5.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.221", "5.2219999999999995", "5.223", "5.223999999999999", "5.225", "5.226", "5.226999999999999", "5.228", "5.229"], "p1_2_xs": ["5.2204999999999995", "5.2215", "5.222499999999999", "5.2235", "5.224499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}105}{12{,}000}, \\dfrac{3{,}222}{12{,}000}, \\dfrac{3{,}610}{12{,}000}, \\dfrac{3{,}733}{12{,}000}, \\dfrac{3{,}753}{12{,}000}, \\dfrac{3{,}878}{12{,}000}, \\dfrac{3{,}883}{12{,}000}, \\dfrac{3{,}893}{12{,}000}, \\text{ and } \\dfrac{3{,}955}{12{,}000}", 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\\dfrac{9{,}621}{35{,}000}", "__seed__": "0266"}}, {"seed": 267, "data": {"p1_how_many": "12", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.325, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001", "8.325000000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}145}{5{,}600}, \\dfrac{2{,}159}{5{,}600}, \\dfrac{2{,}162}{5{,}600}, \\dfrac{2{,}166}{5{,}600}, \\dfrac{2{,}198}{5{,}600}, \\dfrac{2{,}215}{5{,}600}, \\dfrac{2{,}239}{5{,}600}, \\dfrac{2{,}251}{5{,}600}, \\dfrac{2{,}271}{5{,}600}, \\dfrac{2{,}281}{5{,}600}, \\dfrac{2{,}282}{5{,}600}, \\text{ and } 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\\dfrac{24{,}942}{30{,}000}", "__seed__": "0268"}}, {"seed": 269, "data": {"p1_how_many": "10", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}880}{15{,}000}, \\dfrac{7{,}082}{15{,}000}, \\dfrac{7{,}144}{15{,}000}, \\dfrac{7{,}946}{15{,}000}, \\dfrac{8{,}345}{15{,}000}, \\dfrac{8{,}490}{15{,}000}, \\dfrac{8{,}867}{15{,}000}, \\dfrac{9{,}015}{15{,}000}, \\dfrac{9{,}843}{15{,}000}, \\dfrac{9{,}848}{15{,}000}, \\text{ and } \\dfrac{9{,}994}{15{,}000}", "__seed__": "0269"}}, {"seed": 270, "data": {"p1_how_many": "11", "p1_a": "7.26", "p1_b": "7.27", "p1_numbers": "7.2605, 7.261, 7.2615, 7.262, 7.263, 7.264, 7.265, 7.266, 7.267, 7.268, and 7.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.261", "7.262", "7.263", "7.263999999999999", "7.265", "7.266", "7.2669999999999995", "7.268", "7.269"], "p1_2_xs": ["7.2604999999999995", "7.2615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{820}{1{,}200}, \\dfrac{822}{1{,}200}, \\dfrac{826}{1{,}200}, \\dfrac{850}{1{,}200}, \\dfrac{851}{1{,}200}, \\dfrac{883}{1{,}200}, \\dfrac{885}{1{,}200}, \\dfrac{888}{1{,}200}, \\text{ and } \\dfrac{894}{1{,}200}", "__seed__": "0270"}}, {"seed": 271, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", 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"\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}010}{4{,}200}, \\dfrac{3{,}037}{4{,}200}, \\dfrac{3{,}051}{4{,}200}, \\dfrac{3{,}057}{4{,}200}, \\dfrac{3{,}085}{4{,}200}, \\dfrac{3{,}093}{4{,}200}, \\dfrac{3{,}113}{4{,}200}, \\dfrac{3{,}131}{4{,}200}, \\dfrac{3{,}184}{4{,}200}, \\dfrac{3{,}380}{4{,}200}, \\dfrac{3{,}424}{4{,}200}, \\text{ and } \\dfrac{3{,}441}{4{,}200}", "__seed__": "0273"}}, {"seed": 274, "data": {"p1_how_many": "11", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{321}{560}, \\dfrac{325}{560}, \\dfrac{328}{560}, \\dfrac{332}{560}, \\dfrac{334}{560}, \\dfrac{338}{560}, \\dfrac{345}{560}, \\dfrac{348}{560}, \\text{ and } \\dfrac{349}{560}", "__seed__": "0274"}}, {"seed": 275, "data": {"p1_how_many": "10", "p1_a": "5.41", "p1_b": "5.42", "p1_numbers": "5.4105, 5.411, 5.412, 5.413, 5.414, 5.415, 5.416, 5.417, 5.418, and 5.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.4110000000000005", "5.412", "5.413", "5.414", "5.415", "5.416", "5.417", "5.418", "5.4190000000000005"], "p1_2_xs": ["5.4105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}039}{12{,}000}, \\dfrac{3{,}052}{12{,}000}, \\dfrac{3{,}171}{12{,}000}, \\dfrac{3{,}272}{12{,}000}, \\dfrac{3{,}362}{12{,}000}, \\dfrac{3{,}368}{12{,}000}, \\dfrac{3{,}466}{12{,}000}, \\dfrac{3{,}487}{12{,}000}, \\dfrac{3{,}489}{12{,}000}, \\dfrac{3{,}563}{12{,}000}, \\dfrac{3{,}651}{12{,}000}, \\text{ and } \\dfrac{3{,}917}{12{,}000}", "__seed__": "0275"}}, {"seed": 276, "data": {"p1_how_many": "14", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.745, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725", "7.735", "7.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}846}{42{,}000}, \\dfrac{30{,}874}{42{,}000}, \\dfrac{32{,}314}{42{,}000}, \\dfrac{33{,}233}{42{,}000}, \\dfrac{33{,}763}{42{,}000}, \\dfrac{34{,}053}{42{,}000}, \\dfrac{34{,}088}{42{,}000}, \\dfrac{34{,}430}{42{,}000}, \\text{ and } \\dfrac{34{,}759}{42{,}000}", "__seed__": "0276"}}, {"seed": 277, "data": {"p1_how_many": "14", "p1_a": "2.06", "p1_b": "2.07", "p1_numbers": "2.0605, 2.061, 2.0615, 2.062, 2.0625, 2.063, 2.0635, 2.064, 2.0645, 2.065, 2.066, 2.067, 2.068, and 2.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.061", "2.062", "2.063", "2.064", "2.065", "2.066", "2.067", "2.068", "2.069"], "p1_2_xs": ["2.0605", "2.0615", "2.0625", "2.0635000000000003", "2.0645000000000002"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}701}{6{,}300}, \\dfrac{2{,}716}{6{,}300}, \\dfrac{2{,}722}{6{,}300}, \\dfrac{2{,}742}{6{,}300}, \\dfrac{2{,}750}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}766}{6{,}300}, \\dfrac{2{,}774}{6{,}300}, \\dfrac{2{,}782}{6{,}300}, \\text{ and } \\dfrac{2{,}793}{6{,}300}", "__seed__": "0277"}}, {"seed": 278, "data": {"p1_how_many": "14", "p1_a": "1.47", "p1_b": "1.48", "p1_numbers": "1.4705, 1.471, 1.4715, 1.472, 1.4725, 1.473, 1.4735, 1.474, 1.4745, 1.475, 1.476, 1.477, 1.478, and 1.479", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4709999999999999", "1.472", "1.4729999999999999", "1.474", "1.4749999999999999", "1.476", "1.4769999999999999", "1.478", "1.4789999999999999"], "p1_2_xs": ["1.4705", "1.4714999999999998", "1.4725", "1.4734999999999998", "1.4745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{353}{560}, \\dfrac{361}{560}, \\dfrac{365}{560}, \\dfrac{388}{560}, \\dfrac{392}{560}, \\dfrac{396}{560}, \\text{ and } \\dfrac{398}{560}", "__seed__": "0278"}}, {"seed": 279, "data": {"p1_how_many": "12", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}515}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}526}{4{,}200}, \\dfrac{3{,}537}{4{,}200}, \\dfrac{3{,}540}{4{,}200}, \\dfrac{3{,}543}{4{,}200}, \\dfrac{3{,}566}{4{,}200}, \\dfrac{3{,}569}{4{,}200}, \\dfrac{3{,}587}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0279"}}, {"seed": 280, "data": {"p1_how_many": "12", "p1_a": "4.86", "p1_b": "4.87", "p1_numbers": "4.8605, 4.861, 4.8615, 4.862, 4.8625, 4.863, 4.864, 4.865, 4.866, 4.867, 4.868, and 4.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.861000000000001", "4.862", "4.863", "4.864", "4.865", "4.8660000000000005", "4.867", "4.868", "4.869000000000001"], "p1_2_xs": ["4.8605", "4.8615", "4.8625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{308}{1{,}200}, \\dfrac{313}{1{,}200}, \\dfrac{326}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{362}{1{,}200}, \\dfrac{371}{1{,}200}, \\text{ and } \\dfrac{387}{1{,}200}", "__seed__": "0280"}}, {"seed": 281, "data": {"p1_how_many": "12", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}371}{42{,}000}, \\dfrac{6{,}420}{42{,}000}, \\dfrac{6{,}486}{42{,}000}, \\dfrac{6{,}514}{42{,}000}, \\dfrac{6{,}517}{42{,}000}, \\dfrac{6{,}531}{42{,}000}, \\dfrac{6{,}548}{42{,}000}, \\dfrac{6{,}626}{42{,}000}, \\dfrac{6{,}744}{42{,}000}, \\dfrac{6{,}795}{42{,}000}, \\dfrac{6{,}865}{42{,}000}, \\text{ and } \\dfrac{6{,}867}{42{,}000}", "__seed__": "0281"}}, {"seed": 282, "data": {"p1_how_many": "14", "p1_a": "2.23", "p1_b": "2.24", "p1_numbers": "2.2305, 2.231, 2.2315, 2.232, 2.2325, 2.233, 2.2335, 2.234, 2.2345, 2.235, 2.236, 2.237, 2.238, and 2.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.231", "2.2319999999999998", "2.233", "2.234", "2.235", "2.2359999999999998", "2.237", "2.238", "2.239"], "p1_2_xs": ["2.2305", "2.2315", "2.2325", "2.2335000000000003", "2.2345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}081}{63{,}000}, \\dfrac{14{,}368}{63{,}000}, \\dfrac{14{,}541}{63{,}000}, \\dfrac{15{,}134}{63{,}000}, \\dfrac{15{,}478}{63{,}000}, \\dfrac{15{,}558}{63{,}000}, \\dfrac{16{,}412}{63{,}000}, \\dfrac{16{,}671}{63{,}000}, \\dfrac{17{,}220}{63{,}000}, \\dfrac{17{,}225}{63{,}000}, \\dfrac{17{,}372}{63{,}000}, \\text{ and } \\dfrac{17{,}626}{63{,}000}", "__seed__": "0282"}}, {"seed": 283, "data": {"p1_how_many": "14", "p1_a": "1.94", "p1_b": "1.95", "p1_numbers": "1.9405, 1.941, 1.9415, 1.942, 1.9425, 1.943, 1.9435, 1.944, 1.9445, 1.945, 1.946, 1.947, 1.948, and 1.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9409999999999998", "1.942", "1.9429999999999998", "1.944", "1.9449999999999998", "1.946", "1.9469999999999998", "1.948", "1.9489999999999998"], "p1_2_xs": ["1.9405", "1.9414999999999998", "1.9425", "1.9434999999999998", "1.9445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{127}{200}, \\dfrac{130}{200}, \\dfrac{131}{200}, \\dfrac{138}{200}, \\dfrac{141}{200}, \\dfrac{143}{200}, \\dfrac{145}{200}, \\text{ and } \\dfrac{147}{200}", "__seed__": "0283"}}, {"seed": 284, "data": {"p1_how_many": "12", "p1_a": "9.31", "p1_b": "9.32", "p1_numbers": "9.3105, 9.311, 9.3115, 9.312, 9.3125, 9.313, 9.314, 9.315, 9.316, 9.317, 9.318, and 9.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.311", "9.312000000000001", "9.313", "9.314", "9.315000000000001", "9.316", "9.317", "9.318", "9.319"], "p1_2_xs": ["9.310500000000001", "9.3115", "9.312500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{667}{1{,}500}, \\dfrac{672}{1{,}500}, \\dfrac{681}{1{,}500}, \\dfrac{717}{1{,}500}, \\dfrac{778}{1{,}500}, \\dfrac{908}{1{,}500}, \\text{ and } \\dfrac{982}{1{,}500}", "__seed__": "0284"}}, {"seed": 285, "data": {"p1_how_many": "14", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.335, 2.34, 2.345, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997", "2.3349999999999995", "2.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}094}{35{,}000}, \\dfrac{10{,}894}{35{,}000}, \\dfrac{11{,}144}{35{,}000}, \\dfrac{11{,}356}{35{,}000}, \\dfrac{11{,}538}{35{,}000}, \\dfrac{12{,}021}{35{,}000}, \\dfrac{12{,}203}{35{,}000}, \\dfrac{12{,}493}{35{,}000}, \\dfrac{13{,}220}{35{,}000}, \\dfrac{13{,}317}{35{,}000}, \\dfrac{13{,}323}{35{,}000}, \\text{ and } \\dfrac{13{,}998}{35{,}000}", "__seed__": "0285"}}, {"seed": 286, "data": {"p1_how_many": "14", "p1_a": "5.5", "p1_b": "5.6", "p1_numbers": "5.505, 5.51, 5.515, 5.52, 5.525, 5.53, 5.535, 5.54, 5.545, 5.55, 5.56, 5.57, 5.58, and 5.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.51", "5.52", "5.53", "5.54", "5.55", "5.56", "5.57", "5.58", "5.59"], "p1_2_xs": ["5.505", "5.515", "5.5249999999999995", "5.535", "5.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}075}{42{,}000}, \\dfrac{35{,}142}{42{,}000}, \\dfrac{35{,}158}{42{,}000}, \\dfrac{35{,}189}{42{,}000}, \\dfrac{35{,}223}{42{,}000}, \\dfrac{35{,}487}{42{,}000}, \\dfrac{35{,}623}{42{,}000}, \\dfrac{35{,}662}{42{,}000}, \\dfrac{35{,}757}{42{,}000}, \\text{ and } \\dfrac{35{,}971}{42{,}000}", "__seed__": "0286"}}, {"seed": 287, "data": {"p1_how_many": "13", "p1_a": "5.51", "p1_b": "5.52", "p1_numbers": "5.5105, 5.511, 5.5115, 5.512, 5.5125, 5.513, 5.5135, 5.514, 5.515, 5.516, 5.517, 5.518, and 5.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.511", "5.512", "5.513", "5.513999999999999", "5.515", "5.516", "5.5169999999999995", "5.518", "5.519"], "p1_2_xs": ["5.5104999999999995", "5.5115", "5.512499999999999", "5.5135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}253}{35{,}000}, \\dfrac{10{,}479}{35{,}000}, \\dfrac{10{,}696}{35{,}000}, \\dfrac{10{,}703}{35{,}000}, \\dfrac{10{,}997}{35{,}000}, \\dfrac{11{,}001}{35{,}000}, \\dfrac{11{,}279}{35{,}000}, \\dfrac{11{,}463}{35{,}000}, \\dfrac{12{,}247}{35{,}000}, \\dfrac{12{,}572}{35{,}000}, \\text{ and } \\dfrac{13{,}259}{35{,}000}", "__seed__": "0287"}}, {"seed": 288, "data": {"p1_how_many": "14", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.215, 6.22, 6.225, 6.23, 6.235, 6.24, 6.245, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205", "6.215", "6.225", "6.235", "6.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0288"}}, {"seed": 289, "data": {"p1_how_many": "12", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{301}{1{,}200}, \\dfrac{303}{1{,}200}, \\dfrac{304}{1{,}200}, \\dfrac{307}{1{,}200}, \\dfrac{334}{1{,}200}, \\dfrac{337}{1{,}200}, \\dfrac{367}{1{,}200}, \\dfrac{381}{1{,}200}, \\text{ and } \\dfrac{383}{1{,}200}", "__seed__": "0289"}}, {"seed": 290, "data": {"p1_how_many": "13", "p1_a": "7.77", "p1_b": "7.78", "p1_numbers": "7.7705, 7.771, 7.7715, 7.772, 7.7725, 7.773, 7.7735, 7.774, 7.775, 7.776, 7.777, 7.778, and 7.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.771", "7.771999999999999", "7.773", "7.773999999999999", "7.7749999999999995", "7.776", "7.776999999999999", "7.778", "7.779"], "p1_2_xs": ["7.770499999999999", "7.7715", "7.772499999999999", "7.773499999999999"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{717}{3{,}500}, \\dfrac{718}{3{,}500}, \\dfrac{752}{3{,}500}, \\dfrac{889}{3{,}500}, \\dfrac{937}{3{,}500}, \\dfrac{940}{3{,}500}, \\dfrac{964}{3{,}500}, \\text{ and } \\dfrac{979}{3{,}500}", "__seed__": "0290"}}, {"seed": 291, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}014}{42{,}000}, \\dfrac{7{,}041}{42{,}000}, \\dfrac{7{,}451}{42{,}000}, \\dfrac{8{,}136}{42{,}000}, \\dfrac{8{,}675}{42{,}000}, \\dfrac{9{,}422}{42{,}000}, \\dfrac{9{,}471}{42{,}000}, \\dfrac{9{,}494}{42{,}000}, \\dfrac{10{,}981}{42{,}000}, \\dfrac{11{,}445}{42{,}000}, \\dfrac{11{,}510}{42{,}000}, \\text{ and } \\dfrac{11{,}612}{42{,}000}", "__seed__": "0291"}}, {"seed": 292, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}103}{42{,}000}, \\dfrac{6{,}155}{42{,}000}, \\dfrac{6{,}237}{42{,}000}, \\dfrac{6{,}526}{42{,}000}, \\dfrac{6{,}535}{42{,}000}, \\dfrac{6{,}545}{42{,}000}, \\dfrac{6{,}546}{42{,}000}, \\dfrac{6{,}762}{42{,}000}, \\dfrac{6{,}807}{42{,}000}, \\dfrac{6{,}817}{42{,}000}, \\dfrac{6{,}938}{42{,}000}, \\text{ and } \\dfrac{6{,}958}{42{,}000}", "__seed__": "0292"}}, {"seed": 293, "data": {"p1_how_many": "11", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0293"}}, {"seed": 294, "data": {"p1_how_many": "10", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.6005, 4.601, 4.602, 4.603, 4.604, 4.605, 4.606, 4.607, 4.608, and 4.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.601", "4.601999999999999", "4.603", "4.603999999999999", "4.6049999999999995", "4.606", "4.606999999999999", "4.608", "4.609"], "p1_2_xs": ["4.600499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}507}{3{,}500}, \\dfrac{1{,}525}{3{,}500}, \\dfrac{1{,}569}{3{,}500}, \\dfrac{1{,}734}{3{,}500}, \\dfrac{1{,}781}{3{,}500}, \\dfrac{1{,}815}{3{,}500}, \\dfrac{1{,}854}{3{,}500}, \\dfrac{1{,}909}{3{,}500}, \\dfrac{2{,}006}{3{,}500}, \\text{ and } \\dfrac{2{,}095}{3{,}500}", "__seed__": "0294"}}, {"seed": 295, "data": {"p1_how_many": "12", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}154}{35{,}000}, \\dfrac{7{,}721}{35{,}000}, \\dfrac{8{,}013}{35{,}000}, \\dfrac{8{,}026}{35{,}000}, \\dfrac{8{,}878}{35{,}000}, \\dfrac{9{,}014}{35{,}000}, \\dfrac{9{,}160}{35{,}000}, \\dfrac{9{,}339}{35{,}000}, \\text{ and } \\dfrac{9{,}998}{35{,}000}", "__seed__": "0295"}}, {"seed": 296, "data": {"p1_how_many": "11", "p1_a": "7.52", "p1_b": "7.53", "p1_numbers": "7.5205, 7.521, 7.5215, 7.522, 7.523, 7.524, 7.525, 7.526, 7.527, 7.528, and 7.529", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.521", "7.521999999999999", "7.523", "7.523999999999999", "7.5249999999999995", "7.526", "7.526999999999999", "7.528", "7.529"], "p1_2_xs": ["7.520499999999999", "7.5215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}047}{35{,}000}, \\dfrac{14{,}116}{35{,}000}, \\dfrac{14{,}340}{35{,}000}, \\dfrac{14{,}433}{35{,}000}, \\dfrac{14{,}508}{35{,}000}, \\dfrac{14{,}560}{35{,}000}, \\dfrac{14{,}570}{35{,}000}, \\dfrac{14{,}628}{35{,}000}, \\text{ and } \\dfrac{14{,}645}{35{,}000}", "__seed__": "0296"}}, {"seed": 297, "data": {"p1_how_many": "12", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.415, 3.42, 3.425, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996", "3.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}144}{42{,}000}, \\dfrac{7{,}736}{42{,}000}, \\dfrac{8{,}360}{42{,}000}, \\dfrac{8{,}461}{42{,}000}, \\dfrac{9{,}478}{42{,}000}, \\dfrac{9{,}678}{42{,}000}, \\dfrac{10{,}143}{42{,}000}, \\dfrac{10{,}214}{42{,}000}, \\dfrac{11{,}799}{42{,}000}, \\text{ and } \\dfrac{11{,}941}{42{,}000}", "__seed__": "0297"}}, {"seed": 298, "data": {"p1_how_many": "10", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.42, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}503}{4{,}200}, \\dfrac{3{,}518}{4{,}200}, \\dfrac{3{,}523}{4{,}200}, \\dfrac{3{,}546}{4{,}200}, \\dfrac{3{,}554}{4{,}200}, \\dfrac{3{,}564}{4{,}200}, \\text{ and } \\dfrac{3{,}580}{4{,}200}", "__seed__": "0298"}}, {"seed": 299, "data": {"p1_how_many": "11", "p1_a": "6.73", "p1_b": "6.74", "p1_numbers": "6.7305, 6.731, 6.7315, 6.732, 6.733, 6.734, 6.735, 6.736, 6.737, 6.738, and 6.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.731000000000001", "6.732", "6.7330000000000005", "6.734", "6.735", "6.736000000000001", "6.737", "6.738", "6.739000000000001"], "p1_2_xs": ["6.7305", "6.7315000000000005"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}092}{42{,}000}, \\dfrac{6{,}251}{42{,}000}, \\dfrac{6{,}285}{42{,}000}, \\dfrac{6{,}389}{42{,}000}, \\dfrac{6{,}444}{42{,}000}, \\dfrac{6{,}528}{42{,}000}, \\dfrac{6{,}796}{42{,}000}, \\text{ and } \\dfrac{6{,}886}{42{,}000}", "__seed__": "0299"}}, {"seed": 300, "data": {"p1_how_many": "11", "p1_a": "9.73", "p1_b": "9.74", "p1_numbers": "9.7305, 9.731, 9.7315, 9.732, 9.733, 9.734, 9.735, 9.736, 9.737, 9.738, and 9.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.731", "9.732000000000001", "9.733", "9.734", "9.735000000000001", "9.736", "9.737", "9.738", "9.739"], "p1_2_xs": ["9.730500000000001", "9.7315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}552}{3{,}500}, \\dfrac{1{,}666}{3{,}500}, \\dfrac{1{,}675}{3{,}500}, \\dfrac{1{,}682}{3{,}500}, \\dfrac{1{,}710}{3{,}500}, \\dfrac{1{,}748}{3{,}500}, \\dfrac{1{,}867}{3{,}500}, \\dfrac{1{,}992}{3{,}500}, \\dfrac{2{,}060}{3{,}500}, \\dfrac{2{,}079}{3{,}500}, \\text{ and } \\dfrac{2{,}085}{3{,}500}", "__seed__": "0300"}}, {"seed": 301, "data": {"p1_how_many": "12", "p1_a": "9.22", "p1_b": "9.23", "p1_numbers": "9.2205, 9.221, 9.2215, 9.222, 9.2225, 9.223, 9.224, 9.225, 9.226, 9.227, 9.228, and 9.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.221", "9.222000000000001", "9.223", "9.224", "9.225000000000001", "9.226", "9.227", "9.228", "9.229000000000001"], "p1_2_xs": ["9.220500000000001", "9.2215", "9.222500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}401}{3{,}000}, \\dfrac{2{,}425}{3{,}000}, \\dfrac{2{,}432}{3{,}000}, \\dfrac{2{,}474}{3{,}000}, \\dfrac{2{,}475}{3{,}000}, \\dfrac{2{,}478}{3{,}000}, \\text{ and } \\dfrac{2{,}491}{3{,}000}", "__seed__": "0301"}}, {"seed": 302, "data": {"p1_how_many": "13", "p1_a": "5.5", "p1_b": "5.6", "p1_numbers": "5.505, 5.51, 5.515, 5.52, 5.525, 5.53, 5.535, 5.54, 5.55, 5.56, 5.57, 5.58, and 5.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.51", "5.52", "5.53", "5.54", "5.55", "5.56", "5.57", "5.58", "5.59"], "p1_2_xs": ["5.505", "5.515", "5.5249999999999995", "5.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}129}{42{,}000}, \\dfrac{7{,}254}{42{,}000}, \\dfrac{7{,}644}{42{,}000}, \\dfrac{8{,}166}{42{,}000}, \\dfrac{8{,}290}{42{,}000}, \\dfrac{8{,}358}{42{,}000}, \\dfrac{8{,}979}{42{,}000}, \\dfrac{9{,}336}{42{,}000}, \\dfrac{10{,}054}{42{,}000}, \\dfrac{10{,}067}{42{,}000}, \\dfrac{10{,}255}{42{,}000}, \\text{ and } \\dfrac{10{,}421}{42{,}000}", "__seed__": "0302"}}, {"seed": 303, "data": {"p1_how_many": "12", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.025, 3.03, 3.04, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997", "3.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}503}{2{,}000}, \\dfrac{1{,}511}{2{,}000}, \\dfrac{1{,}515}{2{,}000}, \\dfrac{1{,}518}{2{,}000}, \\dfrac{1{,}525}{2{,}000}, \\dfrac{1{,}526}{2{,}000}, \\dfrac{1{,}535}{2{,}000}, \\dfrac{1{,}540}{2{,}000}, \\dfrac{1{,}541}{2{,}000}, \\dfrac{1{,}555}{2{,}000}, \\dfrac{1{,}557}{2{,}000}, \\text{ and } \\dfrac{1{,}574}{2{,}000}", "__seed__": "0303"}}, {"seed": 304, "data": {"p1_how_many": "11", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{95}{630}, \\dfrac{97}{630}, \\dfrac{107}{630}, \\dfrac{108}{630}, \\dfrac{112}{630}, \\dfrac{114}{630}, \\dfrac{131}{630}, \\dfrac{135}{630}, \\text{ and } \\dfrac{138}{630}", "__seed__": "0304"}}, {"seed": 305, "data": {"p1_how_many": "12", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{42{,}043}{77{,}000}, \\dfrac{43{,}117}{77{,}000}, \\dfrac{50{,}651}{77{,}000}, \\dfrac{51{,}345}{77{,}000}, \\dfrac{51{,}890}{77{,}000}, \\dfrac{53{,}036}{77{,}000}, \\dfrac{56{,}346}{77{,}000}, \\dfrac{60{,}768}{77{,}000}, \\dfrac{63{,}689}{77{,}000}, \\text{ and } \\dfrac{64{,}413}{77{,}000}", "__seed__": "0305"}}, {"seed": 306, "data": {"p1_how_many": "13", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.325, 9.33, 9.335, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001", "9.325000000000001", "9.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}009}{20{,}000}, \\dfrac{5{,}448}{20{,}000}, \\dfrac{5{,}461}{20{,}000}, \\dfrac{5{,}746}{20{,}000}, \\dfrac{6{,}014}{20{,}000}, \\dfrac{6{,}464}{20{,}000}, \\dfrac{6{,}579}{20{,}000}, \\dfrac{7{,}025}{20{,}000}, \\dfrac{7{,}119}{20{,}000}, \\text{ and } \\dfrac{7{,}658}{20{,}000}", "__seed__": "0306"}}, {"seed": 307, "data": {"p1_how_many": "14", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.445, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998", "1.4449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}043}{12{,}000}, \\dfrac{3{,}378}{12{,}000}, \\dfrac{3{,}561}{12{,}000}, \\dfrac{3{,}586}{12{,}000}, \\dfrac{3{,}603}{12{,}000}, \\dfrac{3{,}763}{12{,}000}, \\dfrac{3{,}778}{12{,}000}, \\dfrac{3{,}780}{12{,}000}, \\dfrac{3{,}825}{12{,}000}, \\dfrac{3{,}832}{12{,}000}, \\text{ and } \\dfrac{3{,}955}{12{,}000}", "__seed__": "0307"}}, {"seed": 308, "data": {"p1_how_many": "12", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.54, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}444}{20{,}000}, \\dfrac{6{,}270}{20{,}000}, \\dfrac{6{,}275}{20{,}000}, \\dfrac{6{,}282}{20{,}000}, \\dfrac{6{,}650}{20{,}000}, \\dfrac{6{,}819}{20{,}000}, \\dfrac{7{,}088}{20{,}000}, \\dfrac{7{,}243}{20{,}000}, \\dfrac{7{,}527}{20{,}000}, \\text{ and } \\dfrac{7{,}769}{20{,}000}", "__seed__": "0308"}}, {"seed": 309, "data": {"p1_how_many": "13", "p1_a": "5.04", "p1_b": "5.05", 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2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997", "2.025", "2.0349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{545}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{554}{1{,}500}, \\dfrac{575}{1{,}500}, \\dfrac{594}{1{,}500}, \\text{ and } \\dfrac{596}{1{,}500}", "__seed__": "0310"}}, {"seed": 311, "data": {"p1_how_many": "12", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}267}{35{,}000}, \\dfrac{10{,}312}{35{,}000}, \\dfrac{10{,}757}{35{,}000}, \\dfrac{10{,}825}{35{,}000}, \\dfrac{10{,}845}{35{,}000}, \\dfrac{12{,}494}{35{,}000}, \\dfrac{12{,}674}{35{,}000}, \\dfrac{13{,}185}{35{,}000}, \\dfrac{13{,}539}{35{,}000}, \\text{ and } \\dfrac{13{,}615}{35{,}000}", "__seed__": "0311"}}, {"seed": 312, "data": {"p1_how_many": "14", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.635, 6.64, 6.645, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999", "6.635", "6.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0312"}}, {"seed": 313, "data": {"p1_how_many": "10", "p1_a": "1.73", "p1_b": "1.74", "p1_numbers": "1.7305, 1.731, 1.732, 1.733, 1.734, 1.735, 1.736, 1.737, 1.738, and 1.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.7309999999999999", "1.732", "1.7329999999999999", "1.734", "1.7349999999999999", "1.736", "1.7369999999999999", "1.738", "1.7389999999999999"], "p1_2_xs": ["1.7305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{621}{4{,}200}, \\dfrac{636}{4{,}200}, \\dfrac{641}{4{,}200}, \\dfrac{643}{4{,}200}, \\dfrac{654}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{661}{4{,}200}, \\dfrac{672}{4{,}200}, \\dfrac{675}{4{,}200}, \\dfrac{694}{4{,}200}, \\text{ and } \\dfrac{698}{4{,}200}", "__seed__": "0313"}}, {"seed": 314, "data": {"p1_how_many": "14", "p1_a": "1.86", "p1_b": "1.87", "p1_numbers": "1.8605, 1.861, 1.8615, 1.862, 1.8625, 1.863, 1.8635, 1.864, 1.8645, 1.865, 1.866, 1.867, 1.868, and 1.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.861", "1.862", "1.863", "1.864", "1.865", "1.866", "1.867", "1.868", "1.869"], "p1_2_xs": ["1.8605", "1.8615", "1.8625", "1.8635", "1.8645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}519}{6{,}300}, \\dfrac{1{,}592}{6{,}300}, \\dfrac{1{,}595}{6{,}300}, \\dfrac{1{,}643}{6{,}300}, \\dfrac{1{,}718}{6{,}300}, \\dfrac{1{,}719}{6{,}300}, \\dfrac{1{,}751}{6{,}300}, \\text{ and } \\dfrac{1{,}755}{6{,}300}", "__seed__": "0314"}}, {"seed": 315, "data": {"p1_how_many": "11", "p1_a": "8.26", "p1_b": "8.27", "p1_numbers": "8.2605, 8.261, 8.2615, 8.262, 8.263, 8.264, 8.265, 8.266, 8.267, 8.268, and 8.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.261", "8.262", "8.263", "8.264", "8.265", "8.266", "8.267", "8.267999999999999", "8.269"], "p1_2_xs": ["8.2605", "8.2615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{802}{1{,}200}, \\dfrac{813}{1{,}200}, \\dfrac{820}{1{,}200}, \\dfrac{828}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{836}{1{,}200}, \\dfrac{849}{1{,}200}, \\dfrac{857}{1{,}200}, \\dfrac{876}{1{,}200}, \\dfrac{882}{1{,}200}, \\dfrac{885}{1{,}200}, \\text{ and } \\dfrac{899}{1{,}200}", "__seed__": "0315"}}, {"seed": 316, "data": {"p1_how_many": "14", "p1_a": "2.32", "p1_b": "2.33", "p1_numbers": "2.3205, 2.321, 2.3215, 2.322, 2.3225, 2.323, 2.3235, 2.324, 2.3245, 2.325, 2.326, 2.327, 2.328, and 2.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3209999999999997", "2.3219999999999996", "2.323", "2.324", "2.3249999999999997", "2.3259999999999996", "2.327", "2.328", "2.3289999999999997"], "p1_2_xs": ["2.3205", "2.3215", "2.3225", "2.3235", "2.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}408}{3{,}000}, \\dfrac{2{,}416}{3{,}000}, \\dfrac{2{,}418}{3{,}000}, \\dfrac{2{,}428}{3{,}000}, \\dfrac{2{,}430}{3{,}000}, \\dfrac{2{,}440}{3{,}000}, \\dfrac{2{,}457}{3{,}000}, \\dfrac{2{,}473}{3{,}000}, \\dfrac{2{,}480}{3{,}000}, \\dfrac{2{,}482}{3{,}000}, \\dfrac{2{,}485}{3{,}000}, \\text{ and } \\dfrac{2{,}497}{3{,}000}", "__seed__": "0316"}}, {"seed": 317, "data": {"p1_how_many": "13", "p1_a": "6.9", "p1_b": "6.1", "p1_numbers": "6.9005, 6.901, 6.9015, 6.902, 6.9025, 6.903, 6.9035, 6.904, 6.905, 6.906, 6.907, 6.908, and 6.909", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.901000000000001", "6.902", "6.9030000000000005", "6.904", "6.905", "6.906000000000001", "6.907", "6.908", "6.909000000000001"], "p1_2_xs": ["6.9005", "6.9015", "6.9025", "6.9035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}037}{12{,}000}, \\dfrac{3{,}306}{12{,}000}, \\dfrac{3{,}389}{12{,}000}, \\dfrac{3{,}456}{12{,}000}, \\dfrac{3{,}543}{12{,}000}, \\dfrac{3{,}600}{12{,}000}, \\dfrac{3{,}606}{12{,}000}, \\dfrac{3{,}621}{12{,}000}, \\dfrac{3{,}739}{12{,}000}, \\dfrac{3{,}762}{12{,}000}, \\text{ and } \\dfrac{3{,}894}{12{,}000}", "__seed__": "0317"}}, {"seed": 318, "data": {"p1_how_many": "14", "p1_a": "8.21", "p1_b": "8.22", "p1_numbers": "8.2105, 8.211, 8.2115, 8.212, 8.2125, 8.213, 8.2135, 8.214, 8.2145, 8.215, 8.216, 8.217, 8.218, and 8.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.211", "8.212000000000002", "8.213000000000001", "8.214", "8.215000000000002", "8.216000000000001", "8.217", "8.218", "8.219000000000001"], "p1_2_xs": ["8.210500000000001", "8.211500000000001", "8.212500000000002", "8.213500000000002", "8.214500000000001"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{731}{4{,}200}, \\dfrac{734}{4{,}200}, \\dfrac{740}{4{,}200}, \\dfrac{795}{4{,}200}, \\dfrac{809}{4{,}200}, \\dfrac{884}{4{,}200}, \\dfrac{912}{4{,}200}, \\dfrac{999}{4{,}200}, \\dfrac{1{,}046}{4{,}200}, \\dfrac{1{,}126}{4{,}200}, \\dfrac{1{,}138}{4{,}200}, \\text{ and } \\dfrac{1{,}157}{4{,}200}", "__seed__": "0318"}}, {"seed": 319, "data": {"p1_how_many": "11", "p1_a": "1.93", "p1_b": "1.94", "p1_numbers": "1.9305, 1.931, 1.9315, 1.932, 1.933, 1.934, 1.935, 1.936, 1.937, 1.938, and 1.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9309999999999998", "1.932", "1.9329999999999998", "1.934", "1.9349999999999998", "1.936", "1.9369999999999998", "1.938", "1.9389999999999998"], "p1_2_xs": ["1.9304999999999999", "1.9314999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{307}{1{,}200}, \\dfrac{323}{1{,}200}, \\dfrac{327}{1{,}200}, \\dfrac{355}{1{,}200}, \\dfrac{363}{1{,}200}, \\dfrac{364}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{385}{1{,}200}, \\dfrac{388}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0319"}}, {"seed": 320, "data": {"p1_how_many": "14", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.245, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235", "5.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}034}{56{,}000}, \\dfrac{48{,}039}{56{,}000}, \\dfrac{48{,}207}{56{,}000}, \\dfrac{48{,}386}{56{,}000}, \\dfrac{48{,}601}{56{,}000}, \\dfrac{48{,}693}{56{,}000}, \\dfrac{48{,}788}{56{,}000}, \\dfrac{48{,}831}{56{,}000}, \\dfrac{48{,}875}{56{,}000}, \\dfrac{48{,}878}{56{,}000}, \\text{ and } \\dfrac{48{,}880}{56{,}000}", "__seed__": "0320"}}, {"seed": 321, "data": {"p1_how_many": "13", "p1_a": "5.31", "p1_b": "5.32", "p1_numbers": "5.3105, 5.311, 5.3115, 5.312, 5.3125, 5.313, 5.3135, 5.314, 5.315, 5.316, 5.317, 5.318, and 5.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.311", "5.311999999999999", "5.313", "5.313999999999999", "5.3149999999999995", "5.316", "5.316999999999999", "5.318", "5.319"], "p1_2_xs": ["5.310499999999999", "5.3115", "5.312499999999999", "5.3134999999999994"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}141}{42{,}000}, \\dfrac{30{,}202}{42{,}000}, \\dfrac{30{,}322}{42{,}000}, \\dfrac{30{,}326}{42{,}000}, \\dfrac{31{,}024}{42{,}000}, \\dfrac{31{,}351}{42{,}000}, \\dfrac{31{,}813}{42{,}000}, \\dfrac{32{,}865}{42{,}000}, \\dfrac{33{,}074}{42{,}000}, \\dfrac{33{,}933}{42{,}000}, \\dfrac{34{,}415}{42{,}000}, \\text{ and } \\dfrac{34{,}872}{42{,}000}", "__seed__": "0321"}}, {"seed": 322, "data": {"p1_how_many": "10", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.62, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}312}{63{,}000}, \\dfrac{30{,}278}{63{,}000}, \\dfrac{30{,}371}{63{,}000}, \\dfrac{31{,}655}{63{,}000}, \\dfrac{31{,}891}{63{,}000}, \\dfrac{31{,}977}{63{,}000}, \\text{ and } 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324, "data": {"p1_how_many": "14", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135", "2.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}502}{2{,}000}, \\dfrac{1{,}529}{2{,}000}, \\dfrac{1{,}539}{2{,}000}, \\dfrac{1{,}543}{2{,}000}, \\dfrac{1{,}547}{2{,}000}, \\dfrac{1{,}548}{2{,}000}, \\dfrac{1{,}549}{2{,}000}, \\dfrac{1{,}573}{2{,}000}, \\dfrac{1{,}586}{2{,}000}, \\dfrac{1{,}589}{2{,}000}, \\text{ and } \\dfrac{1{,}592}{2{,}000}", "__seed__": "0324"}}, {"seed": 325, "data": {"p1_how_many": "13", "p1_a": "7.55", "p1_b": "7.56", 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number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{2{,}000}, \\dfrac{546}{2{,}000}, \\dfrac{552}{2{,}000}, \\dfrac{586}{2{,}000}, \\dfrac{601}{2{,}000}, \\dfrac{659}{2{,}000}, \\dfrac{750}{2{,}000}, \\dfrac{761}{2{,}000}, \\text{ and } \\dfrac{780}{2{,}000}", "__seed__": "0329"}}, {"seed": 330, "data": {"p1_how_many": "10", "p1_a": "6.93", "p1_b": "6.94", "p1_numbers": "6.9305, 6.931, 6.932, 6.933, 6.934, 6.935, 6.936, 6.937, 6.938, and 6.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.931", "6.9319999999999995", "6.933", "6.933999999999999", "6.935", "6.936", "6.936999999999999", "6.938", "6.939"], "p1_2_xs": ["6.930499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}032}{3{,}500}, \\dfrac{1{,}060}{3{,}500}, 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\\dfrac{24{,}916}{30{,}000}, \\text{ and } \\dfrac{24{,}974}{30{,}000}", "__seed__": "0331"}}, {"seed": 332, "data": {"p1_how_many": "14", "p1_a": "3.22", "p1_b": "3.23", "p1_numbers": "3.2205, 3.221, 3.2215, 3.222, 3.2225, 3.223, 3.2235, 3.224, 3.2245, 3.225, 3.226, 3.227, 3.228, and 3.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.221", "3.222", "3.2230000000000003", "3.224", "3.225", "3.226", "3.2270000000000003", "3.228", "3.229"], "p1_2_xs": ["3.2205000000000004", "3.2215000000000003", "3.2225", "3.2235000000000005", "3.2245000000000004"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}803}{5{,}600}, \\dfrac{4{,}814}{5{,}600}, \\dfrac{4{,}823}{5{,}600}, \\dfrac{4{,}873}{5{,}600}, \\dfrac{4{,}877}{5{,}600}, \\dfrac{4{,}886}{5{,}600}, \\text{ and } \\dfrac{4{,}891}{5{,}600}", "__seed__": 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"p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7410000000000005", "5.742", "5.743", "5.744", "5.745", "5.746", "5.747", "5.748", "5.7490000000000006"], "p1_2_xs": ["5.7405", "5.7415", "5.7425", "5.7435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{603}{4{,}200}, \\dfrac{625}{4{,}200}, \\dfrac{638}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{652}{4{,}200}, \\dfrac{658}{4{,}200}, \\dfrac{667}{4{,}200}, \\dfrac{687}{4{,}200}, \\dfrac{693}{4{,}200}, \\text{ and } \\dfrac{695}{4{,}200}", "__seed__": "0335"}}, {"seed": 336, "data": {"p1_how_many": "14", "p1_a": "9.34", "p1_b": "9.35", "p1_numbers": "9.3405, 9.341, 9.3415, 9.342, 9.3425, 9.343, 9.3435, 9.344, 9.3445, 9.345, 9.346, 9.347, 9.348, and 9.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.341", "9.342", "9.343", "9.344", 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"7.337", "7.338", "7.339"], "p1_2_xs": ["7.3305", "7.3315", "7.3325", "7.3335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}736}{3{,}500}, \\dfrac{1{,}785}{3{,}500}, \\dfrac{1{,}787}{3{,}500}, \\dfrac{1{,}926}{3{,}500}, \\dfrac{1{,}943}{3{,}500}, \\dfrac{1{,}996}{3{,}500}, \\dfrac{1{,}998}{3{,}500}, \\dfrac{2{,}019}{3{,}500}, \\dfrac{2{,}076}{3{,}500}, \\text{ and } \\dfrac{2{,}083}{3{,}500}", "__seed__": "0339"}}, {"seed": 340, "data": {"p1_how_many": "10", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}217}{2{,}000}, \\dfrac{1{,}231}{2{,}000}, \\dfrac{1{,}266}{2{,}000}, \\dfrac{1{,}272}{2{,}000}, \\dfrac{1{,}274}{2{,}000}, \\dfrac{1{,}279}{2{,}000}, \\dfrac{1{,}320}{2{,}000}, \\dfrac{1{,}347}{2{,}000}, \\dfrac{1{,}371}{2{,}000}, \\dfrac{1{,}387}{2{,}000}, \\dfrac{1{,}413}{2{,}000}, \\text{ and } \\dfrac{1{,}452}{2{,}000}", "__seed__": "0340"}}, {"seed": 341, "data": {"p1_how_many": "11", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}527}{2{,}000}, \\dfrac{1{,}547}{2{,}000}, \\dfrac{1{,}553}{2{,}000}, \\dfrac{1{,}554}{2{,}000}, \\dfrac{1{,}567}{2{,}000}, \\dfrac{1{,}568}{2{,}000}, \\dfrac{1{,}572}{2{,}000}, \\text{ and } \\dfrac{1{,}599}{2{,}000}", "__seed__": "0341"}}, {"seed": 342, "data": {"p1_how_many": "12", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.4005, 1.401, 1.4015, 1.402, 1.4025, 1.403, 1.404, 1.405, 1.406, 1.407, 1.408, and 1.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4009999999999998", "1.402", "1.4029999999999998", "1.404", "1.4049999999999998", "1.406", "1.4069999999999998", "1.408", "1.4089999999999998"], "p1_2_xs": ["1.4004999999999999", "1.4014999999999997", "1.4024999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{310}{1{,}200}, \\dfrac{316}{1{,}200}, \\dfrac{329}{1{,}200}, \\dfrac{332}{1{,}200}, \\dfrac{333}{1{,}200}, \\dfrac{335}{1{,}200}, \\dfrac{377}{1{,}200}, \\text{ and } \\dfrac{399}{1{,}200}", "__seed__": "0342"}}, {"seed": 343, "data": {"p1_how_many": "11", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.015, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005", "8.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{402}{2{,}000}, \\dfrac{408}{2{,}000}, \\dfrac{434}{2{,}000}, \\dfrac{435}{2{,}000}, \\dfrac{441}{2{,}000}, \\dfrac{450}{2{,}000}, \\dfrac{467}{2{,}000}, \\dfrac{469}{2{,}000}, \\dfrac{471}{2{,}000}, \\dfrac{474}{2{,}000}, \\text{ and } \\dfrac{479}{2{,}000}", "__seed__": "0343"}}, {"seed": 344, "data": {"p1_how_many": "14", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.7005, 5.701, 5.7015, 5.702, 5.7025, 5.703, 5.7035, 5.704, 5.7045, 5.705, 5.706, 5.707, 5.708, and 5.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7010000000000005", "5.702", "5.703", "5.704", "5.705", "5.706", "5.707", "5.708", "5.7090000000000005"], "p1_2_xs": ["5.7005", "5.7015", "5.7025", "5.7035", "5.7044999999999995"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{516}{1{,}500}, \\dfrac{528}{1{,}500}, \\dfrac{535}{1{,}500}, \\dfrac{538}{1{,}500}, \\dfrac{561}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{579}{1{,}500}, \\dfrac{580}{1{,}500}, \\dfrac{593}{1{,}500}, \\dfrac{596}{1{,}500}, \\dfrac{597}{1{,}500}, \\text{ and } \\dfrac{598}{1{,}500}", "__seed__": "0344"}}, {"seed": 345, "data": {"p1_how_many": "12", "p1_a": "3.96", "p1_b": "3.97", "p1_numbers": "3.9605, 3.961, 3.9615, 3.962, 3.9625, 3.963, 3.964, 3.965, 3.966, 3.967, 3.968, and 3.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.961", "3.9619999999999997", "3.963", "3.964", "3.965", "3.9659999999999997", "3.967", "3.968", "3.969"], "p1_2_xs": ["3.9605", "3.9615", "3.9625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}030}{42{,}000}, \\dfrac{35{,}197}{42{,}000}, \\dfrac{35{,}423}{42{,}000}, \\dfrac{35{,}547}{42{,}000}, \\dfrac{35{,}577}{42{,}000}, \\dfrac{35{,}606}{42{,}000}, \\dfrac{35{,}710}{42{,}000}, \\dfrac{35{,}816}{42{,}000}, \\dfrac{35{,}829}{42{,}000}, \\text{ and } \\dfrac{35{,}940}{42{,}000}", "__seed__": "0345"}}, {"seed": 346, "data": {"p1_how_many": "10", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}061}{42{,}000}, \\dfrac{7{,}891}{42{,}000}, \\dfrac{8{,}037}{42{,}000}, \\dfrac{9{,}295}{42{,}000}, \\dfrac{9{,}815}{42{,}000}, \\dfrac{10{,}188}{42{,}000}, \\dfrac{10{,}253}{42{,}000}, \\dfrac{11{,}202}{42{,}000}, \\text{ and } \\dfrac{11{,}403}{42{,}000}", "__seed__": "0346"}}, {"seed": 347, "data": {"p1_how_many": "10", "p1_a": "4.61", "p1_b": "4.62", "p1_numbers": "4.6105, 4.611, 4.612, 4.613, 4.614, 4.615, 4.616, 4.617, 4.618, and 4.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.611000000000001", "4.612", "4.613", "4.614", "4.615", "4.6160000000000005", "4.617", "4.618", "4.619000000000001"], "p1_2_xs": ["4.6105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}127}{4{,}200}, \\dfrac{3{,}173}{4{,}200}, \\dfrac{3{,}186}{4{,}200}, \\dfrac{3{,}204}{4{,}200}, \\dfrac{3{,}328}{4{,}200}, \\dfrac{3{,}423}{4{,}200}, \\text{ and } \\dfrac{3{,}451}{4{,}200}", "__seed__": "0347"}}, {"seed": 348, "data": {"p1_how_many": "12", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.24, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}266}{20{,}000}, \\dfrac{5{,}307}{20{,}000}, \\dfrac{6{,}488}{20{,}000}, \\dfrac{6{,}530}{20{,}000}, \\dfrac{6{,}540}{20{,}000}, \\dfrac{6{,}577}{20{,}000}, \\dfrac{6{,}635}{20{,}000}, \\dfrac{6{,}909}{20{,}000}, \\dfrac{7{,}046}{20{,}000}, \\dfrac{7{,}415}{20{,}000}, \\text{ and } \\dfrac{7{,}477}{20{,}000}", "__seed__": "0348"}}, {"seed": 349, "data": {"p1_how_many": "12", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}236}{2{,}000}, \\dfrac{1{,}269}{2{,}000}, \\dfrac{1{,}336}{2{,}000}, \\dfrac{1{,}346}{2{,}000}, \\dfrac{1{,}361}{2{,}000}, \\dfrac{1{,}380}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\text{ and } \\dfrac{1{,}499}{2{,}000}", "__seed__": "0349"}}, {"seed": 350, "data": {"p1_how_many": "12", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.025, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015", "6.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{325}{1{,}200}, \\dfrac{339}{1{,}200}, \\dfrac{342}{1{,}200}, \\dfrac{349}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{358}{1{,}200}, \\dfrac{364}{1{,}200}, \\dfrac{381}{1{,}200}, \\dfrac{389}{1{,}200}, \\dfrac{390}{1{,}200}, \\dfrac{396}{1{,}200}, \\text{ and } \\dfrac{399}{1{,}200}", "__seed__": "0350"}}, {"seed": 351, "data": {"p1_how_many": "14", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.415, 3.42, 3.425, 3.43, 3.435, 3.44, 3.445, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996", "3.425", "3.4349999999999996", "3.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}450}{63{,}000}, \\dfrac{10{,}665}{63{,}000}, \\dfrac{10{,}758}{63{,}000}, \\dfrac{11{,}086}{63{,}000}, \\dfrac{11{,}317}{63{,}000}, \\dfrac{11{,}424}{63{,}000}, \\dfrac{11{,}740}{63{,}000}, \\dfrac{11{,}978}{63{,}000}, \\dfrac{12{,}110}{63{,}000}, \\dfrac{12{,}206}{63{,}000}, \\text{ and } \\dfrac{13{,}720}{63{,}000}", "__seed__": "0351"}}, {"seed": 352, "data": {"p1_how_many": "11", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.13, 9.14, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}177}{20{,}000}, \\dfrac{4{,}248}{20{,}000}, \\dfrac{4{,}328}{20{,}000}, \\dfrac{4{,}332}{20{,}000}, \\dfrac{4{,}363}{20{,}000}, \\dfrac{4{,}420}{20{,}000}, \\dfrac{4{,}443}{20{,}000}, \\dfrac{4{,}680}{20{,}000}, \\dfrac{4{,}791}{20{,}000}, \\text{ and } \\dfrac{4{,}804}{20{,}000}", "__seed__": "0352"}}, {"seed": 353, "data": {"p1_how_many": "10", "p1_a": "7.62", "p1_b": "7.63", "p1_numbers": "7.6205, 7.621, 7.622, 7.623, 7.624, 7.625, 7.626, 7.627, 7.628, and 7.629", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.621", "7.622", "7.623", "7.624", "7.625", "7.626", "7.627", "7.628", "7.6290000000000004"], "p1_2_xs": ["7.6205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}085}{12{,}000}, \\dfrac{8{,}394}{12{,}000}, \\dfrac{8{,}462}{12{,}000}, \\dfrac{8{,}585}{12{,}000}, \\dfrac{8{,}621}{12{,}000}, \\dfrac{8{,}713}{12{,}000}, \\dfrac{8{,}777}{12{,}000}, \\text{ and } \\dfrac{8{,}940}{12{,}000}", "__seed__": "0353"}}, {"seed": 354, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{310}{1{,}200}, \\dfrac{326}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{339}{1{,}200}, \\dfrac{356}{1{,}200}, \\dfrac{361}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{388}{1{,}200}, \\text{ and } \\dfrac{399}{1{,}200}", "__seed__": "0354"}}, {"seed": 355, "data": {"p1_how_many": "13", "p1_a": "2.67", "p1_b": "2.68", "p1_numbers": "2.6705, 2.671, 2.6715, 2.672, 2.6725, 2.673, 2.6735, 2.674, 2.675, 2.676, 2.677, 2.678, and 2.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.671", "2.6719999999999997", "2.673", "2.674", "2.675", "2.6759999999999997", "2.677", "2.678", "2.679"], "p1_2_xs": ["2.6705", "2.6715", "2.6725", "2.6735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}056}{15{,}000}, \\dfrac{5{,}305}{15{,}000}, \\dfrac{5{,}448}{15{,}000}, \\dfrac{5{,}522}{15{,}000}, \\dfrac{5{,}618}{15{,}000}, \\dfrac{5{,}689}{15{,}000}, \\dfrac{5{,}793}{15{,}000}, \\text{ and } \\dfrac{5{,}838}{15{,}000}", "__seed__": "0355"}}, {"seed": 356, "data": {"p1_how_many": "14", "p1_a": "4.43", "p1_b": "4.44", "p1_numbers": "4.4305, 4.431, 4.4315, 4.432, 4.4325, 4.433, 4.4335, 4.434, 4.4345, 4.435, 4.436, 4.437, 4.438, and 4.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.431", "4.4319999999999995", "4.433", "4.433999999999999", "4.435", "4.436", "4.436999999999999", "4.438", "4.439"], "p1_2_xs": ["4.430499999999999", "4.4315", "4.432499999999999", "4.4334999999999996", "4.434499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{309}{1{,}200}, \\dfrac{312}{1{,}200}, \\dfrac{315}{1{,}200}, \\dfrac{333}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{345}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{370}{1{,}200}, \\dfrac{380}{1{,}200}, \\text{ and } \\dfrac{390}{1{,}200}", "__seed__": "0356"}}, {"seed": 357, "data": {"p1_how_many": "10", "p1_a": "7.22", "p1_b": "7.23", "p1_numbers": "7.2205, 7.221, 7.222, 7.223, 7.224, 7.225, 7.226, 7.227, 7.228, and 7.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.221", "7.2219999999999995", "7.223", "7.223999999999999", "7.225", "7.226", "7.226999999999999", "7.228", "7.229"], "p1_2_xs": ["7.2204999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0357"}}, {"seed": 358, "data": {"p1_how_many": "14", "p1_a": "2.37", "p1_b": "2.38", "p1_numbers": "2.3705, 2.371, 2.3715, 2.372, 2.3725, 2.373, 2.3735, 2.374, 2.3745, 2.375, 2.376, 2.377, 2.378, and 2.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.371", "2.372", "2.373", "2.374", "2.375", "2.376", "2.3770000000000002", "2.378", "2.379"], "p1_2_xs": ["2.3705000000000003", "2.3715", "2.3725", "2.3735000000000004", "2.3745000000000003"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}159}{20{,}000}, \\dfrac{12{,}286}{20{,}000}, \\dfrac{12{,}568}{20{,}000}, \\dfrac{12{,}903}{20{,}000}, \\dfrac{12{,}920}{20{,}000}, \\dfrac{13{,}312}{20{,}000}, \\dfrac{13{,}489}{20{,}000}, \\dfrac{13{,}999}{20{,}000}, \\dfrac{14{,}562}{20{,}000}, \\dfrac{14{,}765}{20{,}000}, \\text{ and } \\dfrac{14{,}930}{20{,}000}", "__seed__": "0358"}}, {"seed": 359, "data": {"p1_how_many": "12", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}019}{15{,}000}, \\dfrac{5{,}022}{15{,}000}, \\dfrac{5{,}109}{15{,}000}, \\dfrac{5{,}114}{15{,}000}, \\dfrac{5{,}159}{15{,}000}, \\dfrac{5{,}570}{15{,}000}, \\dfrac{5{,}599}{15{,}000}, \\dfrac{5{,}686}{15{,}000}, \\dfrac{5{,}763}{15{,}000}, \\dfrac{5{,}765}{15{,}000}, \\dfrac{5{,}812}{15{,}000}, \\text{ and } \\dfrac{5{,}905}{15{,}000}", "__seed__": "0359"}}, {"seed": 360, "data": {"p1_how_many": "10", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{8{,}605}{42{,}000}, \\dfrac{8{,}702}{42{,}000}, \\dfrac{8{,}926}{42{,}000}, \\dfrac{9{,}543}{42{,}000}, \\dfrac{10{,}628}{42{,}000}, \\dfrac{10{,}853}{42{,}000}, \\dfrac{11{,}227}{42{,}000}, \\dfrac{11{,}436}{42{,}000}, \\dfrac{11{,}611}{42{,}000}, \\dfrac{11{,}736}{42{,}000}, \\text{ and } \\dfrac{11{,}982}{42{,}000}", "__seed__": "0360"}}, {"seed": 361, "data": {"p1_how_many": "12", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}023}{12{,}000}, \\dfrac{8{,}138}{12{,}000}, \\dfrac{8{,}205}{12{,}000}, \\dfrac{8{,}393}{12{,}000}, \\dfrac{8{,}398}{12{,}000}, \\dfrac{8{,}423}{12{,}000}, \\dfrac{8{,}535}{12{,}000}, \\dfrac{8{,}573}{12{,}000}, \\dfrac{8{,}761}{12{,}000}, \\dfrac{8{,}770}{12{,}000}, \\dfrac{8{,}846}{12{,}000}, \\text{ and } \\dfrac{8{,}990}{12{,}000}", "__seed__": "0361"}}, {"seed": 362, "data": {"p1_how_many": "14", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.745, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735", "2.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}952}{63{,}000}, \\dfrac{10{,}052}{63{,}000}, \\dfrac{10{,}987}{63{,}000}, \\dfrac{11{,}495}{63{,}000}, \\dfrac{12{,}515}{63{,}000}, \\dfrac{12{,}762}{63{,}000}, \\dfrac{13{,}507}{63{,}000}, \\dfrac{13{,}562}{63{,}000}, \\text{ and } \\dfrac{13{,}601}{63{,}000}", "__seed__": "0362"}}, {"seed": 363, "data": {"p1_how_many": "14", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.025, 6.03, 6.035, 6.04, 6.045, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015", "6.0249999999999995", "6.035", "6.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}235}{7{,}700}, \\dfrac{4{,}512}{7{,}700}, \\dfrac{4{,}552}{7{,}700}, \\dfrac{4{,}649}{7{,}700}, \\dfrac{4{,}727}{7{,}700}, \\dfrac{4{,}748}{7{,}700}, \\dfrac{4{,}812}{7{,}700}, \\dfrac{5{,}091}{7{,}700}, \\dfrac{5{,}180}{7{,}700}, \\dfrac{5{,}423}{7{,}700}, \\dfrac{5{,}474}{7{,}700}, \\text{ and } \\dfrac{5{,}494}{7{,}700}", "__seed__": "0363"}}, {"seed": 364, "data": {"p1_how_many": "10", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}809}{6{,}300}, \\dfrac{2{,}837}{6{,}300}, \\dfrac{3{,}023}{6{,}300}, \\dfrac{3{,}224}{6{,}300}, \\dfrac{3{,}279}{6{,}300}, \\dfrac{3{,}338}{6{,}300}, \\dfrac{3{,}398}{6{,}300}, \\dfrac{3{,}422}{6{,}300}, \\dfrac{3{,}454}{6{,}300}, \\dfrac{3{,}546}{6{,}300}, \\text{ and } \\dfrac{3{,}596}{6{,}300}", "__seed__": "0364"}}, {"seed": 365, "data": {"p1_how_many": "14", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.635, 4.64, 4.645, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999", "4.635", "4.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}355}{7{,}700}, \\dfrac{4{,}697}{7{,}700}, \\dfrac{5{,}150}{7{,}700}, \\dfrac{5{,}432}{7{,}700}, \\dfrac{5{,}525}{7{,}700}, \\dfrac{5{,}786}{7{,}700}, \\dfrac{5{,}977}{7{,}700}, \\dfrac{6{,}017}{7{,}700}, \\dfrac{6{,}184}{7{,}700}, \\dfrac{6{,}253}{7{,}700}, \\text{ and } \\dfrac{6{,}276}{7{,}700}", "__seed__": "0365"}}, {"seed": 366, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}288}{56{,}000}, \\dfrac{35{,}717}{56{,}000}, \\dfrac{36{,}763}{56{,}000}, \\dfrac{37{,}706}{56{,}000}, \\dfrac{37{,}929}{56{,}000}, \\dfrac{38{,}855}{56{,}000}, \\dfrac{38{,}905}{56{,}000}, \\dfrac{39{,}016}{56{,}000}, \\dfrac{39{,}093}{56{,}000}, \\dfrac{39{,}412}{56{,}000}, \\dfrac{39{,}827}{56{,}000}, \\text{ and } \\dfrac{39{,}932}{56{,}000}", "__seed__": "0366"}}, {"seed": 367, "data": {"p1_how_many": "12", "p1_a": "2.04", "p1_b": "2.05", "p1_numbers": "2.0405, 2.041, 2.0415, 2.042, 2.0425, 2.043, 2.044, 2.045, 2.046, 2.047, 2.048, and 2.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.041", "2.042", "2.043", "2.044", "2.045", "2.046", "2.047", "2.048", "2.049"], "p1_2_xs": ["2.0405", "2.0415", "2.0425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}474}{63{,}000}, \\dfrac{10{,}011}{63{,}000}, \\dfrac{10{,}104}{63{,}000}, \\dfrac{11{,}362}{63{,}000}, \\dfrac{11{,}599}{63{,}000}, \\dfrac{12{,}510}{63{,}000}, \\dfrac{13{,}013}{63{,}000}, \\dfrac{13{,}465}{63{,}000}, \\dfrac{13{,}727}{63{,}000}, \\dfrac{13{,}743}{63{,}000}, \\text{ and } \\dfrac{13{,}955}{63{,}000}", "__seed__": "0367"}}, {"seed": 368, "data": {"p1_how_many": "11", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{421}{2{,}000}, \\dfrac{424}{2{,}000}, \\dfrac{429}{2{,}000}, \\dfrac{437}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{457}{2{,}000}, \\dfrac{460}{2{,}000}, \\dfrac{462}{2{,}000}, \\text{ and } \\dfrac{474}{2{,}000}", "__seed__": "0368"}}, {"seed": 369, "data": {"p1_how_many": "13", "p1_a": "8.96", "p1_b": "8.97", "p1_numbers": "8.9605, 8.961, 8.9615, 8.962, 8.9625, 8.963, 8.9635, 8.964, 8.965, 8.966, 8.967, 8.968, and 8.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.961", "8.962000000000002", "8.963000000000001", "8.964", "8.965000000000002", "8.966000000000001", "8.967", "8.968", "8.969000000000001"], "p1_2_xs": ["8.960500000000001", "8.961500000000001", "8.962500000000002", "8.963500000000002"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}120}{42{,}000}, \\dfrac{35{,}232}{42{,}000}, \\dfrac{35{,}257}{42{,}000}, \\dfrac{35{,}377}{42{,}000}, \\dfrac{35{,}396}{42{,}000}, \\dfrac{35{,}417}{42{,}000}, \\dfrac{35{,}429}{42{,}000}, \\dfrac{35{,}673}{42{,}000}, \\text{ and } \\dfrac{35{,}948}{42{,}000}", "__seed__": "0369"}}, {"seed": 370, "data": {"p1_how_many": "12", "p1_a": "4.91", "p1_b": "4.92", "p1_numbers": "4.9105, 4.911, 4.9115, 4.912, 4.9125, 4.913, 4.914, 4.915, 4.916, 4.917, 4.918, and 4.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.9110000000000005", "4.912", "4.913", "4.914", "4.915", "4.916", "4.917", "4.918", "4.9190000000000005"], "p1_2_xs": ["4.9105", "4.9115", "4.9125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}076}{35{,}000}, \\dfrac{14{,}182}{35{,}000}, \\dfrac{14{,}197}{35{,}000}, \\dfrac{14{,}255}{35{,}000}, \\dfrac{14{,}327}{35{,}000}, \\dfrac{14{,}507}{35{,}000}, \\text{ and } \\dfrac{14{,}729}{35{,}000}", "__seed__": "0370"}}, {"seed": 371, "data": {"p1_how_many": "11", "p1_a": "1.95", "p1_b": "1.96", "p1_numbers": "1.9505, 1.951, 1.9515, 1.952, 1.953, 1.954, 1.955, 1.956, 1.957, 1.958, and 1.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9509999999999998", "1.952", "1.9529999999999998", "1.954", "1.9549999999999998", "1.956", "1.9569999999999999", "1.958", "1.9589999999999999"], "p1_2_xs": ["1.9505", "1.9514999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{623}{4{,}200}, \\dfrac{631}{4{,}200}, \\dfrac{654}{4{,}200}, \\dfrac{662}{4{,}200}, \\dfrac{664}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{673}{4{,}200}, \\dfrac{689}{4{,}200}, \\dfrac{690}{4{,}200}, \\text{ and } \\dfrac{691}{4{,}200}", "__seed__": "0371"}}, {"seed": 372, "data": {"p1_how_many": "13", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.235, 9.24, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225", "9.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}506}{42{,}000}, \\dfrac{30{,}521}{42{,}000}, \\dfrac{30{,}922}{42{,}000}, \\dfrac{30{,}951}{42{,}000}, \\dfrac{31{,}011}{42{,}000}, \\dfrac{32{,}730}{42{,}000}, \\dfrac{33{,}209}{42{,}000}, \\dfrac{33{,}535}{42{,}000}, \\dfrac{33{,}616}{42{,}000}, \\dfrac{33{,}956}{42{,}000}, \\dfrac{34{,}192}{42{,}000}, \\text{ and } \\dfrac{34{,}193}{42{,}000}", "__seed__": "0372"}}, {"seed": 373, "data": {"p1_how_many": "14", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.6005, 2.601, 2.6015, 2.602, 2.6025, 2.603, 2.6035, 2.604, 2.6045, 2.605, 2.606, 2.607, 2.608, and 2.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.601", "2.602", "2.603", "2.604", "2.605", "2.606", "2.607", "2.608", "2.609"], "p1_2_xs": ["2.6005000000000003", "2.6015", "2.6025", "2.6035000000000004", "2.6045000000000003"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{327}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{343}{1{,}200}, \\dfrac{349}{1{,}200}, \\dfrac{352}{1{,}200}, \\dfrac{361}{1{,}200}, \\dfrac{383}{1{,}200}, \\dfrac{386}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0373"}}, {"seed": 374, "data": {"p1_how_many": "10", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", 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\\dfrac{9{,}327}{15{,}000}, \\dfrac{9{,}425}{15{,}000}, \\text{ and } \\dfrac{9{,}681}{15{,}000}", "__seed__": "0378"}}, {"seed": 379, "data": {"p1_how_many": "14", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.635, 3.64, 3.645, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625", "3.635", "3.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{743}{4{,}200}, \\dfrac{787}{4{,}200}, \\dfrac{796}{4{,}200}, \\dfrac{831}{4{,}200}, \\dfrac{884}{4{,}200}, \\dfrac{960}{4{,}200}, \\dfrac{969}{4{,}200}, \\dfrac{994}{4{,}200}, \\dfrac{1{,}131}{4{,}200}, \\text{ and } \\dfrac{1{,}140}{4{,}200}", "__seed__": "0379"}}, {"seed": 380, "data": {"p1_how_many": "10", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.7005, 5.701, 5.702, 5.703, 5.704, 5.705, 5.706, 5.707, 5.708, and 5.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7010000000000005", "5.702", "5.703", "5.704", "5.705", "5.706", "5.707", "5.708", "5.7090000000000005"], "p1_2_xs": ["5.7005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}204}{2{,}000}, \\dfrac{1{,}236}{2{,}000}, \\dfrac{1{,}301}{2{,}000}, \\dfrac{1{,}347}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\dfrac{1{,}445}{2{,}000}, \\text{ and } \\dfrac{1{,}465}{2{,}000}", "__seed__": "0380"}}, {"seed": 381, "data": {"p1_how_many": "12", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{305}{420}, \\dfrac{309}{420}, \\dfrac{312}{420}, \\dfrac{315}{420}, \\dfrac{328}{420}, \\dfrac{329}{420}, \\text{ and } \\dfrac{341}{420}", "__seed__": "0381"}}, {"seed": 382, "data": {"p1_how_many": "12", "p1_a": "8.33", "p1_b": "8.34", "p1_numbers": "8.3305, 8.331, 8.3315, 8.332, 8.3325, 8.333, 8.334, 8.335, 8.336, 8.337, 8.338, and 8.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.331", "8.332", "8.333", "8.334", "8.335", "8.336", "8.337", "8.338", "8.339"], "p1_2_xs": ["8.3305", "8.3315", "8.332500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{516}{1{,}500}, \\dfrac{521}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{531}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{551}{1{,}500}, \\text{ and } \\dfrac{577}{1{,}500}", "__seed__": "0382"}}, {"seed": 383, "data": {"p1_how_many": "14", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.025, 3.03, 3.035, 3.04, 3.045, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997", "3.025", "3.0349999999999997", "3.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}606}{5{,}600}, \\dfrac{1{,}635}{5{,}600}, \\dfrac{1{,}775}{5{,}600}, \\dfrac{1{,}786}{5{,}600}, \\dfrac{1{,}869}{5{,}600}, \\dfrac{1{,}904}{5{,}600}, \\dfrac{1{,}994}{5{,}600}, \\text{ and } \\dfrac{2{,}014}{5{,}600}", "__seed__": "0383"}}, {"seed": 384, "data": {"p1_how_many": "10", "p1_a": "7.37", "p1_b": "7.38", "p1_numbers": "7.3705, 7.371, 7.372, 7.373, 7.374, 7.375, 7.376, 7.377, 7.378, and 7.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.371", "7.372", "7.373", "7.374", "7.375", "7.376", "7.377", "7.378", "7.3790000000000004"], "p1_2_xs": ["7.3705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}012}{15{,}000}, \\dfrac{5{,}068}{15{,}000}, \\dfrac{5{,}131}{15{,}000}, \\dfrac{5{,}312}{15{,}000}, \\dfrac{5{,}426}{15{,}000}, \\dfrac{5{,}623}{15{,}000}, \\text{ and } \\dfrac{5{,}823}{15{,}000}", "__seed__": "0384"}}, {"seed": 385, "data": {"p1_how_many": "11", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.7005, 8.701, 8.7015, 8.702, 8.703, 8.704, 8.705, 8.706, 8.707, 8.708, and 8.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.700999999999999", "8.702", "8.703", "8.703999999999999", "8.705", "8.706", "8.706999999999999", "8.707999999999998", "8.709"], "p1_2_xs": ["8.7005", "8.7015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0385"}}, {"seed": 386, "data": {"p1_how_many": "12", "p1_a": "9.12", "p1_b": "9.13", "p1_numbers": "9.1205, 9.121, 9.1215, 9.122, 9.1225, 9.123, 9.124, 9.125, 9.126, 9.127, 9.128, and 9.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.120999999999999", "9.122", "9.123", "9.123999999999999", "9.125", "9.126", "9.126999999999999", "9.127999999999998", "9.129"], "p1_2_xs": ["9.1205", "9.1215", "9.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{64}{150}, \\dfrac{67}{150}, \\dfrac{70}{150}, \\dfrac{72}{150}, \\dfrac{74}{150}, \\dfrac{81}{150}, \\dfrac{85}{150}, \\dfrac{87}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0386"}}, {"seed": 387, "data": {"p1_how_many": "13", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{801}{1{,}200}, \\dfrac{826}{1{,}200}, \\dfrac{827}{1{,}200}, \\dfrac{829}{1{,}200}, \\dfrac{846}{1{,}200}, \\dfrac{848}{1{,}200}, \\dfrac{865}{1{,}200}, \\dfrac{869}{1{,}200}, \\dfrac{871}{1{,}200}, \\dfrac{878}{1{,}200}, \\dfrac{880}{1{,}200}, \\text{ and } \\dfrac{882}{1{,}200}", "__seed__": "0387"}}, {"seed": 388, "data": {"p1_how_many": "13", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.635, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999", "4.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}517}{5{,}600}, \\dfrac{3{,}546}{5{,}600}, \\dfrac{3{,}599}{5{,}600}, \\dfrac{3{,}618}{5{,}600}, \\dfrac{3{,}660}{5{,}600}, \\dfrac{3{,}726}{5{,}600}, \\dfrac{3{,}883}{5{,}600}, \\text{ and } \\dfrac{3{,}906}{5{,}600}", "__seed__": "0388"}}, {"seed": 389, "data": {"p1_how_many": "14", "p1_a": "4.62", "p1_b": "4.63", "p1_numbers": "4.6205, 4.621, 4.6215, 4.622, 4.6225, 4.623, 4.6235, 4.624, 4.6245, 4.625, 4.626, 4.627, 4.628, and 4.629", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.621", "4.622", "4.623", "4.624", "4.625", "4.626", "4.627", "4.628", "4.6290000000000004"], "p1_2_xs": ["4.6205", "4.6215", "4.6225", "4.6235", "4.624499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}216}{3{,}500}, \\dfrac{2{,}339}{3{,}500}, \\dfrac{2{,}442}{3{,}500}, \\dfrac{2{,}498}{3{,}500}, \\dfrac{2{,}548}{3{,}500}, \\dfrac{2{,}594}{3{,}500}, \\dfrac{2{,}612}{3{,}500}, \\dfrac{2{,}686}{3{,}500}, \\text{ and } \\dfrac{2{,}727}{3{,}500}", "__seed__": "0389"}}, {"seed": 390, "data": {"p1_how_many": "11", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{514}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{557}{1{,}500}, \\dfrac{559}{1{,}500}, \\dfrac{570}{1{,}500}, \\dfrac{572}{1{,}500}, \\text{ and } \\dfrac{599}{1{,}500}", "__seed__": "0390"}}, {"seed": 391, "data": {"p1_how_many": "13", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}502}{2{,}000}, \\dfrac{1{,}512}{2{,}000}, \\dfrac{1{,}525}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}532}{2{,}000}, \\dfrac{1{,}540}{2{,}000}, \\dfrac{1{,}550}{2{,}000}, \\dfrac{1{,}561}{2{,}000}, \\text{ and } \\dfrac{1{,}573}{2{,}000}", "__seed__": "0391"}}, {"seed": 392, "data": {"p1_how_many": "13", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.735, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725", "9.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{162}{350}, \\dfrac{163}{350}, \\dfrac{167}{350}, \\dfrac{185}{350}, \\dfrac{187}{350}, \\dfrac{197}{350}, \\text{ and } \\dfrac{199}{350}", "__seed__": "0392"}}, {"seed": 393, "data": {"p1_how_many": "12", "p1_a": "3.31", "p1_b": 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4.517, 4.518, and 4.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.511", "4.512", "4.513", "4.513999999999999", "4.515", "4.516", "4.5169999999999995", "4.518", "4.519"], "p1_2_xs": ["4.5104999999999995", "4.5115", "4.512499999999999", "4.5135", "4.514499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{16{,}619}{35{,}000}, \\dfrac{18{,}247}{35{,}000}, \\dfrac{18{,}586}{35{,}000}, \\dfrac{19{,}184}{35{,}000}, \\dfrac{19{,}860}{35{,}000}, \\dfrac{20{,}529}{35{,}000}, \\text{ and } \\dfrac{20{,}550}{35{,}000}", "__seed__": "0394"}}, {"seed": 395, "data": {"p1_how_many": "11", "p1_a": "7.71", "p1_b": "7.72", "p1_numbers": "7.7105, 7.711, 7.7115, 7.712, 7.713, 7.714, 7.715, 7.716, 7.717, 7.718, and 7.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.711", "7.712", "7.713", "7.7139999999999995", "7.715", "7.716", "7.717", "7.718", "7.719"], "p1_2_xs": ["7.7105", "7.7115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{721}{4{,}200}, \\dfrac{746}{4{,}200}, \\dfrac{766}{4{,}200}, \\dfrac{806}{4{,}200}, \\dfrac{882}{4{,}200}, \\dfrac{928}{4{,}200}, \\dfrac{1{,}054}{4{,}200}, \\dfrac{1{,}066}{4{,}200}, \\dfrac{1{,}078}{4{,}200}, \\dfrac{1{,}092}{4{,}200}, \\text{ and } \\dfrac{1{,}164}{4{,}200}", "__seed__": "0395"}}, {"seed": 396, "data": {"p1_how_many": "14", "p1_a": "2.44", "p1_b": "2.45", "p1_numbers": "2.4405, 2.441, 2.4415, 2.442, 2.4425, 2.443, 2.4435, 2.444, 2.4445, 2.445, 2.446, 2.447, 2.448, and 2.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.441", "2.4419999999999997", "2.443", "2.444", "2.445", "2.4459999999999997", "2.447", "2.448", "2.449"], "p1_2_xs": ["2.4405", "2.4415", "2.4425", "2.4435000000000002", "2.4445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{81}{420}, \\dfrac{83}{420}, \\dfrac{85}{420}, \\dfrac{86}{420}, \\dfrac{89}{420}, \\dfrac{96}{420}, \\dfrac{97}{420}, \\dfrac{115}{420}, \\text{ and } \\dfrac{117}{420}", "__seed__": "0396"}}, {"seed": 397, "data": {"p1_how_many": "12", "p1_a": "4.0", "p1_b": "4.1", "p1_numbers": "4.005, 4.01, 4.015, 4.02, 4.025, 4.03, 4.04, 4.05, 4.06, 4.07, 4.08, and 4.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.01", "4.02", "4.03", "4.04", "4.05", "4.06", "4.07", "4.08", "4.09"], "p1_2_xs": ["4.005", "4.015", "4.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{303}{420}, \\dfrac{308}{420}, \\dfrac{318}{420}, \\dfrac{322}{420}, \\dfrac{324}{420}, \\dfrac{337}{420}, \\dfrac{340}{420}, \\dfrac{341}{420}, \\text{ and } \\dfrac{349}{420}", "__seed__": "0397"}}, {"seed": 398, "data": {"p1_how_many": "10", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}510}{2{,}000}, \\dfrac{1{,}518}{2{,}000}, \\dfrac{1{,}524}{2{,}000}, \\dfrac{1{,}534}{2{,}000}, \\dfrac{1{,}541}{2{,}000}, \\dfrac{1{,}547}{2{,}000}, \\dfrac{1{,}570}{2{,}000}, \\dfrac{1{,}582}{2{,}000}, \\dfrac{1{,}583}{2{,}000}, \\dfrac{1{,}584}{2{,}000}, \\dfrac{1{,}592}{2{,}000}, \\text{ and } \\dfrac{1{,}594}{2{,}000}", "__seed__": "0398"}}, {"seed": 399, "data": {"p1_how_many": "14", "p1_a": "3.06", "p1_b": "3.07", "p1_numbers": "3.0605, 3.061, 3.0615, 3.062, 3.0625, 3.063, 3.0635, 3.064, 3.0645, 3.065, 3.066, 3.067, 3.068, and 3.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.061", "3.062", "3.063", "3.064", "3.065", "3.066", "3.067", "3.068", "3.069"], "p1_2_xs": ["3.0605", "3.0615", "3.0625", "3.0635000000000003", "3.0645000000000002"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{312}{420}, \\dfrac{315}{420}, \\dfrac{319}{420}, \\dfrac{324}{420}, \\dfrac{327}{420}, \\dfrac{339}{420}, \\text{ and } \\dfrac{344}{420}", "__seed__": "0399"}}, {"seed": 400, "data": {"p1_how_many": "10", "p1_a": "9.87", "p1_b": "9.88", "p1_numbers": "9.8705, 9.871, 9.872, 9.873, 9.874, 9.875, 9.876, 9.877, 9.878, and 9.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.870999999999999", "9.872", "9.873", "9.873999999999999", "9.875", "9.876", "9.876999999999999", "9.877999999999998", "9.879"], "p1_2_xs": ["9.8705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}085}{35{,}000}, \\dfrac{10{,}247}{35{,}000}, \\dfrac{11{,}014}{35{,}000}, \\dfrac{11{,}230}{35{,}000}, \\dfrac{11{,}657}{35{,}000}, \\dfrac{11{,}850}{35{,}000}, \\text{ and } \\dfrac{13{,}791}{35{,}000}", "__seed__": "0400"}}, {"seed": 401, "data": {"p1_how_many": "13", "p1_a": "2.55", "p1_b": "2.56", "p1_numbers": "2.5505, 2.551, 2.5515, 2.552, 2.5525, 2.553, 2.5535, 2.554, 2.555, 2.556, 2.557, 2.558, and 2.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5509999999999997", "2.5519999999999996", "2.553", "2.554", "2.5549999999999997", "2.5559999999999996", "2.557", "2.558", "2.5589999999999997"], "p1_2_xs": ["2.5505", "2.5515", "2.5524999999999998", "2.5535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{641}{1{,}500}, \\dfrac{665}{1{,}500}, \\dfrac{745}{1{,}500}, \\dfrac{766}{1{,}500}, \\dfrac{811}{1{,}500}, \\dfrac{926}{1{,}500}, \\text{ and } \\dfrac{967}{1{,}500}", "__seed__": "0401"}}, {"seed": 402, "data": {"p1_how_many": "14", "p1_a": "4.24", "p1_b": "4.25", "p1_numbers": "4.2405, 4.241, 4.2415, 4.242, 4.2425, 4.243, 4.2435, 4.244, 4.2445, 4.245, 4.246, 4.247, 4.248, and 4.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.2410000000000005", "4.242", "4.243", "4.244", "4.245", "4.246", "4.247", "4.248", "4.2490000000000006"], "p1_2_xs": ["4.2405", "4.2415", "4.2425", "4.2435", "4.2444999999999995"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{802}{1{,}200}, \\dfrac{804}{1{,}200}, \\dfrac{807}{1{,}200}, \\dfrac{841}{1{,}200}, \\dfrac{855}{1{,}200}, \\dfrac{869}{1{,}200}, \\dfrac{870}{1{,}200}, \\dfrac{875}{1{,}200}, \\dfrac{879}{1{,}200}, \\dfrac{896}{1{,}200}, \\text{ and } \\dfrac{899}{1{,}200}", "__seed__": "0402"}}, {"seed": 403, "data": {"p1_how_many": "13", "p1_a": "6.15", "p1_b": "6.16", "p1_numbers": "6.1505, 6.151, 6.1515, 6.152, 6.1525, 6.153, 6.1535, 6.154, 6.155, 6.156, 6.157, 6.158, and 6.159", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.151000000000001", "6.152", "6.1530000000000005", "6.154", "6.155", "6.156000000000001", "6.157", "6.158", "6.159000000000001"], "p1_2_xs": ["6.1505", "6.1515", "6.1525", "6.1535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}646}{42{,}000}, \\dfrac{8{,}020}{42{,}000}, \\dfrac{8{,}455}{42{,}000}, \\dfrac{8{,}767}{42{,}000}, \\dfrac{9{,}119}{42{,}000}, \\dfrac{9{,}961}{42{,}000}, \\dfrac{11{,}103}{42{,}000}, \\dfrac{11{,}121}{42{,}000}, \\text{ and } \\dfrac{11{,}865}{42{,}000}", "__seed__": "0403"}}, {"seed": 404, "data": {"p1_how_many": "12", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}030}{4{,}200}, \\dfrac{3{,}049}{4{,}200}, \\dfrac{3{,}109}{4{,}200}, \\dfrac{3{,}136}{4{,}200}, \\dfrac{3{,}152}{4{,}200}, \\dfrac{3{,}167}{4{,}200}, \\dfrac{3{,}234}{4{,}200}, \\dfrac{3{,}244}{4{,}200}, \\dfrac{3{,}366}{4{,}200}, \\text{ and } \\dfrac{3{,}374}{4{,}200}", "__seed__": "0404"}}, {"seed": 405, "data": {"p1_how_many": "10", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.22, 6.23, 6.24, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}015}{56{,}000}, \\dfrac{32{,}386}{56{,}000}, \\dfrac{32{,}502}{56{,}000}, \\dfrac{33{,}170}{56{,}000}, \\dfrac{33{,}285}{56{,}000}, \\dfrac{33{,}701}{56{,}000}, \\dfrac{34{,}384}{56{,}000}, \\text{ and } \\dfrac{34{,}851}{56{,}000}", "__seed__": "0405"}}, {"seed": 406, "data": {"p1_how_many": "11", "p1_a": "7.16", "p1_b": "7.17", "p1_numbers": "7.1605, 7.161, 7.1615, 7.162, 7.163, 7.164, 7.165, 7.166, 7.167, 7.168, and 7.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.1610000000000005", "7.162", "7.163", "7.164", "7.165", "7.166", "7.167", "7.168", "7.1690000000000005"], "p1_2_xs": ["7.1605", "7.1615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{68}{150}, \\dfrac{84}{150}, \\dfrac{86}{150}, \\dfrac{90}{150}, \\dfrac{92}{150}, \\dfrac{96}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0406"}}, {"seed": 407, "data": {"p1_how_many": "13", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{127}{200}, \\dfrac{129}{200}, \\dfrac{135}{200}, \\dfrac{136}{200}, \\dfrac{139}{200}, \\dfrac{141}{200}, \\dfrac{142}{200}, \\text{ and } \\dfrac{145}{200}", "__seed__": "0407"}}, {"seed": 408, "data": {"p1_how_many": "11", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}541}{5{,}600}, \\dfrac{3{,}552}{5{,}600}, \\dfrac{3{,}581}{5{,}600}, \\dfrac{3{,}611}{5{,}600}, \\dfrac{3{,}620}{5{,}600}, \\dfrac{3{,}635}{5{,}600}, \\dfrac{3{,}758}{5{,}600}, \\dfrac{3{,}787}{5{,}600}, \\dfrac{3{,}839}{5{,}600}, \\text{ and } \\dfrac{3{,}890}{5{,}600}", "__seed__": "0408"}}, {"seed": 409, "data": {"p1_how_many": "14", "p1_a": "1.42", "p1_b": "1.43", "p1_numbers": "1.4205, 1.421, 1.4215, 1.422, 1.4225, 1.423, 1.4235, 1.424, 1.4245, 1.425, 1.426, 1.427, 1.428, and 1.429", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4209999999999998", "1.422", "1.4229999999999998", "1.424", "1.4249999999999998", "1.426", "1.4269999999999998", "1.428", "1.4289999999999998"], "p1_2_xs": ["1.4204999999999999", "1.4214999999999998", "1.4224999999999999", "1.4234999999999998", "1.4244999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}506}{4{,}200}, \\dfrac{3{,}528}{4{,}200}, \\dfrac{3{,}542}{4{,}200}, \\dfrac{3{,}544}{4{,}200}, \\dfrac{3{,}545}{4{,}200}, \\dfrac{3{,}548}{4{,}200}, \\dfrac{3{,}554}{4{,}200}, \\dfrac{3{,}569}{4{,}200}, \\dfrac{3{,}574}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\dfrac{3{,}587}{4{,}200}, \\text{ and } \\dfrac{3{,}588}{4{,}200}", "__seed__": "0409"}}, {"seed": 410, "data": {"p1_how_many": "14", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.125, 9.13, 9.135, 9.14, 9.145, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125", "9.135", "9.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}286}{56{,}000}, \\dfrac{16{,}728}{56{,}000}, \\dfrac{17{,}082}{56{,}000}, \\dfrac{17{,}272}{56{,}000}, \\dfrac{17{,}364}{56{,}000}, \\dfrac{17{,}800}{56{,}000}, \\dfrac{18{,}047}{56{,}000}, \\dfrac{18{,}117}{56{,}000}, \\dfrac{18{,}143}{56{,}000}, \\dfrac{20{,}275}{56{,}000}, \\dfrac{20{,}307}{56{,}000}, \\text{ and } \\dfrac{20{,}387}{56{,}000}", "__seed__": "0410"}}, {"seed": 411, "data": {"p1_how_many": "10", "p1_a": "5.02", "p1_b": "5.03", "p1_numbers": "5.0205, 5.021, 5.022, 5.023, 5.024, 5.025, 5.026, 5.027, 5.028, and 5.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.021", "5.021999999999999", "5.023", "5.023999999999999", "5.0249999999999995", "5.026", "5.026999999999999", "5.028", "5.029"], "p1_2_xs": ["5.020499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{411}{2{,}000}, \\dfrac{415}{2{,}000}, \\dfrac{424}{2{,}000}, \\dfrac{439}{2{,}000}, \\dfrac{440}{2{,}000}, \\dfrac{447}{2{,}000}, \\dfrac{451}{2{,}000}, \\dfrac{459}{2{,}000}, \\dfrac{476}{2{,}000}, \\text{ and } \\dfrac{480}{2{,}000}", "__seed__": "0411"}}, {"seed": 412, "data": {"p1_how_many": "10", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}889}{6{,}300}, \\dfrac{2{,}904}{6{,}300}, \\dfrac{3{,}053}{6{,}300}, \\dfrac{3{,}110}{6{,}300}, \\dfrac{3{,}213}{6{,}300}, \\dfrac{3{,}366}{6{,}300}, \\dfrac{3{,}426}{6{,}300}, \\dfrac{3{,}451}{6{,}300}, \\text{ and } \\dfrac{3{,}470}{6{,}300}", "__seed__": "0412"}}, {"seed": 413, "data": {"p1_how_many": "14", "p1_a": "6.25", "p1_b": "6.26", "p1_numbers": "6.2505, 6.251, 6.2515, 6.252, 6.2525, 6.253, 6.2535, 6.254, 6.2545, 6.255, 6.256, 6.257, 6.258, and 6.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.251", "6.252", "6.253", "6.254", "6.255", "6.256", "6.257", "6.258", "6.259"], "p1_2_xs": ["6.2505", "6.2515", "6.2524999999999995", "6.2535", "6.254499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}632}{5{,}600}, \\dfrac{1{,}716}{5{,}600}, \\dfrac{1{,}849}{5{,}600}, \\dfrac{1{,}891}{5{,}600}, \\dfrac{1{,}948}{5{,}600}, \\dfrac{1{,}954}{5{,}600}, \\dfrac{1{,}977}{5{,}600}, \\text{ and } \\dfrac{2{,}075}{5{,}600}", "__seed__": "0413"}}, {"seed": 414, "data": {"p1_how_many": "11", "p1_a": "5.05", "p1_b": "5.06", "p1_numbers": "5.0505, 5.051, 5.0515, 5.052, 5.053, 5.054, 5.055, 5.056, 5.057, 5.058, and 5.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.051", "5.052", "5.053", "5.053999999999999", "5.055", "5.056", "5.0569999999999995", "5.058", "5.059"], "p1_2_xs": ["5.0504999999999995", "5.0515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}208}{2{,}000}, \\dfrac{1{,}209}{2{,}000}, \\dfrac{1{,}217}{2{,}000}, \\dfrac{1{,}252}{2{,}000}, \\dfrac{1{,}253}{2{,}000}, \\dfrac{1{,}278}{2{,}000}, \\dfrac{1{,}288}{2{,}000}, \\dfrac{1{,}301}{2{,}000}, \\dfrac{1{,}337}{2{,}000}, \\dfrac{1{,}389}{2{,}000}, \\dfrac{1{,}413}{2{,}000}, \\text{ and } \\dfrac{1{,}444}{2{,}000}", "__seed__": "0414"}}, {"seed": 415, "data": {"p1_how_many": "13", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}108}{30{,}000}, \\dfrac{5{,}297}{30{,}000}, \\dfrac{5{,}313}{30{,}000}, \\dfrac{5{,}374}{30{,}000}, \\dfrac{5{,}483}{30{,}000}, \\dfrac{5{,}553}{30{,}000}, \\dfrac{5{,}563}{30{,}000}, \\dfrac{5{,}587}{30{,}000}, \\dfrac{5{,}651}{30{,}000}, \\text{ and } \\dfrac{5{,}668}{30{,}000}", "__seed__": "0415"}}, {"seed": 416, "data": {"p1_how_many": "14", "p1_a": "5.72", "p1_b": "5.73", "p1_numbers": "5.7205, 5.721, 5.7215, 5.722, 5.7225, 5.723, 5.7235, 5.724, 5.7245, 5.725, 5.726, 5.727, 5.728, and 5.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.721", "5.7219999999999995", "5.723", "5.723999999999999", "5.725", "5.726", "5.726999999999999", "5.728", "5.729"], "p1_2_xs": ["5.7204999999999995", "5.7215", "5.722499999999999", "5.7235", "5.724499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}134}{42{,}000}, \\dfrac{35{,}328}{42{,}000}, \\dfrac{35{,}341}{42{,}000}, \\dfrac{35{,}414}{42{,}000}, \\dfrac{35{,}561}{42{,}000}, \\dfrac{35{,}721}{42{,}000}, \\text{ and } \\dfrac{35{,}866}{42{,}000}", "__seed__": "0416"}}, {"seed": 417, "data": {"p1_how_many": "11", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.015, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{736}{3{,}500}, \\dfrac{761}{3{,}500}, \\dfrac{768}{3{,}500}, \\dfrac{808}{3{,}500}, \\dfrac{822}{3{,}500}, \\dfrac{848}{3{,}500}, \\dfrac{872}{3{,}500}, \\dfrac{876}{3{,}500}, \\text{ and } \\dfrac{959}{3{,}500}", "__seed__": "0417"}}, {"seed": 418, "data": {"p1_how_many": "12", "p1_a": "9.76", "p1_b": "9.77", "p1_numbers": "9.7605, 9.761, 9.7615, 9.762, 9.7625, 9.763, 9.764, 9.765, 9.766, 9.767, 9.768, and 9.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.761", "9.762", "9.763", "9.764", "9.765", "9.766", "9.767", "9.767999999999999", "9.769"], "p1_2_xs": ["9.7605", "9.7615", "9.762500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}457}{56{,}000}, \\dfrac{18{,}198}{56{,}000}, \\dfrac{18{,}692}{56{,}000}, \\dfrac{19{,}228}{56{,}000}, \\dfrac{19{,}467}{56{,}000}, \\dfrac{19{,}519}{56{,}000}, \\dfrac{19{,}617}{56{,}000}, \\dfrac{20{,}106}{56{,}000}, \\dfrac{20{,}772}{56{,}000}, \\dfrac{20{,}829}{56{,}000}, \\dfrac{20{,}878}{56{,}000}, \\text{ and } \\dfrac{20{,}900}{56{,}000}", "__seed__": "0418"}}, {"seed": 419, "data": {"p1_how_many": "11", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}862}{35{,}000}, \\dfrac{16{,}238}{35{,}000}, \\dfrac{16{,}292}{35{,}000}, \\dfrac{17{,}024}{35{,}000}, \\dfrac{17{,}159}{35{,}000}, \\dfrac{17{,}190}{35{,}000}, \\dfrac{18{,}106}{35{,}000}, \\dfrac{19{,}544}{35{,}000}, \\dfrac{20{,}117}{35{,}000}, \\text{ and } \\dfrac{20{,}636}{35{,}000}", "__seed__": "0419"}}, {"seed": 420, "data": {"p1_how_many": "14", "p1_a": "6.82", "p1_b": "6.83", "p1_numbers": "6.8205, 6.821, 6.8215, 6.822, 6.8225, 6.823, 6.8235, 6.824, 6.8245, 6.825, 6.826, 6.827, 6.828, and 6.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.821000000000001", "6.822", "6.823", "6.824", "6.825", "6.8260000000000005", "6.827", "6.828", "6.829000000000001"], "p1_2_xs": ["6.8205", "6.8215", "6.8225", "6.8235", "6.8245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}271}{42{,}000}, \\dfrac{31{,}067}{42{,}000}, \\dfrac{31{,}299}{42{,}000}, \\dfrac{31{,}470}{42{,}000}, \\dfrac{31{,}897}{42{,}000}, \\dfrac{32{,}338}{42{,}000}, \\dfrac{32{,}617}{42{,}000}, \\dfrac{32{,}685}{42{,}000}, \\text{ and } \\dfrac{33{,}992}{42{,}000}", "__seed__": "0420"}}, {"seed": 421, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", "2.4349999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{6{,}017}{20{,}000}, \\dfrac{6{,}050}{20{,}000}, \\dfrac{6{,}171}{20{,}000}, \\dfrac{6{,}218}{20{,}000}, \\dfrac{6{,}432}{20{,}000}, \\dfrac{6{,}796}{20{,}000}, \\dfrac{6{,}885}{20{,}000}, \\dfrac{7{,}460}{20{,}000}, \\text{ and } \\dfrac{7{,}910}{20{,}000}", "__seed__": "0421"}}, {"seed": 422, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", "2.4349999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, \\dfrac{243}{300}, \\dfrac{244}{300}, \\dfrac{245}{300}, \\dfrac{246}{300}, \\dfrac{247}{300}, \\text{ and } \\dfrac{249}{300}", "__seed__": "0422"}}, {"seed": 423, "data": {"p1_how_many": "12", "p1_a": "6.26", "p1_b": "6.27", "p1_numbers": "6.2605, 6.261, 6.2615, 6.262, 6.2625, 6.263, 6.264, 6.265, 6.266, 6.267, 6.268, and 6.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.261", "6.262", "6.263", "6.263999999999999", "6.265", "6.266", "6.2669999999999995", "6.268", "6.269"], "p1_2_xs": ["6.2604999999999995", "6.2615", "6.262499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}510}{4{,}200}, \\dfrac{3{,}511}{4{,}200}, \\dfrac{3{,}526}{4{,}200}, \\dfrac{3{,}531}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}540}{4{,}200}, \\dfrac{3{,}549}{4{,}200}, \\dfrac{3{,}550}{4{,}200}, \\dfrac{3{,}563}{4{,}200}, \\dfrac{3{,}566}{4{,}200}, \\dfrac{3{,}568}{4{,}200}, \\text{ and } \\dfrac{3{,}572}{4{,}200}", "__seed__": "0423"}}, {"seed": 424, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0424"}}, {"seed": 425, "data": {"p1_how_many": "12", "p1_a": "8.82", "p1_b": "8.83", "p1_numbers": "8.8205, 8.821, 8.8215, 8.822, 8.8225, 8.823, 8.824, 8.825, 8.826, 8.827, 8.828, and 8.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.821", "8.822000000000001", "8.823", "8.824", "8.825000000000001", "8.826", "8.827", "8.828", "8.829"], "p1_2_xs": ["8.820500000000001", "8.8215", "8.822500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{534}{2{,}000}, \\dfrac{566}{2{,}000}, \\dfrac{673}{2{,}000}, \\dfrac{695}{2{,}000}, \\dfrac{704}{2{,}000}, \\dfrac{747}{2{,}000}, \\dfrac{783}{2{,}000}, \\text{ and } \\dfrac{790}{2{,}000}", "__seed__": "0425"}}, {"seed": 426, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{205}{350}, \\dfrac{215}{350}, \\dfrac{218}{350}, \\dfrac{221}{350}, \\dfrac{225}{350}, \\dfrac{229}{350}, \\text{ and } \\dfrac{260}{350}", "__seed__": "0426"}}, {"seed": 427, "data": {"p1_how_many": "14", "p1_a": "6.33", "p1_b": "6.34", "p1_numbers": "6.3305, 6.331, 6.3315, 6.332, 6.3325, 6.333, 6.3335, 6.334, 6.3345, 6.335, 6.336, 6.337, 6.338, and 6.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.331", "6.332", "6.333", "6.334", "6.335", "6.336", "6.337", "6.338", "6.339"], "p1_2_xs": ["6.3305", "6.3315", "6.3325", "6.3335", "6.334499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}563}{42{,}000}, \\dfrac{30{,}646}{42{,}000}, \\dfrac{30{,}777}{42{,}000}, \\dfrac{31{,}489}{42{,}000}, \\dfrac{32{,}615}{42{,}000}, \\dfrac{32{,}739}{42{,}000}, \\dfrac{33{,}281}{42{,}000}, \\dfrac{33{,}927}{42{,}000}, \\dfrac{34{,}215}{42{,}000}, \\text{ and } \\dfrac{34{,}635}{42{,}000}", "__seed__": "0427"}}, {"seed": 428, "data": {"p1_how_many": "12", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.125, 9.13, 9.14, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}058}{15{,}000}, \\dfrac{5{,}121}{15{,}000}, \\dfrac{5{,}312}{15{,}000}, \\dfrac{5{,}330}{15{,}000}, \\dfrac{5{,}339}{15{,}000}, \\dfrac{5{,}378}{15{,}000}, \\dfrac{5{,}383}{15{,}000}, \\dfrac{5{,}428}{15{,}000}, \\dfrac{5{,}435}{15{,}000}, \\dfrac{5{,}684}{15{,}000}, \\dfrac{5{,}755}{15{,}000}, \\text{ and } \\dfrac{5{,}829}{15{,}000}", "__seed__": "0428"}}, {"seed": 429, "data": {"p1_how_many": "14", "p1_a": "2.55", "p1_b": "2.56", "p1_numbers": "2.5505, 2.551, 2.5515, 2.552, 2.5525, 2.553, 2.5535, 2.554, 2.5545, 2.555, 2.556, 2.557, 2.558, and 2.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5509999999999997", "2.5519999999999996", "2.553", "2.554", "2.5549999999999997", "2.5559999999999996", "2.557", "2.558", "2.5589999999999997"], "p1_2_xs": ["2.5505", "2.5515", "2.5524999999999998", "2.5535", "2.5545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}233}{2{,}000}, \\dfrac{1{,}235}{2{,}000}, \\dfrac{1{,}251}{2{,}000}, \\dfrac{1{,}311}{2{,}000}, \\dfrac{1{,}408}{2{,}000}, \\dfrac{1{,}440}{2{,}000}, \\dfrac{1{,}464}{2{,}000}, \\text{ and } \\dfrac{1{,}475}{2{,}000}", "__seed__": "0429"}}, {"seed": 430, "data": {"p1_how_many": "12", "p1_a": "6.95", "p1_b": "6.96", "p1_numbers": "6.9505, 6.951, 6.9515, 6.952, 6.9525, 6.953, 6.954, 6.955, 6.956, 6.957, 6.958, and 6.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.9510000000000005", "6.952", "6.953", "6.954", "6.955", "6.956", "6.957", "6.958", "6.9590000000000005"], "p1_2_xs": ["6.9505", "6.9515", "6.9525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}306}{7{,}700}, \\dfrac{4{,}658}{7{,}700}, \\dfrac{4{,}801}{7{,}700}, \\dfrac{4{,}863}{7{,}700}, \\dfrac{4{,}886}{7{,}700}, \\dfrac{4{,}987}{7{,}700}, \\dfrac{5{,}144}{7{,}700}, \\dfrac{5{,}652}{7{,}700}, \\dfrac{6{,}029}{7{,}700}, \\dfrac{6{,}103}{7{,}700}, \\text{ and } \\dfrac{6{,}120}{7{,}700}", "__seed__": "0430"}}, {"seed": 431, "data": {"p1_how_many": "12", "p1_a": "9.35", "p1_b": "9.36", "p1_numbers": "9.3505, 9.351, 9.3515, 9.352, 9.3525, 9.353, 9.354, 9.355, 9.356, 9.357, 9.358, and 9.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.350999999999999", "9.352", "9.353", "9.354", "9.355", "9.356", "9.357", "9.357999999999999", "9.359"], "p1_2_xs": ["9.3505", "9.3515", "9.352500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}016}{30{,}000}, \\dfrac{5{,}055}{30{,}000}, \\dfrac{5{,}309}{30{,}000}, \\dfrac{5{,}322}{30{,}000}, \\dfrac{5{,}529}{30{,}000}, \\dfrac{5{,}530}{30{,}000}, \\dfrac{5{,}669}{30{,}000}, \\dfrac{5{,}686}{30{,}000}, \\dfrac{5{,}732}{30{,}000}, \\dfrac{5{,}787}{30{,}000}, \\dfrac{5{,}847}{30{,}000}, \\text{ and } \\dfrac{5{,}904}{30{,}000}", "__seed__": "0431"}}, {"seed": 432, "data": {"p1_how_many": "14", "p1_a": "1.85", "p1_b": "1.86", "p1_numbers": "1.8505, 1.851, 1.8515, 1.852, 1.8525, 1.853, 1.8535, 1.854, 1.8545, 1.855, 1.856, 1.857, 1.858, and 1.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.851", "1.852", "1.853", "1.854", "1.855", "1.856", "1.857", "1.858", "1.859"], "p1_2_xs": ["1.8505", "1.8515", "1.8525", "1.8535", "1.8545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}133}{30{,}000}, \\dfrac{24{,}148}{30{,}000}, \\dfrac{24{,}177}{30{,}000}, \\dfrac{24{,}322}{30{,}000}, \\dfrac{24{,}350}{30{,}000}, \\dfrac{24{,}371}{30{,}000}, \\dfrac{24{,}497}{30{,}000}, \\dfrac{24{,}502}{30{,}000}, \\dfrac{24{,}848}{30{,}000}, \\text{ and } \\dfrac{24{,}932}{30{,}000}", "__seed__": "0432"}}, {"seed": 433, "data": {"p1_how_many": "12", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.125, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999", "5.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{151}{350}, \\dfrac{157}{350}, \\dfrac{158}{350}, \\dfrac{159}{350}, \\dfrac{178}{350}, \\dfrac{179}{350}, \\dfrac{199}{350}, \\dfrac{202}{350}, \\text{ and } \\dfrac{205}{350}", "__seed__": "0433"}}, {"seed": 434, "data": {"p1_how_many": "10", "p1_a": "2.14", "p1_b": "2.15", "p1_numbers": "2.1405, 2.141, 2.142, 2.143, 2.144, 2.145, 2.146, 2.147, 2.148, and 2.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.141", "2.142", "2.1430000000000002", "2.144", "2.145", "2.146", "2.1470000000000002", "2.148", "2.149"], "p1_2_xs": ["2.1405000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}851}{6{,}300}, \\dfrac{2{,}903}{6{,}300}, \\dfrac{2{,}962}{6{,}300}, \\dfrac{3{,}129}{6{,}300}, \\dfrac{3{,}248}{6{,}300}, \\dfrac{3{,}270}{6{,}300}, \\dfrac{3{,}450}{6{,}300}, \\text{ and } \\dfrac{3{,}510}{6{,}300}", "__seed__": "0434"}}, {"seed": 435, "data": {"p1_how_many": "11", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}045}{35{,}000}, \\dfrac{7{,}172}{35{,}000}, \\dfrac{7{,}520}{35{,}000}, \\dfrac{8{,}103}{35{,}000}, \\dfrac{8{,}664}{35{,}000}, \\dfrac{8{,}873}{35{,}000}, \\dfrac{9{,}327}{35{,}000}, \\text{ and } \\dfrac{9{,}407}{35{,}000}", "__seed__": "0435"}}, {"seed": 436, "data": {"p1_how_many": "12", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}077}{4{,}200}, \\dfrac{3{,}166}{4{,}200}, \\dfrac{3{,}227}{4{,}200}, \\dfrac{3{,}336}{4{,}200}, \\dfrac{3{,}393}{4{,}200}, \\dfrac{3{,}397}{4{,}200}, \\dfrac{3{,}430}{4{,}200}, \\text{ and } \\dfrac{3{,}432}{4{,}200}", "__seed__": "0436"}}, {"seed": 437, "data": {"p1_how_many": "14", "p1_a": "8.73", "p1_b": "8.74", "p1_numbers": "8.7305, 8.731, 8.7315, 8.732, 8.7325, 8.733, 8.7335, 8.734, 8.7345, 8.735, 8.736, 8.737, 8.738, and 8.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.731", "8.732000000000001", "8.733", "8.734", "8.735000000000001", "8.736", "8.737", "8.738", "8.739"], "p1_2_xs": ["8.730500000000001", "8.7315", "8.732500000000002", "8.733500000000001", "8.7345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}406}{6{,}300}, \\dfrac{1{,}415}{6{,}300}, \\dfrac{1{,}438}{6{,}300}, \\dfrac{1{,}520}{6{,}300}, \\dfrac{1{,}544}{6{,}300}, \\dfrac{1{,}563}{6{,}300}, \\dfrac{1{,}568}{6{,}300}, \\dfrac{1{,}640}{6{,}300}, \\dfrac{1{,}682}{6{,}300}, \\dfrac{1{,}697}{6{,}300}, \\text{ and } \\dfrac{1{,}767}{6{,}300}", "__seed__": "0437"}}, {"seed": 438, "data": {"p1_how_many": "11", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{806}{1{,}200}, \\dfrac{821}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{838}{1{,}200}, \\dfrac{845}{1{,}200}, \\dfrac{853}{1{,}200}, \\dfrac{854}{1{,}200}, \\dfrac{855}{1{,}200}, \\dfrac{868}{1{,}200}, \\dfrac{896}{1{,}200}, \\dfrac{897}{1{,}200}, \\text{ and } \\dfrac{898}{1{,}200}", "__seed__": "0438"}}, {"seed": 439, "data": {"p1_how_many": "12", "p1_a": "8.02", "p1_b": "8.03", "p1_numbers": "8.0205, 8.021, 8.0215, 8.022, 8.0225, 8.023, 8.024, 8.025, 8.026, 8.027, 8.028, and 8.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.020999999999999", "8.022", "8.023", "8.024", "8.025", "8.026", "8.027", "8.027999999999999", "8.029"], "p1_2_xs": ["8.0205", "8.0215", "8.0225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}701}{6{,}300}, \\dfrac{2{,}720}{6{,}300}, \\dfrac{2{,}738}{6{,}300}, \\dfrac{2{,}761}{6{,}300}, \\dfrac{2{,}762}{6{,}300}, \\dfrac{2{,}765}{6{,}300}, \\dfrac{2{,}782}{6{,}300}, \\dfrac{2{,}783}{6{,}300}, \\dfrac{2{,}789}{6{,}300}, \\dfrac{2{,}790}{6{,}300}, \\text{ and } \\dfrac{2{,}793}{6{,}300}", "__seed__": "0439"}}, {"seed": 440, "data": {"p1_how_many": "10", "p1_a": "7.2", "p1_b": "7.3", "p1_numbers": "7.205, 7.21, 7.22, 7.23, 7.24, 7.25, 7.26, 7.27, 7.28, and 7.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.21", "7.22", "7.23", "7.24", "7.25", "7.26", "7.2700000000000005", "7.28", "7.29"], "p1_2_xs": ["7.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}033}{3{,}500}, \\dfrac{2{,}081}{3{,}500}, \\dfrac{2{,}148}{3{,}500}, \\dfrac{2{,}213}{3{,}500}, \\dfrac{2{,}416}{3{,}500}, \\dfrac{2{,}425}{3{,}500}, \\dfrac{2{,}467}{3{,}500}, \\dfrac{2{,}513}{3{,}500}, \\dfrac{2{,}652}{3{,}500}, \\dfrac{2{,}653}{3{,}500}, \\text{ and } \\dfrac{2{,}683}{3{,}500}", "__seed__": "0440"}}, {"seed": 441, "data": {"p1_how_many": "11", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{17{,}506}{35{,}000}, \\dfrac{17{,}643}{35{,}000}, \\dfrac{18{,}243}{35{,}000}, \\dfrac{19{,}130}{35{,}000}, \\dfrac{19{,}441}{35{,}000}, \\dfrac{19{,}564}{35{,}000}, \\dfrac{19{,}794}{35{,}000}, \\text{ and } \\dfrac{20{,}232}{35{,}000}", "__seed__": "0441"}}, {"seed": 442, "data": {"p1_how_many": "13", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.535, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995", "6.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{271}{630}, \\dfrac{272}{630}, \\dfrac{273}{630}, \\dfrac{275}{630}, \\dfrac{276}{630}, \\dfrac{277}{630}, \\text{ and } \\dfrac{279}{630}", "__seed__": "0442"}}, {"seed": 443, "data": {"p1_how_many": "12", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.625, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}229}{56{,}000}, \\dfrac{48{,}339}{56{,}000}, \\dfrac{48{,}501}{56{,}000}, \\dfrac{48{,}548}{56{,}000}, \\dfrac{48{,}643}{56{,}000}, \\dfrac{48{,}729}{56{,}000}, \\dfrac{48{,}744}{56{,}000}, \\dfrac{48{,}769}{56{,}000}, \\text{ and } \\dfrac{48{,}854}{56{,}000}", "__seed__": "0443"}}, {"seed": 444, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0444"}}, {"seed": 445, "data": {"p1_how_many": "14", "p1_a": "1.83", "p1_b": "1.84", "p1_numbers": "1.8305, 1.831, 1.8315, 1.832, 1.8325, 1.833, 1.8335, 1.834, 1.8345, 1.835, 1.836, 1.837, 1.838, and 1.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.831", "1.832", "1.833", "1.834", "1.835", "1.836", "1.837", "1.838", "1.839"], "p1_2_xs": ["1.8305", "1.8315", "1.8325", "1.8335", "1.8345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}143}{20{,}000}, \\dfrac{5{,}297}{20{,}000}, \\dfrac{5{,}377}{20{,}000}, \\dfrac{5{,}661}{20{,}000}, \\dfrac{6{,}272}{20{,}000}, \\dfrac{7{,}021}{20{,}000}, \\dfrac{7{,}471}{20{,}000}, \\dfrac{7{,}518}{20{,}000}, \\text{ and } \\dfrac{7{,}819}{20{,}000}", "__seed__": "0445"}}, {"seed": 446, "data": {"p1_how_many": "11", "p1_a": "2.45", "p1_b": "2.46", "p1_numbers": "2.4505, 2.451, 2.4515, 2.452, 2.453, 2.454, 2.455, 2.456, 2.457, 2.458, and 2.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.451", "2.452", "2.4530000000000003", "2.454", "2.455", "2.456", "2.4570000000000003", "2.458", "2.459"], "p1_2_xs": ["2.4505000000000003", "2.4515000000000002"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}492}{7{,}700}, \\dfrac{4{,}537}{7{,}700}, \\dfrac{4{,}601}{7{,}700}, \\dfrac{4{,}883}{7{,}700}, \\dfrac{4{,}979}{7{,}700}, \\dfrac{5{,}187}{7{,}700}, \\dfrac{5{,}626}{7{,}700}, \\dfrac{5{,}710}{7{,}700}, \\dfrac{6{,}223}{7{,}700}, \\dfrac{6{,}366}{7{,}700}, \\dfrac{6{,}454}{7{,}700}, \\text{ and } \\dfrac{6{,}483}{7{,}700}", "__seed__": "0446"}}, {"seed": 447, "data": {"p1_how_many": "12", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{21{,}201}{35{,}000}, \\dfrac{21{,}919}{35{,}000}, \\dfrac{23{,}160}{35{,}000}, \\dfrac{23{,}939}{35{,}000}, \\dfrac{24{,}265}{35{,}000}, \\dfrac{25{,}519}{35{,}000}, \\text{ and } \\dfrac{27{,}088}{35{,}000}", "__seed__": "0447"}}, {"seed": 448, "data": {"p1_how_many": "10", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.02, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}702}{42{,}000}, \\dfrac{30{,}727}{42{,}000}, \\dfrac{31{,}440}{42{,}000}, \\dfrac{31{,}961}{42{,}000}, \\dfrac{32{,}003}{42{,}000}, \\dfrac{32{,}196}{42{,}000}, \\dfrac{32{,}214}{42{,}000}, \\dfrac{33{,}414}{42{,}000}, \\text{ and } \\dfrac{34{,}845}{42{,}000}", "__seed__": "0448"}}, {"seed": 449, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}213}{20{,}000}, \\dfrac{4{,}354}{20{,}000}, \\dfrac{4{,}439}{20{,}000}, \\dfrac{4{,}667}{20{,}000}, \\dfrac{4{,}721}{20{,}000}, \\dfrac{4{,}804}{20{,}000}, \\dfrac{4{,}836}{20{,}000}, \\dfrac{4{,}878}{20{,}000}, \\dfrac{4{,}886}{20{,}000}, \\text{ and } \\dfrac{4{,}967}{20{,}000}", "__seed__": "0449"}}, {"seed": 450, "data": {"p1_how_many": "14", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.545, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535", "7.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{200}, \\dfrac{58}{200}, \\dfrac{60}{200}, \\dfrac{63}{200}, \\dfrac{65}{200}, \\dfrac{72}{200}, \\dfrac{75}{200}, \\text{ and } \\dfrac{79}{200}", "__seed__": "0450"}}, {"seed": 451, "data": {"p1_how_many": "10", "p1_a": "9.93", "p1_b": "9.94", "p1_numbers": "9.9305, 9.931, 9.932, 9.933, 9.934, 9.935, 9.936, 9.937, 9.938, and 9.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.931", "9.932", "9.933", "9.934", "9.935", "9.936", "9.937", "9.937999999999999", "9.939"], "p1_2_xs": ["9.9305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}218}{2{,}000}, \\dfrac{1{,}226}{2{,}000}, \\dfrac{1{,}245}{2{,}000}, \\dfrac{1{,}274}{2{,}000}, \\dfrac{1{,}295}{2{,}000}, \\dfrac{1{,}303}{2{,}000}, \\dfrac{1{,}316}{2{,}000}, \\dfrac{1{,}321}{2{,}000}, \\dfrac{1{,}388}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\dfrac{1{,}434}{2{,}000}, \\text{ and } \\dfrac{1{,}446}{2{,}000}", "__seed__": "0451"}}, {"seed": 452, "data": {"p1_how_many": "10", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.02, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}807}{5{,}600}, \\dfrac{4{,}818}{5{,}600}, \\dfrac{4{,}819}{5{,}600}, \\dfrac{4{,}825}{5{,}600}, \\dfrac{4{,}839}{5{,}600}, \\dfrac{4{,}847}{5{,}600}, \\dfrac{4{,}855}{5{,}600}, \\dfrac{4{,}863}{5{,}600}, \\dfrac{4{,}880}{5{,}600}, \\text{ and } \\dfrac{4{,}887}{5{,}600}", "__seed__": "0452"}}, {"seed": 453, "data": {"p1_how_many": "11", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}375}{15{,}000}, \\dfrac{5{,}504}{15{,}000}, \\dfrac{5{,}545}{15{,}000}, \\dfrac{5{,}619}{15{,}000}, \\dfrac{5{,}758}{15{,}000}, \\dfrac{5{,}806}{15{,}000}, \\dfrac{5{,}846}{15{,}000}, \\dfrac{5{,}914}{15{,}000}, \\dfrac{5{,}975}{15{,}000}, \\text{ and } \\dfrac{5{,}992}{15{,}000}", "__seed__": "0453"}}, {"seed": 454, "data": {"p1_how_many": "11", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.005, 5.01, 5.015, 5.02, 5.03, 5.04, 5.05, 5.06, 5.07, 5.08, and 5.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005", "5.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}213}{35{,}000}, \\dfrac{15{,}311}{35{,}000}, \\dfrac{15{,}670}{35{,}000}, \\dfrac{16{,}424}{35{,}000}, \\dfrac{18{,}356}{35{,}000}, \\dfrac{18{,}360}{35{,}000}, \\dfrac{18{,}633}{35{,}000}, \\dfrac{19{,}073}{35{,}000}, \\text{ and } \\dfrac{19{,}718}{35{,}000}", "__seed__": "0454"}}, {"seed": 455, "data": {"p1_how_many": "11", "p1_a": "4.27", "p1_b": "4.28", "p1_numbers": "4.2705, 4.271, 4.2715, 4.272, 4.273, 4.274, 4.275, 4.276, 4.277, 4.278, and 4.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.271", "4.271999999999999", "4.273", "4.273999999999999", "4.2749999999999995", "4.276", "4.276999999999999", "4.278", "4.279"], "p1_2_xs": ["4.270499999999999", "4.2715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}154}{42{,}000}, \\dfrac{30{,}495}{42{,}000}, \\dfrac{30{,}523}{42{,}000}, \\dfrac{32{,}051}{42{,}000}, \\dfrac{33{,}036}{42{,}000}, \\dfrac{33{,}098}{42{,}000}, \\dfrac{33{,}318}{42{,}000}, \\dfrac{33{,}337}{42{,}000}, \\text{ and } \\dfrac{33{,}447}{42{,}000}", "__seed__": "0455"}}, {"seed": 456, "data": {"p1_how_many": "11", "p1_a": "8.77", "p1_b": "8.78", "p1_numbers": "8.7705, 8.771, 8.7715, 8.772, 8.773, 8.774, 8.775, 8.776, 8.777, 8.778, and 8.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.770999999999999", "8.772", "8.773", "8.774", "8.775", "8.776", "8.777", "8.777999999999999", "8.779"], "p1_2_xs": ["8.7705", "8.7715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}075}{42{,}000}, \\dfrac{7{,}579}{42{,}000}, \\dfrac{9{,}538}{42{,}000}, \\dfrac{9{,}646}{42{,}000}, \\dfrac{9{,}804}{42{,}000}, \\dfrac{10{,}397}{42{,}000}, \\dfrac{11{,}563}{42{,}000}, \\text{ and } \\dfrac{11{,}959}{42{,}000}", "__seed__": "0456"}}, {"seed": 457, "data": {"p1_how_many": "12", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.215, 4.22, 4.225, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205", "4.215", "4.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}086}{20{,}000}, \\dfrac{4{,}140}{20{,}000}, \\dfrac{4{,}247}{20{,}000}, \\dfrac{4{,}362}{20{,}000}, \\dfrac{4{,}655}{20{,}000}, \\dfrac{4{,}679}{20{,}000}, \\dfrac{4{,}966}{20{,}000}, \\dfrac{4{,}988}{20{,}000}, \\text{ and } \\dfrac{4{,}996}{20{,}000}", "__seed__": "0457"}}, {"seed": 458, "data": {"p1_how_many": "13", "p1_a": "9.67", "p1_b": "9.68", "p1_numbers": "9.6705, 9.671, 9.6715, 9.672, 9.6725, 9.673, 9.6735, 9.674, 9.675, 9.676, 9.677, 9.678, and 9.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.671", "9.672", "9.673", "9.674", "9.675", "9.676", "9.677", "9.677999999999999", "9.679"], "p1_2_xs": ["9.6705", "9.6715", "9.672500000000001", "9.6735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}369}{7{,}700}, \\dfrac{4{,}508}{7{,}700}, \\dfrac{4{,}644}{7{,}700}, \\dfrac{4{,}789}{7{,}700}, \\dfrac{4{,}895}{7{,}700}, \\dfrac{4{,}942}{7{,}700}, \\dfrac{5{,}472}{7{,}700}, \\text{ and } \\dfrac{5{,}487}{7{,}700}", "__seed__": "0458"}}, {"seed": 459, "data": {"p1_how_many": "14", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.345, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335", "5.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}471}{42{,}000}, \\dfrac{7{,}886}{42{,}000}, \\dfrac{8{,}262}{42{,}000}, \\dfrac{9{,}648}{42{,}000}, \\dfrac{10{,}353}{42{,}000}, \\dfrac{10{,}711}{42{,}000}, \\dfrac{10{,}833}{42{,}000}, \\text{ and } \\dfrac{11{,}609}{42{,}000}", "__seed__": "0459"}}, {"seed": 460, "data": {"p1_how_many": "11", "p1_a": "8.32", "p1_b": "8.33", "p1_numbers": "8.3205, 8.321, 8.3215, 8.322, 8.323, 8.324, 8.325, 8.326, 8.327, 8.328, and 8.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.321", "8.322000000000001", "8.323", "8.324", "8.325000000000001", "8.326", "8.327", "8.328", "8.329"], "p1_2_xs": ["8.320500000000001", "8.3215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}007}{3{,}500}, \\dfrac{2{,}052}{3{,}500}, \\dfrac{2{,}089}{3{,}500}, \\dfrac{2{,}144}{3{,}500}, \\dfrac{2{,}192}{3{,}500}, \\dfrac{2{,}204}{3{,}500}, \\dfrac{2{,}284}{3{,}500}, \\dfrac{2{,}320}{3{,}500}, \\dfrac{2{,}397}{3{,}500}, \\dfrac{2{,}487}{3{,}500}, \\dfrac{2{,}625}{3{,}500}, \\text{ and } \\dfrac{2{,}762}{3{,}500}", "__seed__": "0460"}}, {"seed": 461, "data": {"p1_how_many": "10", "p1_a": "3.56", "p1_b": "3.57", "p1_numbers": "3.5605, 3.561, 3.562, 3.563, 3.564, 3.565, 3.566, 3.567, 3.568, and 3.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.561", "3.562", "3.563", "3.564", "3.565", "3.566", "3.567", "3.568", "3.569"], "p1_2_xs": ["3.5605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}084}{63{,}000}, \\dfrac{14{,}368}{63{,}000}, \\dfrac{14{,}822}{63{,}000}, \\dfrac{15{,}111}{63{,}000}, \\dfrac{15{,}179}{63{,}000}, \\dfrac{15{,}400}{63{,}000}, \\dfrac{15{,}413}{63{,}000}, \\dfrac{15{,}819}{63{,}000}, \\dfrac{17{,}345}{63{,}000}, \\dfrac{17{,}655}{63{,}000}, \\text{ and } \\dfrac{17{,}818}{63{,}000}", "__seed__": "0461"}}, {"seed": 462, "data": {"p1_how_many": "14", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.145, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135", "4.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}052}{56{,}000}, \\dfrac{48{,}151}{56{,}000}, \\dfrac{48{,}328}{56{,}000}, \\dfrac{48{,}341}{56{,}000}, \\dfrac{48{,}486}{56{,}000}, \\dfrac{48{,}516}{56{,}000}, \\dfrac{48{,}598}{56{,}000}, \\dfrac{48{,}803}{56{,}000}, \\dfrac{48{,}904}{56{,}000}, \\text{ and } \\dfrac{48{,}906}{56{,}000}", "__seed__": "0462"}}, {"seed": 463, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}712}{6{,}300}, \\dfrac{2{,}713}{6{,}300}, \\dfrac{2{,}715}{6{,}300}, \\dfrac{2{,}725}{6{,}300}, \\dfrac{2{,}729}{6{,}300}, \\dfrac{2{,}754}{6{,}300}, \\dfrac{2{,}762}{6{,}300}, \\dfrac{2{,}770}{6{,}300}, \\dfrac{2{,}782}{6{,}300}, \\text{ and } \\dfrac{2{,}790}{6{,}300}", "__seed__": "0463"}}, {"seed": 464, "data": {"p1_how_many": "14", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.735, 6.74, 6.745, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725", "6.735", "6.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}402}{3{,}500}, \\dfrac{1{,}414}{3{,}500}, \\dfrac{1{,}436}{3{,}500}, \\dfrac{1{,}447}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}480}{3{,}500}, \\text{ and } \\dfrac{1{,}493}{3{,}500}", "__seed__": "0464"}}, {"seed": 465, "data": {"p1_how_many": "10", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.5005, 4.501, 4.502, 4.503, 4.504, 4.505, 4.506, 4.507, 4.508, and 4.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.501", "4.502", "4.503", "4.504", "4.505", "4.506", "4.507", "4.508", "4.509"], "p1_2_xs": ["4.5005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}167}{30{,}000}, \\dfrac{24{,}326}{30{,}000}, \\dfrac{24{,}363}{30{,}000}, \\dfrac{24{,}410}{30{,}000}, \\dfrac{24{,}417}{30{,}000}, \\dfrac{24{,}450}{30{,}000}, \\dfrac{24{,}547}{30{,}000}, \\dfrac{24{,}690}{30{,}000}, \\dfrac{24{,}860}{30{,}000}, \\dfrac{24{,}862}{30{,}000}, \\text{ and } \\dfrac{24{,}966}{30{,}000}", "__seed__": "0465"}}, {"seed": 466, "data": {"p1_how_many": "10", "p1_a": "3.14", "p1_b": "3.15", "p1_numbers": "3.1405, 3.141, 3.142, 3.143, 3.144, 3.145, 3.146, 3.147, 3.148, and 3.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.141", "3.142", "3.1430000000000002", "3.144", "3.145", "3.146", "3.1470000000000002", "3.148", "3.149"], "p1_2_xs": ["3.1405000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{43{,}510}{77{,}000}, \\dfrac{47{,}026}{77{,}000}, \\dfrac{47{,}537}{77{,}000}, \\dfrac{51{,}915}{77{,}000}, \\dfrac{51{,}917}{77{,}000}, \\dfrac{52{,}676}{77{,}000}, \\dfrac{53{,}168}{77{,}000}, \\dfrac{56{,}479}{77{,}000}, \\dfrac{56{,}820}{77{,}000}, \\dfrac{60{,}894}{77{,}000}, \\dfrac{61{,}024}{77{,}000}, \\text{ and } \\dfrac{63{,}989}{77{,}000}", "__seed__": "0466"}}, {"seed": 467, "data": {"p1_how_many": "13", "p1_a": "1.44", "p1_b": "1.45", "p1_numbers": "1.4405, 1.441, 1.4415, 1.442, 1.4425, 1.443, 1.4435, 1.444, 1.445, 1.446, 1.447, 1.448, and 1.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4409999999999998", "1.442", "1.4429999999999998", "1.444", "1.4449999999999998", "1.446", "1.4469999999999998", "1.448", "1.4489999999999998"], "p1_2_xs": ["1.4405", "1.4414999999999998", "1.4425", "1.4434999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{504}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{516}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{535}{1{,}500}, \\dfrac{539}{1{,}500}, \\dfrac{545}{1{,}500}, \\text{ and } \\dfrac{558}{1{,}500}", "__seed__": "0467"}}, {"seed": 468, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{74}{350}, \\dfrac{75}{350}, \\dfrac{76}{350}, \\dfrac{77}{350}, \\dfrac{78}{350}, \\dfrac{80}{350}, \\dfrac{86}{350}, \\dfrac{90}{350}, \\text{ and } \\dfrac{98}{350}", "__seed__": "0468"}}, {"seed": 469, "data": {"p1_how_many": "12", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{32}{120}, \\dfrac{33}{120}, \\dfrac{34}{120}, \\dfrac{35}{120}, \\dfrac{36}{120}, \\dfrac{37}{120}, \\dfrac{38}{120}, \\text{ and } \\dfrac{39}{120}", "__seed__": "0469"}}, {"seed": 470, "data": {"p1_how_many": "13", "p1_a": "7.45", "p1_b": "7.46", "p1_numbers": "7.4505, 7.451, 7.4515, 7.452, 7.4525, 7.453, 7.4535, 7.454, 7.455, 7.456, 7.457, 7.458, and 7.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.4510000000000005", "7.452", "7.453", "7.454", "7.455", "7.456", "7.457", "7.458", "7.4590000000000005"], "p1_2_xs": ["7.4505", "7.4515", "7.4525", "7.4535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}324}{35{,}000}, \\dfrac{7{,}569}{35{,}000}, \\dfrac{7{,}972}{35{,}000}, \\dfrac{7{,}985}{35{,}000}, \\dfrac{9{,}025}{35{,}000}, \\dfrac{9{,}360}{35{,}000}, \\dfrac{9{,}580}{35{,}000}, \\dfrac{9{,}671}{35{,}000}, \\text{ and } \\dfrac{9{,}989}{35{,}000}", "__seed__": "0470"}}, {"seed": 471, "data": {"p1_how_many": "12", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}140}{12{,}000}, \\dfrac{8{,}194}{12{,}000}, \\dfrac{8{,}307}{12{,}000}, \\dfrac{8{,}354}{12{,}000}, \\dfrac{8{,}684}{12{,}000}, \\dfrac{8{,}699}{12{,}000}, \\text{ and } \\dfrac{8{,}834}{12{,}000}", "__seed__": "0471"}}, {"seed": 472, "data": {"p1_how_many": "13", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.425, 5.43, 5.435, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415", "5.425", "5.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}610}{56{,}000}, \\dfrac{21{,}678}{56{,}000}, \\dfrac{22{,}078}{56{,}000}, \\dfrac{22{,}169}{56{,}000}, \\dfrac{22{,}617}{56{,}000}, \\dfrac{22{,}820}{56{,}000}, \\dfrac{23{,}102}{56{,}000}, \\text{ and } \\dfrac{23{,}619}{56{,}000}", "__seed__": "0472"}}, {"seed": 473, "data": {"p1_how_many": "14", "p1_a": "3.53", "p1_b": "3.54", "p1_numbers": "3.5305, 3.531, 3.5315, 3.532, 3.5325, 3.533, 3.5335, 3.534, 3.5345, 3.535, 3.536, 3.537, 3.538, and 3.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.5309999999999997", "3.5319999999999996", "3.533", "3.534", "3.5349999999999997", "3.5359999999999996", "3.537", "3.538", "3.5389999999999997"], "p1_2_xs": ["3.5305", "3.5315", "3.5324999999999998", "3.5335", "3.5345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}425}{3{,}500}, \\dfrac{1{,}431}{3{,}500}, \\dfrac{1{,}447}{3{,}500}, \\dfrac{1{,}454}{3{,}500}, \\dfrac{1{,}460}{3{,}500}, \\dfrac{1{,}480}{3{,}500}, \\text{ and } \\dfrac{1{,}485}{3{,}500}", "__seed__": "0473"}}, {"seed": 474, "data": {"p1_how_many": "12", "p1_a": "2.84", "p1_b": "2.85", "p1_numbers": "2.8405, 2.841, 2.8415, 2.842, 2.8425, 2.843, 2.844, 2.845, 2.846, 2.847, 2.848, and 2.849", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.8409999999999997", "2.8419999999999996", "2.843", "2.844", "2.8449999999999998", "2.8459999999999996", "2.847", "2.848", "2.8489999999999998"], "p1_2_xs": ["2.8405", "2.8415", "2.8425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{313}{1{,}200}, \\dfrac{341}{1{,}200}, \\dfrac{353}{1{,}200}, \\dfrac{363}{1{,}200}, \\dfrac{377}{1{,}200}, \\dfrac{393}{1{,}200}, \\text{ and } \\dfrac{397}{1{,}200}", "__seed__": "0474"}}, {"seed": 475, "data": {"p1_how_many": "14", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.745, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725", "7.735", "7.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}222}{42{,}000}, \\dfrac{35{,}229}{42{,}000}, \\dfrac{35{,}264}{42{,}000}, \\dfrac{35{,}296}{42{,}000}, \\dfrac{35{,}302}{42{,}000}, \\dfrac{35{,}536}{42{,}000}, \\dfrac{35{,}839}{42{,}000}, \\text{ and } \\dfrac{35{,}873}{42{,}000}", "__seed__": "0475"}}, {"seed": 476, "data": {"p1_how_many": "13", "p1_a": "6.82", "p1_b": "6.83", "p1_numbers": "6.8205, 6.821, 6.8215, 6.822, 6.8225, 6.823, 6.8235, 6.824, 6.825, 6.826, 6.827, 6.828, and 6.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.821000000000001", "6.822", "6.823", "6.824", "6.825", "6.8260000000000005", "6.827", "6.828", "6.829000000000001"], "p1_2_xs": ["6.8205", "6.8215", "6.8225", "6.8235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}317}{56{,}000}, \\dfrac{35{,}387}{56{,}000}, \\dfrac{36{,}302}{56{,}000}, \\dfrac{36{,}466}{56{,}000}, \\dfrac{36{,}516}{56{,}000}, \\dfrac{37{,}080}{56{,}000}, \\dfrac{37{,}307}{56{,}000}, \\dfrac{38{,}020}{56{,}000}, \\dfrac{39{,}479}{56{,}000}, \\text{ and } \\dfrac{39{,}757}{56{,}000}", "__seed__": "0476"}}, {"seed": 477, "data": {"p1_how_many": "10", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}179}{15{,}000}, \\dfrac{6{,}256}{15{,}000}, \\dfrac{6{,}364}{15{,}000}, \\dfrac{6{,}393}{15{,}000}, \\dfrac{7{,}082}{15{,}000}, \\dfrac{8{,}386}{15{,}000}, \\dfrac{8{,}776}{15{,}000}, \\dfrac{8{,}823}{15{,}000}, \\dfrac{9{,}324}{15{,}000}, \\text{ and } \\dfrac{9{,}718}{15{,}000}", "__seed__": "0477"}}, {"seed": 478, "data": {"p1_how_many": "14", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.345, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335", "6.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0478"}}, {"seed": 479, "data": {"p1_how_many": "13", "p1_a": "2.43", "p1_b": "2.44", "p1_numbers": "2.4305, 2.431, 2.4315, 2.432, 2.4325, 2.433, 2.4335, 2.434, 2.435, 2.436, 2.437, 2.438, and 2.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.431", "2.432", "2.4330000000000003", "2.434", "2.435", "2.436", "2.4370000000000003", "2.438", "2.439"], "p1_2_xs": ["2.4305000000000003", "2.4315", "2.4325", "2.4335000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{548}{1{,}500}, \\dfrac{558}{1{,}500}, \\dfrac{560}{1{,}500}, \\dfrac{570}{1{,}500}, \\dfrac{579}{1{,}500}, \\text{ and } \\dfrac{595}{1{,}500}", "__seed__": "0479"}}, {"seed": 480, "data": {"p1_how_many": "11", "p1_a": "5.35", "p1_b": "5.36", "p1_numbers": "5.3505, 5.351, 5.3515, 5.352, 5.353, 5.354, 5.355, 5.356, 5.357, 5.358, and 5.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.351", "5.351999999999999", "5.353", "5.353999999999999", "5.3549999999999995", "5.356", "5.356999999999999", "5.358", "5.359"], "p1_2_xs": ["5.350499999999999", "5.3515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{13{,}029}{20{,}000}, \\dfrac{13{,}118}{20{,}000}, \\dfrac{13{,}157}{20{,}000}, \\dfrac{13{,}528}{20{,}000}, \\dfrac{13{,}713}{20{,}000}, \\dfrac{13{,}739}{20{,}000}, \\dfrac{13{,}941}{20{,}000}, \\dfrac{13{,}990}{20{,}000}, \\dfrac{14{,}236}{20{,}000}, \\dfrac{14{,}459}{20{,}000}, \\text{ and } \\dfrac{14{,}849}{20{,}000}", "__seed__": "0480"}}, {"seed": 481, "data": {"p1_how_many": "14", "p1_a": "5.36", "p1_b": "5.37", "p1_numbers": "5.3605, 5.361, 5.3615, 5.362, 5.3625, 5.363, 5.3635, 5.364, 5.3645, 5.365, 5.366, 5.367, 5.368, and 5.369", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.361000000000001", "5.362", "5.363", "5.364", "5.365", "5.3660000000000005", "5.367", "5.368", "5.369000000000001"], "p1_2_xs": ["5.3605", "5.3615", "5.3625", "5.3635", "5.3645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}326}{42{,}000}, \\dfrac{30{,}355}{42{,}000}, \\dfrac{30{,}685}{42{,}000}, \\dfrac{31{,}074}{42{,}000}, \\dfrac{32{,}090}{42{,}000}, \\dfrac{32{,}407}{42{,}000}, \\dfrac{32{,}708}{42{,}000}, \\dfrac{33{,}254}{42{,}000}, \\dfrac{34{,}082}{42{,}000}, \\dfrac{34{,}113}{42{,}000}, \\text{ and } \\dfrac{34{,}956}{42{,}000}", "__seed__": "0481"}}, {"seed": 482, "data": {"p1_how_many": "13", "p1_a": "6.73", "p1_b": "6.74", "p1_numbers": "6.7305, 6.731, 6.7315, 6.732, 6.7325, 6.733, 6.7335, 6.734, 6.735, 6.736, 6.737, 6.738, and 6.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.731000000000001", "6.732", "6.7330000000000005", "6.734", "6.735", "6.736000000000001", "6.737", "6.738", "6.739000000000001"], "p1_2_xs": ["6.7305", "6.7315000000000005", "6.7325", "6.7335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{728}{4{,}200}, \\dfrac{858}{4{,}200}, \\dfrac{879}{4{,}200}, \\dfrac{932}{4{,}200}, \\dfrac{952}{4{,}200}, \\dfrac{963}{4{,}200}, \\dfrac{1{,}034}{4{,}200}, \\dfrac{1{,}058}{4{,}200}, \\dfrac{1{,}073}{4{,}200}, \\dfrac{1{,}087}{4{,}200}, \\text{ and } \\dfrac{1{,}092}{4{,}200}", "__seed__": "0482"}}, {"seed": 483, "data": {"p1_how_many": "10", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}043}{35{,}000}, \\dfrac{14{,}325}{35{,}000}, \\dfrac{14{,}355}{35{,}000}, \\dfrac{14{,}365}{35{,}000}, \\dfrac{14{,}385}{35{,}000}, \\dfrac{14{,}489}{35{,}000}, \\dfrac{14{,}554}{35{,}000}, \\dfrac{14{,}560}{35{,}000}, \\dfrac{14{,}602}{35{,}000}, \\dfrac{14{,}788}{35{,}000}, \\dfrac{14{,}819}{35{,}000}, \\text{ and } \\dfrac{14{,}822}{35{,}000}", "__seed__": "0483"}}, {"seed": 484, "data": {"p1_how_many": "10", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.005, 5.01, 5.02, 5.03, 5.04, 5.05, 5.06, 5.07, 5.08, and 5.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{271}{630}, \\dfrac{272}{630}, \\dfrac{273}{630}, \\dfrac{274}{630}, \\dfrac{275}{630}, \\dfrac{276}{630}, \\dfrac{277}{630}, \\text{ and } \\dfrac{278}{630}", "__seed__": "0484"}}, {"seed": 485, "data": {"p1_how_many": "12", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}477}{15{,}000}, \\dfrac{6{,}872}{15{,}000}, \\dfrac{7{,}019}{15{,}000}, \\dfrac{7{,}394}{15{,}000}, \\dfrac{7{,}671}{15{,}000}, \\dfrac{8{,}494}{15{,}000}, \\dfrac{8{,}742}{15{,}000}, \\dfrac{8{,}749}{15{,}000}, \\dfrac{8{,}822}{15{,}000}, \\dfrac{9{,}018}{15{,}000}, \\dfrac{9{,}422}{15{,}000}, \\text{ and } \\dfrac{9{,}983}{15{,}000}", "__seed__": "0485"}}, {"seed": 486, "data": {"p1_how_many": "10", "p1_a": "2.2", "p1_b": "2.3", "p1_numbers": "2.205, 2.21, 2.22, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, and 2.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.21", "2.22", "2.23", "2.24", "2.25", "2.2600000000000002", "2.27", "2.2800000000000002", "2.29"], "p1_2_xs": ["2.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}073}{63{,}000}, \\dfrac{14{,}114}{63{,}000}, \\dfrac{14{,}628}{63{,}000}, \\dfrac{15{,}070}{63{,}000}, \\dfrac{15{,}936}{63{,}000}, \\dfrac{16{,}095}{63{,}000}, \\dfrac{17{,}308}{63{,}000}, \\text{ and } \\dfrac{17{,}958}{63{,}000}", "__seed__": "0486"}}, {"seed": 487, "data": {"p1_how_many": "14", "p1_a": "1.91", "p1_b": "1.92", "p1_numbers": "1.9105, 1.911, 1.9115, 1.912, 1.9125, 1.913, 1.9135, 1.914, 1.9145, 1.915, 1.916, 1.917, 1.918, and 1.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9109999999999998", "1.912", "1.9129999999999998", "1.914", "1.9149999999999998", "1.916", "1.9169999999999998", "1.918", "1.9189999999999998"], "p1_2_xs": ["1.9104999999999999", "1.9114999999999998", "1.9124999999999999", "1.9134999999999998", "1.9144999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}115}{3{,}500}, \\dfrac{2{,}311}{3{,}500}, \\dfrac{2{,}489}{3{,}500}, \\dfrac{2{,}508}{3{,}500}, \\dfrac{2{,}518}{3{,}500}, \\dfrac{2{,}548}{3{,}500}, \\text{ and } \\dfrac{2{,}656}{3{,}500}", "__seed__": "0487"}}, {"seed": 488, "data": {"p1_how_many": "10", "p1_a": "9.74", "p1_b": "9.75", "p1_numbers": "9.7405, 9.741, 9.742, 9.743, 9.744, 9.745, 9.746, 9.747, 9.748, and 9.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.741", "9.742", "9.743", "9.744", "9.745000000000001", "9.746", "9.747", "9.748", "9.749"], "p1_2_xs": ["9.7405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}253}{7{,}700}, \\dfrac{4{,}311}{7{,}700}, \\dfrac{4{,}405}{7{,}700}, \\dfrac{4{,}414}{7{,}700}, \\dfrac{4{,}506}{7{,}700}, \\dfrac{4{,}735}{7{,}700}, \\dfrac{4{,}878}{7{,}700}, \\dfrac{5{,}116}{7{,}700}, \\dfrac{5{,}198}{7{,}700}, \\dfrac{5{,}224}{7{,}700}, \\text{ and } \\dfrac{5{,}284}{7{,}700}", "__seed__": "0488"}}, {"seed": 489, "data": {"p1_how_many": "13", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}626}{5{,}600}, \\dfrac{1{,}658}{5{,}600}, \\dfrac{1{,}712}{5{,}600}, \\dfrac{1{,}745}{5{,}600}, \\dfrac{1{,}798}{5{,}600}, \\dfrac{1{,}843}{5{,}600}, \\dfrac{1{,}933}{5{,}600}, \\dfrac{1{,}940}{5{,}600}, \\text{ and } \\dfrac{1{,}963}{5{,}600}", "__seed__": "0489"}}, {"seed": 490, "data": {"p1_how_many": "10", "p1_a": "2.55", "p1_b": "2.56", "p1_numbers": "2.5505, 2.551, 2.552, 2.553, 2.554, 2.555, 2.556, 2.557, 2.558, and 2.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5509999999999997", "2.5519999999999996", "2.553", "2.554", "2.5549999999999997", "2.5559999999999996", "2.557", "2.558", "2.5589999999999997"], "p1_2_xs": ["2.5505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}314}{20{,}000}, \\dfrac{5{,}501}{20{,}000}, \\dfrac{5{,}594}{20{,}000}, \\dfrac{5{,}642}{20{,}000}, \\dfrac{6{,}227}{20{,}000}, \\dfrac{6{,}604}{20{,}000}, \\dfrac{6{,}660}{20{,}000}, \\dfrac{7{,}183}{20{,}000}, \\dfrac{7{,}641}{20{,}000}, \\text{ and } \\dfrac{7{,}937}{20{,}000}", "__seed__": "0490"}}, {"seed": 491, "data": {"p1_how_many": "12", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}193}{35{,}000}, \\dfrac{14{,}255}{35{,}000}, \\dfrac{14{,}262}{35{,}000}, \\dfrac{14{,}650}{35{,}000}, \\dfrac{14{,}701}{35{,}000}, \\dfrac{14{,}742}{35{,}000}, \\dfrac{14{,}753}{35{,}000}, \\dfrac{14{,}795}{35{,}000}, \\dfrac{14{,}806}{35{,}000}, \\dfrac{14{,}976}{35{,}000}, \\text{ and } \\dfrac{14{,}979}{35{,}000}", "__seed__": "0491"}}, {"seed": 492, "data": {"p1_how_many": "11", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.015, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005", "8.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{7{,}028}{56{,}000}, \\dfrac{7{,}112}{56{,}000}, \\dfrac{7{,}164}{56{,}000}, \\dfrac{7{,}207}{56{,}000}, \\dfrac{7{,}224}{56{,}000}, \\dfrac{7{,}330}{56{,}000}, \\dfrac{7{,}402}{56{,}000}, \\dfrac{7{,}403}{56{,}000}, \\dfrac{7{,}460}{56{,}000}, \\dfrac{7{,}821}{56{,}000}, \\dfrac{7{,}937}{56{,}000}, \\text{ and } \\dfrac{7{,}951}{56{,}000}", "__seed__": "0492"}}, {"seed": 493, "data": {"p1_how_many": "12", "p1_a": "2.76", "p1_b": "2.77", "p1_numbers": "2.7605, 2.761, 2.7615, 2.762, 2.7625, 2.763, 2.764, 2.765, 2.766, 2.767, 2.768, and 2.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.7609999999999997", "2.7619999999999996", "2.763", "2.764", "2.7649999999999997", "2.7659999999999996", "2.767", "2.768", "2.7689999999999997"], "p1_2_xs": ["2.7605", "2.7615", "2.7624999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{435}{770}, \\dfrac{453}{770}, \\dfrac{463}{770}, \\dfrac{464}{770}, \\dfrac{476}{770}, \\dfrac{493}{770}, \\dfrac{498}{770}, \\dfrac{508}{770}, \\text{ and } \\dfrac{529}{770}", "__seed__": "0493"}}, {"seed": 494, "data": {"p1_how_many": "12", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{302}{1{,}200}, \\dfrac{310}{1{,}200}, \\dfrac{324}{1{,}200}, \\dfrac{325}{1{,}200}, \\dfrac{326}{1{,}200}, \\dfrac{329}{1{,}200}, \\dfrac{333}{1{,}200}, \\dfrac{334}{1{,}200}, \\dfrac{364}{1{,}200}, \\dfrac{374}{1{,}200}, \\dfrac{381}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0494"}}, {"seed": 495, "data": {"p1_how_many": "10", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": 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\\dfrac{1{,}496}{3{,}500}", "__seed__": "0497"}}, {"seed": 498, "data": {"p1_how_many": "13", "p1_a": "2.05", "p1_b": "2.06", "p1_numbers": "2.0505, 2.051, 2.0515, 2.052, 2.0525, 2.053, 2.0535, 2.054, 2.055, 2.056, 2.057, 2.058, and 2.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.0509999999999997", "2.0519999999999996", "2.053", "2.054", "2.0549999999999997", "2.0559999999999996", "2.057", "2.058", "2.0589999999999997"], "p1_2_xs": ["2.0505", "2.0515", "2.0524999999999998", "2.0535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}097}{30{,}000}, \\dfrac{5{,}220}{30{,}000}, \\dfrac{5{,}465}{30{,}000}, \\dfrac{5{,}515}{30{,}000}, \\dfrac{5{,}540}{30{,}000}, \\dfrac{5{,}666}{30{,}000}, \\dfrac{5{,}742}{30{,}000}, \\dfrac{5{,}773}{30{,}000}, \\text{ and } \\dfrac{5{,}975}{30{,}000}", "__seed__": 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"9.852500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}074}{20{,}000}, \\dfrac{5{,}192}{20{,}000}, \\dfrac{6{,}026}{20{,}000}, \\dfrac{6{,}069}{20{,}000}, \\dfrac{6{,}591}{20{,}000}, \\dfrac{6{,}860}{20{,}000}, \\dfrac{6{,}963}{20{,}000}, \\dfrac{7{,}217}{20{,}000}, \\text{ and } \\dfrac{7{,}804}{20{,}000}", "__seed__": "0502"}}, {"seed": 503, "data": {"p1_how_many": "13", "p1_a": "6.92", "p1_b": "6.93", "p1_numbers": "6.9205, 6.921, 6.9215, 6.922, 6.9225, 6.923, 6.9235, 6.924, 6.925, 6.926, 6.927, 6.928, and 6.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.921", "6.922", "6.923", "6.9239999999999995", "6.925", "6.926", "6.927", "6.928", "6.929"], "p1_2_xs": ["6.9205", "6.9215", "6.922499999999999", "6.9235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}358}{35{,}000}, \\dfrac{21{,}296}{35{,}000}, \\dfrac{23{,}012}{35{,}000}, \\dfrac{23{,}520}{35{,}000}, \\dfrac{24{,}047}{35{,}000}, \\dfrac{24{,}520}{35{,}000}, \\dfrac{24{,}751}{35{,}000}, \\dfrac{25{,}984}{35{,}000}, \\text{ and } \\dfrac{26{,}908}{35{,}000}", "__seed__": "0503"}}, {"seed": 504, "data": {"p1_how_many": "12", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}182}{20{,}000}, \\dfrac{4{,}268}{20{,}000}, \\dfrac{4{,}532}{20{,}000}, \\dfrac{4{,}802}{20{,}000}, \\dfrac{4{,}917}{20{,}000}, \\dfrac{4{,}920}{20{,}000}, \\dfrac{4{,}960}{20{,}000}, \\text{ and } \\dfrac{4{,}966}{20{,}000}", "__seed__": "0504"}}, {"seed": 505, "data": {"p1_how_many": "10", "p1_a": "3.26", "p1_b": "3.27", "p1_numbers": "3.2605, 3.261, 3.262, 3.263, 3.264, 3.265, 3.266, 3.267, 3.268, and 3.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.2609999999999997", "3.2619999999999996", "3.263", "3.264", "3.2649999999999997", "3.2659999999999996", "3.267", "3.268", "3.2689999999999997"], "p1_2_xs": ["3.2605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}216}{2{,}000}, \\dfrac{1{,}229}{2{,}000}, \\dfrac{1{,}323}{2{,}000}, \\dfrac{1{,}344}{2{,}000}, \\dfrac{1{,}362}{2{,}000}, \\dfrac{1{,}364}{2{,}000}, \\text{ and } \\dfrac{1{,}399}{2{,}000}", "__seed__": "0505"}}, {"seed": 506, "data": {"p1_how_many": "14", "p1_a": "9.9", "p1_b": "9.1", "p1_numbers": "9.9005, 9.901, 9.9015, 9.902, 9.9025, 9.903, 9.9035, 9.904, 9.9045, 9.905, 9.906, 9.907, 9.908, and 9.909", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.901", "9.902000000000001", "9.903", "9.904", "9.905000000000001", "9.906", "9.907", "9.908", "9.909"], "p1_2_xs": ["9.900500000000001", "9.9015", "9.902500000000002", "9.903500000000001", "9.9045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}160}{35{,}000}, \\dfrac{20{,}204}{35{,}000}, \\dfrac{20{,}247}{35{,}000}, \\dfrac{20{,}511}{35{,}000}, \\dfrac{20{,}517}{35{,}000}, \\dfrac{20{,}560}{35{,}000}, \\dfrac{20{,}683}{35{,}000}, \\dfrac{20{,}721}{35{,}000}, \\dfrac{20{,}789}{35{,}000}, \\dfrac{20{,}840}{35{,}000}, \\text{ and } \\dfrac{20{,}926}{35{,}000}", "__seed__": "0506"}}, {"seed": 507, "data": {"p1_how_many": "14", "p1_a": "6.4", "p1_b": "6.5", "p1_numbers": "6.405, 6.41, 6.415, 6.42, 6.425, 6.43, 6.435, 6.44, 6.445, 6.45, 6.46, 6.47, 6.48, and 6.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.41", "6.42", "6.430000000000001", "6.44", "6.45", "6.46", "6.470000000000001", "6.48", "6.49"], "p1_2_xs": ["6.405", "6.415", "6.425", "6.4350000000000005", "6.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}895}{56{,}000}, \\dfrac{35{,}908}{56{,}000}, \\dfrac{36{,}003}{56{,}000}, \\dfrac{37{,}767}{56{,}000}, \\dfrac{38{,}131}{56{,}000}, \\dfrac{38{,}258}{56{,}000}, \\dfrac{39{,}354}{56{,}000}, \\text{ and } \\dfrac{39{,}953}{56{,}000}", "__seed__": 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"p1_numbers": "6.6405, 6.641, 6.6415, 6.642, 6.643, 6.644, 6.645, 6.646, 6.647, 6.648, and 6.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.641", "6.6419999999999995", "6.643", "6.643999999999999", "6.645", "6.646", "6.646999999999999", "6.648", "6.649"], "p1_2_xs": ["6.640499999999999", "6.6415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}495}{63{,}000}, \\dfrac{28{,}759}{63{,}000}, \\dfrac{29{,}127}{63{,}000}, \\dfrac{29{,}288}{63{,}000}, \\dfrac{30{,}829}{63{,}000}, \\dfrac{30{,}844}{63{,}000}, \\dfrac{31{,}710}{63{,}000}, \\dfrac{32{,}323}{63{,}000}, \\dfrac{32{,}370}{63{,}000}, \\text{ and } \\dfrac{35{,}606}{63{,}000}", "__seed__": "0510"}}, {"seed": 511, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}042}{15{,}000}, \\dfrac{5{,}056}{15{,}000}, \\dfrac{5{,}127}{15{,}000}, \\dfrac{5{,}190}{15{,}000}, \\dfrac{5{,}303}{15{,}000}, \\dfrac{5{,}375}{15{,}000}, \\dfrac{5{,}461}{15{,}000}, \\dfrac{5{,}692}{15{,}000}, \\dfrac{5{,}744}{15{,}000}, \\dfrac{5{,}938}{15{,}000}, \\text{ and } \\dfrac{5{,}972}{15{,}000}", "__seed__": "0511"}}, {"seed": 512, "data": {"p1_how_many": "10", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{702}{3{,}500}, \\dfrac{776}{3{,}500}, \\dfrac{825}{3{,}500}, \\dfrac{836}{3{,}500}, \\dfrac{844}{3{,}500}, \\dfrac{883}{3{,}500}, \\dfrac{888}{3{,}500}, \\dfrac{946}{3{,}500}, \\dfrac{959}{3{,}500}, \\dfrac{977}{3{,}500}, \\dfrac{994}{3{,}500}, \\text{ and } \\dfrac{995}{3{,}500}", "__seed__": "0512"}}, {"seed": 513, "data": {"p1_how_many": "12", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.015, 8.02, 8.025, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005", "8.015", "8.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}066}{63{,}000}, \\dfrac{9{,}714}{63{,}000}, \\dfrac{9{,}778}{63{,}000}, \\dfrac{10{,}756}{63{,}000}, \\dfrac{10{,}903}{63{,}000}, \\dfrac{11{,}302}{63{,}000}, \\dfrac{11{,}761}{63{,}000}, \\dfrac{11{,}789}{63{,}000}, \\dfrac{12{,}801}{63{,}000}, \\text{ and } \\dfrac{13{,}006}{63{,}000}", "__seed__": "0513"}}, {"seed": 514, "data": {"p1_how_many": "14", "p1_a": "5.05", "p1_b": "5.06", "p1_numbers": "5.0505, 5.051, 5.0515, 5.052, 5.0525, 5.053, 5.0535, 5.054, 5.0545, 5.055, 5.056, 5.057, 5.058, and 5.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.051", "5.052", "5.053", "5.053999999999999", "5.055", "5.056", "5.0569999999999995", "5.058", "5.059"], "p1_2_xs": ["5.0504999999999995", "5.0515", "5.052499999999999", "5.0535", "5.054499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}513}{35{,}000}, \\dfrac{11{,}498}{35{,}000}, \\dfrac{12{,}794}{35{,}000}, \\dfrac{12{,}948}{35{,}000}, \\dfrac{13{,}680}{35{,}000}, \\dfrac{13{,}868}{35{,}000}, \\dfrac{13{,}886}{35{,}000}, \\text{ and } \\dfrac{13{,}904}{35{,}000}", "__seed__": "0514"}}, {"seed": 515, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{714}{3{,}500}, \\dfrac{734}{3{,}500}, 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4.361, 4.3615, 4.362, 4.3625, 4.363, 4.3635, 4.364, 4.3645, 4.365, 4.366, 4.367, 4.368, and 4.369", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.361000000000001", "4.362", "4.363", "4.364", "4.365", "4.3660000000000005", "4.367", "4.368", "4.369000000000001"], "p1_2_xs": ["4.3605", "4.3615", "4.3625", "4.3635", "4.3645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}073}{42{,}000}, \\dfrac{7{,}106}{42{,}000}, \\dfrac{7{,}314}{42{,}000}, \\dfrac{7{,}600}{42{,}000}, \\dfrac{8{,}041}{42{,}000}, \\dfrac{9{,}025}{42{,}000}, \\text{ and } \\dfrac{10{,}614}{42{,}000}", "__seed__": "0517"}}, {"seed": 518, "data": {"p1_how_many": "13", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}337}{77{,}000}, \\dfrac{42{,}634}{77{,}000}, \\dfrac{43{,}292}{77{,}000}, \\dfrac{45{,}663}{77{,}000}, \\dfrac{48{,}115}{77{,}000}, \\dfrac{49{,}453}{77{,}000}, \\dfrac{49{,}740}{77{,}000}, \\dfrac{50{,}224}{77{,}000}, \\text{ and } \\dfrac{51{,}358}{77{,}000}", "__seed__": "0518"}}, {"seed": 519, "data": {"p1_how_many": "11", "p1_a": "4.97", "p1_b": "4.98", "p1_numbers": "4.9705, 4.971, 4.9715, 4.972, 4.973, 4.974, 4.975, 4.976, 4.977, 4.978, and 4.979", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.971", "4.9719999999999995", "4.973", "4.973999999999999", "4.975", "4.976", "4.976999999999999", "4.978", "4.979"], "p1_2_xs": ["4.9704999999999995", "4.9715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\text{ and } \\dfrac{158}{200}", "__seed__": "0519"}}, {"seed": 520, "data": {"p1_how_many": "14", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.345, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335", "6.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{740}{3{,}500}, \\dfrac{755}{3{,}500}, \\dfrac{786}{3{,}500}, \\dfrac{830}{3{,}500}, \\dfrac{839}{3{,}500}, \\dfrac{861}{3{,}500}, \\dfrac{909}{3{,}500}, \\dfrac{938}{3{,}500}, \\dfrac{964}{3{,}500}, \\dfrac{976}{3{,}500}, \\dfrac{988}{3{,}500}, \\text{ and } \\dfrac{990}{3{,}500}", "__seed__": "0520"}}, {"seed": 521, "data": {"p1_how_many": "10", "p1_a": "1.77", "p1_b": "1.78", "p1_numbers": "1.7705, 1.771, 1.772, 1.773, 1.774, 1.775, 1.776, 1.777, 1.778, and 1.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.771", "1.772", "1.773", "1.774", "1.775", "1.776", "1.777", "1.778", "1.779"], "p1_2_xs": ["1.7705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}020}{20{,}000}, \\dfrac{4{,}099}{20{,}000}, \\dfrac{4{,}195}{20{,}000}, \\dfrac{4{,}200}{20{,}000}, \\dfrac{4{,}319}{20{,}000}, \\dfrac{4{,}430}{20{,}000}, \\dfrac{4{,}535}{20{,}000}, \\dfrac{4{,}673}{20{,}000}, \\dfrac{4{,}760}{20{,}000}, \\text{ and } \\dfrac{4{,}868}{20{,}000}", "__seed__": "0521"}}, {"seed": 522, "data": {"p1_how_many": "10", "p1_a": "9.33", "p1_b": "9.34", "p1_numbers": "9.3305, 9.331, 9.332, 9.333, 9.334, 9.335, 9.336, 9.337, 9.338, and 9.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.331", "9.332", "9.333", "9.334", "9.335", "9.336", "9.337", "9.338", "9.339"], "p1_2_xs": ["9.3305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}501}{2{,}000}, \\dfrac{1{,}503}{2{,}000}, \\dfrac{1{,}505}{2{,}000}, \\dfrac{1{,}511}{2{,}000}, \\dfrac{1{,}526}{2{,}000}, \\dfrac{1{,}539}{2{,}000}, \\dfrac{1{,}540}{2{,}000}, \\dfrac{1{,}561}{2{,}000}, \\dfrac{1{,}567}{2{,}000}, \\text{ and } \\dfrac{1{,}585}{2{,}000}", "__seed__": "0522"}}, {"seed": 523, "data": {"p1_how_many": "13", "p1_a": "7.45", "p1_b": "7.46", "p1_numbers": "7.4505, 7.451, 7.4515, 7.452, 7.4525, 7.453, 7.4535, 7.454, 7.455, 7.456, 7.457, 7.458, and 7.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.4510000000000005", "7.452", "7.453", "7.454", "7.455", "7.456", "7.457", "7.458", "7.4590000000000005"], "p1_2_xs": ["7.4505", "7.4515", "7.4525", "7.4535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{634}{1{,}500}, \\dfrac{645}{1{,}500}, \\dfrac{755}{1{,}500}, \\dfrac{783}{1{,}500}, \\dfrac{808}{1{,}500}, \\dfrac{814}{1{,}500}, \\dfrac{874}{1{,}500}, \\dfrac{883}{1{,}500}, \\dfrac{900}{1{,}500}, \\text{ and } \\dfrac{996}{1{,}500}", "__seed__": "0523"}}, {"seed": 524, "data": {"p1_how_many": "14", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.125, 5.13, 5.135, 5.14, 5.145, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999", "5.124999999999999", "5.135", "5.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}624}{35{,}000}, \\dfrac{22{,}395}{35{,}000}, \\dfrac{23{,}911}{35{,}000}, \\dfrac{24{,}077}{35{,}000}, \\dfrac{24{,}083}{35{,}000}, \\dfrac{24{,}575}{35{,}000}, \\dfrac{25{,}738}{35{,}000}, \\dfrac{25{,}980}{35{,}000}, \\dfrac{26{,}870}{35{,}000}, \\dfrac{27{,}664}{35{,}000}, \\text{ and } \\dfrac{27{,}796}{35{,}000}", "__seed__": "0524"}}, {"seed": 525, "data": {"p1_how_many": "14", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.035, 7.04, 7.045, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995", "7.035", "7.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}088}{42{,}000}, \\dfrac{6{,}117}{42{,}000}, \\dfrac{6{,}140}{42{,}000}, \\dfrac{6{,}234}{42{,}000}, \\dfrac{6{,}282}{42{,}000}, \\dfrac{6{,}399}{42{,}000}, \\dfrac{6{,}507}{42{,}000}, \\dfrac{6{,}852}{42{,}000}, \\dfrac{6{,}907}{42{,}000}, 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"p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.770999999999999", "9.772", "9.773", "9.774", "9.775", "9.776", "9.777", "9.777999999999999", "9.779"], "p1_2_xs": ["9.7705", "9.7715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}917}{6{,}300}, \\dfrac{2{,}934}{6{,}300}, \\dfrac{2{,}966}{6{,}300}, \\dfrac{3{,}085}{6{,}300}, \\dfrac{3{,}104}{6{,}300}, \\dfrac{3{,}124}{6{,}300}, \\dfrac{3{,}380}{6{,}300}, \\dfrac{3{,}406}{6{,}300}, \\dfrac{3{,}415}{6{,}300}, \\dfrac{3{,}419}{6{,}300}, \\dfrac{3{,}488}{6{,}300}, \\text{ and } \\dfrac{3{,}543}{6{,}300}", "__seed__": "0527"}}, {"seed": 528, "data": {"p1_how_many": "10", "p1_a": "6.01", "p1_b": "6.02", "p1_numbers": "6.0105, 6.011, 6.012, 6.013, 6.014, 6.015, 6.016, 6.017, 6.018, and 6.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.011", "6.012", "6.013", "6.013999999999999", "6.015", "6.016", "6.0169999999999995", "6.018", "6.019"], "p1_2_xs": ["6.0104999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}514}{15{,}000}, \\dfrac{7{,}210}{15{,}000}, \\dfrac{7{,}414}{15{,}000}, \\dfrac{7{,}573}{15{,}000}, \\dfrac{8{,}206}{15{,}000}, \\dfrac{8{,}311}{15{,}000}, \\dfrac{8{,}508}{15{,}000}, \\dfrac{8{,}877}{15{,}000}, \\dfrac{9{,}115}{15{,}000}, \\text{ and } \\dfrac{9{,}194}{15{,}000}", "__seed__": "0528"}}, {"seed": 529, "data": {"p1_how_many": "12", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{67}{150}, \\dfrac{69}{150}, \\dfrac{72}{150}, \\dfrac{75}{150}, \\dfrac{76}{150}, \\dfrac{84}{150}, \\dfrac{89}{150}, \\dfrac{91}{150}, \\text{ and } \\dfrac{95}{150}", "__seed__": "0529"}}, {"seed": 530, "data": {"p1_how_many": "14", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.545, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535", "9.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}582}{20{,}000}, \\dfrac{5{,}645}{20{,}000}, \\dfrac{5{,}680}{20{,}000}, \\dfrac{6{,}034}{20{,}000}, \\dfrac{6{,}074}{20{,}000}, \\dfrac{7{,}102}{20{,}000}, \\dfrac{7{,}334}{20{,}000}, \\text{ and } \\dfrac{7{,}458}{20{,}000}", "__seed__": "0530"}}, {"seed": 531, "data": {"p1_how_many": "12", "p1_a": "1.47", "p1_b": "1.48", "p1_numbers": "1.4705, 1.471, 1.4715, 1.472, 1.4725, 1.473, 1.474, 1.475, 1.476, 1.477, 1.478, and 1.479", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4709999999999999", "1.472", "1.4729999999999999", "1.474", "1.4749999999999999", "1.476", "1.4769999999999999", "1.478", "1.4789999999999999"], "p1_2_xs": ["1.4705", "1.4714999999999998", "1.4725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}279}{35{,}000}, 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\\dfrac{113}{350}, \\dfrac{115}{350}, \\dfrac{137}{350}, \\text{ and } \\dfrac{138}{350}", "__seed__": "0532"}}, {"seed": 533, "data": {"p1_how_many": "11", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}296}{5{,}600}, \\dfrac{3{,}346}{5{,}600}, \\dfrac{3{,}363}{5{,}600}, \\dfrac{3{,}378}{5{,}600}, \\dfrac{3{,}383}{5{,}600}, \\dfrac{3{,}390}{5{,}600}, \\dfrac{3{,}391}{5{,}600}, \\dfrac{3{,}396}{5{,}600}, \\dfrac{3{,}435}{5{,}600}, \\dfrac{3{,}465}{5{,}600}, \\dfrac{3{,}476}{5{,}600}, \\text{ and } \\dfrac{3{,}480}{5{,}600}", "__seed__": "0533"}}, {"seed": 534, "data": {"p1_how_many": "14", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.325, 3.33, 3.335, 3.34, 3.345, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995", "3.3249999999999997", "3.3349999999999995", "3.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{705}{3{,}500}, \\dfrac{818}{3{,}500}, \\dfrac{833}{3{,}500}, \\dfrac{836}{3{,}500}, \\dfrac{853}{3{,}500}, \\dfrac{891}{3{,}500}, \\dfrac{907}{3{,}500}, \\text{ and } \\dfrac{934}{3{,}500}", "__seed__": "0534"}}, {"seed": 535, "data": {"p1_how_many": "11", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}003}{4{,}200}, \\dfrac{3{,}013}{4{,}200}, \\dfrac{3{,}028}{4{,}200}, \\dfrac{3{,}034}{4{,}200}, \\dfrac{3{,}047}{4{,}200}, \\dfrac{3{,}048}{4{,}200}, \\dfrac{3{,}158}{4{,}200}, \\dfrac{3{,}214}{4{,}200}, \\dfrac{3{,}257}{4{,}200}, \\dfrac{3{,}309}{4{,}200}, \\text{ and } \\dfrac{3{,}370}{4{,}200}", "__seed__": "0535"}}, {"seed": 536, "data": {"p1_how_many": "13", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315", "1.325", "1.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}694}{15{,}000}, \\dfrac{7{,}315}{15{,}000}, \\dfrac{7{,}583}{15{,}000}, \\dfrac{8{,}023}{15{,}000}, \\dfrac{8{,}113}{15{,}000}, \\dfrac{8{,}206}{15{,}000}, \\dfrac{9{,}405}{15{,}000}, \\dfrac{9{,}797}{15{,}000}, \\dfrac{9{,}849}{15{,}000}, \\text{ and } \\dfrac{9{,}956}{15{,}000}", "__seed__": "0536"}}, {"seed": 537, "data": {"p1_how_many": "14", "p1_a": "1.9", "p1_b": "1.1", "p1_numbers": "1.9005, 1.901, 1.9015, 1.902, 1.9025, 1.903, 1.9035, 1.904, 1.9045, 1.905, 1.906, 1.907, 1.908, and 1.909", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9009999999999998", "1.902", "1.9029999999999998", "1.904", "1.9049999999999998", "1.906", "1.9069999999999998", "1.908", "1.9089999999999998"], "p1_2_xs": ["1.9004999999999999", "1.9014999999999997", "1.9024999999999999", "1.9034999999999997", "1.9044999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}158}{56{,}000}, \\dfrac{36{,}370}{56{,}000}, \\dfrac{37{,}311}{56{,}000}, \\dfrac{37{,}692}{56{,}000}, \\dfrac{38{,}111}{56{,}000}, \\dfrac{38{,}316}{56{,}000}, \\text{ and } \\dfrac{39{,}223}{56{,}000}", "__seed__": "0537"}}, {"seed": 538, "data": {"p1_how_many": "10", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.6005, 4.601, 4.602, 4.603, 4.604, 4.605, 4.606, 4.607, 4.608, and 4.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.601", "4.601999999999999", "4.603", "4.603999999999999", "4.6049999999999995", "4.606", "4.606999999999999", "4.608", "4.609"], "p1_2_xs": ["4.600499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}021}{35{,}000}, \\dfrac{15{,}128}{35{,}000}, \\dfrac{16{,}261}{35{,}000}, \\dfrac{16{,}279}{35{,}000}, \\dfrac{18{,}272}{35{,}000}, \\dfrac{18{,}728}{35{,}000}, \\dfrac{19{,}044}{35{,}000}, \\dfrac{19{,}046}{35{,}000}, \\dfrac{20{,}188}{35{,}000}, \\dfrac{20{,}356}{35{,}000}, \\dfrac{20{,}660}{35{,}000}, \\text{ and } \\dfrac{20{,}796}{35{,}000}", "__seed__": "0538"}}, {"seed": 539, "data": {"p1_how_many": "13", "p1_a": "8.64", "p1_b": "8.65", "p1_numbers": "8.6405, 8.641, 8.6415, 8.642, 8.6425, 8.643, 8.6435, 8.644, 8.645, 8.646, 8.647, 8.648, and 8.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.641", "8.642000000000001", "8.643", "8.644", "8.645000000000001", "8.646", "8.647", "8.648", "8.649000000000001"], "p1_2_xs": ["8.640500000000001", "8.6415", "8.642500000000002", "8.643500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}218}{2{,}000}, \\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}251}{2{,}000}, \\dfrac{1{,}296}{2{,}000}, \\dfrac{1{,}352}{2{,}000}, \\dfrac{1{,}383}{2{,}000}, \\dfrac{1{,}387}{2{,}000}, \\dfrac{1{,}389}{2{,}000}, \\dfrac{1{,}396}{2{,}000}, \\dfrac{1{,}412}{2{,}000}, \\text{ and } \\dfrac{1{,}468}{2{,}000}", "__seed__": "0539"}}, {"seed": 540, "data": {"p1_how_many": "12", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0540"}}, {"seed": 541, "data": {"p1_how_many": "13", "p1_a": "7.75", "p1_b": "7.76", "p1_numbers": "7.7505, 7.751, 7.7515, 7.752, 7.7525, 7.753, 7.7535, 7.754, 7.755, 7.756, 7.757, 7.758, and 7.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.751", "7.752", "7.753", "7.754", "7.755", "7.756", "7.757", "7.758", "7.759"], "p1_2_xs": ["7.7505", "7.7515", "7.7524999999999995", "7.7535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}233}{2{,}000}, \\dfrac{1{,}237}{2{,}000}, \\dfrac{1{,}293}{2{,}000}, \\dfrac{1{,}296}{2{,}000}, \\dfrac{1{,}311}{2{,}000}, \\dfrac{1{,}379}{2{,}000}, \\dfrac{1{,}419}{2{,}000}, \\dfrac{1{,}437}{2{,}000}, \\dfrac{1{,}452}{2{,}000}, \\dfrac{1{,}462}{2{,}000}, \\dfrac{1{,}465}{2{,}000}, \\text{ and } \\dfrac{1{,}476}{2{,}000}", "__seed__": "0541"}}, {"seed": 542, "data": {"p1_how_many": "12", "p1_a": "1.44", "p1_b": "1.45", "p1_numbers": "1.4405, 1.441, 1.4415, 1.442, 1.4425, 1.443, 1.444, 1.445, 1.446, 1.447, 1.448, and 1.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4409999999999998", "1.442", "1.4429999999999998", "1.444", "1.4449999999999998", "1.446", "1.4469999999999998", "1.448", "1.4489999999999998"], "p1_2_xs": ["1.4405", "1.4414999999999998", "1.4425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{549}{2{,}000}, \\dfrac{563}{2{,}000}, \\dfrac{564}{2{,}000}, \\dfrac{634}{2{,}000}, \\dfrac{638}{2{,}000}, \\dfrac{653}{2{,}000}, \\dfrac{663}{2{,}000}, \\dfrac{674}{2{,}000}, \\dfrac{716}{2{,}000}, \\text{ and } \\dfrac{791}{2{,}000}", "__seed__": "0542"}}, {"seed": 543, "data": {"p1_how_many": "13", "p1_a": "9.51", "p1_b": "9.52", "p1_numbers": "9.5105, 9.511, 9.5115, 9.512, 9.5125, 9.513, 9.5135, 9.514, 9.515, 9.516, 9.517, 9.518, and 9.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.511", "9.512", "9.513", "9.514", "9.515", "9.516", "9.517", "9.517999999999999", "9.519"], "p1_2_xs": ["9.5105", "9.5115", "9.512500000000001", "9.5135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}112}{12{,}000}, \\dfrac{3{,}177}{12{,}000}, \\dfrac{3{,}256}{12{,}000}, \\dfrac{3{,}405}{12{,}000}, \\dfrac{3{,}484}{12{,}000}, \\dfrac{3{,}510}{12{,}000}, \\dfrac{3{,}613}{12{,}000}, \\dfrac{3{,}645}{12{,}000}, \\dfrac{3{,}932}{12{,}000}, \\dfrac{3{,}964}{12{,}000}, \\text{ and } \\dfrac{3{,}966}{12{,}000}", "__seed__": "0543"}}, {"seed": 544, "data": {"p1_how_many": "11", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.615, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995", "7.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\text{ and } \\dfrac{358}{420}", "__seed__": "0544"}}, {"seed": 545, "data": {"p1_how_many": "12", "p1_a": "2.35", "p1_b": "2.36", "p1_numbers": "2.3505, 2.351, 2.3515, 2.352, 2.3525, 2.353, 2.354, 2.355, 2.356, 2.357, 2.358, and 2.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.351", "2.352", "2.353", "2.354", "2.355", "2.356", "2.357", "2.358", "2.359"], "p1_2_xs": ["2.3505000000000003", "2.3515", "2.3525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{521}{3{,}000}, \\dfrac{525}{3{,}000}, \\dfrac{529}{3{,}000}, \\dfrac{551}{3{,}000}, \\dfrac{577}{3{,}000}, \\dfrac{583}{3{,}000}, \\dfrac{590}{3{,}000}, \\dfrac{591}{3{,}000}, \\text{ and } \\dfrac{593}{3{,}000}", "__seed__": "0545"}}, {"seed": 546, "data": {"p1_how_many": "14", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.535, 1.54, 1.545, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525", "1.535", "1.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}250}{5{,}600}, \\dfrac{3{,}252}{5{,}600}, \\dfrac{3{,}308}{5{,}600}, \\dfrac{3{,}328}{5{,}600}, \\dfrac{3{,}361}{5{,}600}, \\dfrac{3{,}392}{5{,}600}, \\dfrac{3{,}456}{5{,}600}, \\dfrac{3{,}469}{5{,}600}, \\dfrac{3{,}471}{5{,}600}, \\dfrac{3{,}473}{5{,}600}, \\text{ and } \\dfrac{3{,}483}{5{,}600}", "__seed__": "0546"}}, {"seed": 547, "data": {"p1_how_many": "10", "p1_a": "4.95", "p1_b": "4.96", "p1_numbers": "4.9505, 4.951, 4.952, 4.953, 4.954, 4.955, 4.956, 4.957, 4.958, and 4.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.9510000000000005", "4.952", "4.953", "4.954", "4.955", "4.956", "4.957", "4.958", "4.9590000000000005"], "p1_2_xs": ["4.9505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}750}{20{,}000}, \\dfrac{5{,}835}{20{,}000}, \\dfrac{6{,}284}{20{,}000}, \\dfrac{6{,}469}{20{,}000}, \\dfrac{6{,}884}{20{,}000}, \\dfrac{7{,}438}{20{,}000}, \\text{ and } \\dfrac{7{,}631}{20{,}000}", "__seed__": "0547"}}, {"seed": 548, "data": {"p1_how_many": "13", "p1_a": "4.66", "p1_b": "4.67", "p1_numbers": "4.6605, 4.661, 4.6615, 4.662, 4.6625, 4.663, 4.6635, 4.664, 4.665, 4.666, 4.667, 4.668, and 4.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.6610000000000005", "4.662", "4.663", "4.664", "4.665", "4.666", "4.667", "4.668", "4.6690000000000005"], "p1_2_xs": ["4.6605", "4.6615", "4.6625", "4.6635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}111}{42{,}000}, \\dfrac{30{,}553}{42{,}000}, \\dfrac{31{,}272}{42{,}000}, \\dfrac{32{,}273}{42{,}000}, \\dfrac{32{,}735}{42{,}000}, \\dfrac{32{,}940}{42{,}000}, \\dfrac{32{,}994}{42{,}000}, \\dfrac{33{,}194}{42{,}000}, \\dfrac{33{,}506}{42{,}000}, \\dfrac{33{,}944}{42{,}000}, \\text{ and } \\dfrac{34{,}136}{42{,}000}", "__seed__": "0548"}}, {"seed": 549, "data": {"p1_how_many": "12", "p1_a": "2.87", "p1_b": "2.88", "p1_numbers": "2.8705, 2.871, 2.8715, 2.872, 2.8725, 2.873, 2.874, 2.875, 2.876, 2.877, 2.878, and 2.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.871", "2.872", "2.873", "2.874", "2.875", "2.876", "2.8770000000000002", "2.878", "2.879"], "p1_2_xs": ["2.8705000000000003", "2.8715", "2.8725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}131}{3{,}500}, \\dfrac{2{,}174}{3{,}500}, \\dfrac{2{,}203}{3{,}500}, \\dfrac{2{,}223}{3{,}500}, \\dfrac{2{,}325}{3{,}500}, \\dfrac{2{,}342}{3{,}500}, \\text{ and } \\dfrac{2{,}529}{3{,}500}", "__seed__": "0549"}}, {"seed": 550, "data": {"p1_how_many": "11", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.3005, 3.301, 3.3015, 3.302, 3.303, 3.304, 3.305, 3.306, 3.307, 3.308, and 3.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.3009999999999997", "3.3019999999999996", "3.303", "3.304", "3.3049999999999997", "3.3059999999999996", "3.307", "3.308", "3.3089999999999997"], "p1_2_xs": ["3.3005", "3.3015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{72}{420}, \\dfrac{84}{420}, \\dfrac{85}{420}, \\dfrac{88}{420}, \\dfrac{94}{420}, \\dfrac{105}{420}, \\dfrac{107}{420}, \\text{ and } \\dfrac{117}{420}", "__seed__": "0550"}}, {"seed": 551, "data": {"p1_how_many": "14", "p1_a": "7.01", "p1_b": "7.02", "p1_numbers": "7.0105, 7.011, 7.0115, 7.012, 7.0125, 7.013, 7.0135, 7.014, 7.0145, 7.015, 7.016, 7.017, 7.018, and 7.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.011", "7.012", "7.013", "7.013999999999999", "7.015", "7.016", "7.0169999999999995", "7.018", "7.019"], "p1_2_xs": ["7.0104999999999995", "7.0115", "7.012499999999999", "7.0135", "7.014499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}812}{15{,}000}, \\dfrac{6{,}975}{15{,}000}, \\dfrac{7{,}146}{15{,}000}, \\dfrac{7{,}922}{15{,}000}, \\dfrac{7{,}931}{15{,}000}, \\dfrac{8{,}248}{15{,}000}, \\dfrac{8{,}672}{15{,}000}, \\dfrac{8{,}725}{15{,}000}, \\dfrac{8{,}741}{15{,}000}, \\dfrac{9{,}355}{15{,}000}, \\dfrac{9{,}393}{15{,}000}, \\text{ and } \\dfrac{9{,}603}{15{,}000}", "__seed__": "0551"}}, {"seed": 552, "data": {"p1_how_many": "13", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.325, 8.33, 8.335, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001", "8.325000000000001", "8.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}406}{6{,}300}, \\dfrac{1{,}493}{6{,}300}, \\dfrac{1{,}616}{6{,}300}, \\dfrac{1{,}642}{6{,}300}, \\dfrac{1{,}655}{6{,}300}, \\dfrac{1{,}659}{6{,}300}, \\dfrac{1{,}737}{6{,}300}, \\text{ and } \\dfrac{1{,}751}{6{,}300}", "__seed__": "0552"}}, {"seed": 553, "data": {"p1_how_many": "11", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}236}{12{,}000}, \\dfrac{3{,}354}{12{,}000}, \\dfrac{3{,}366}{12{,}000}, \\dfrac{3{,}405}{12{,}000}, \\dfrac{3{,}502}{12{,}000}, \\dfrac{3{,}829}{12{,}000}, \\text{ and } \\dfrac{3{,}913}{12{,}000}", "__seed__": "0553"}}, {"seed": 554, "data": {"p1_how_many": "14", "p1_a": "7.03", "p1_b": "7.04", "p1_numbers": "7.0305, 7.031, 7.0315, 7.032, 7.0325, 7.033, 7.0335, 7.034, 7.0345, 7.035, 7.036, 7.037, 7.038, and 7.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.031000000000001", "7.032", "7.033", "7.034", "7.035", "7.0360000000000005", "7.037", "7.038", "7.039000000000001"], "p1_2_xs": ["7.0305", "7.0315", "7.0325", "7.0335", "7.0344999999999995"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{739}{4{,}200}, \\dfrac{815}{4{,}200}, \\dfrac{817}{4{,}200}, \\dfrac{819}{4{,}200}, \\dfrac{859}{4{,}200}, \\dfrac{967}{4{,}200}, \\dfrac{1{,}000}{4{,}200}, \\dfrac{1{,}011}{4{,}200}, \\dfrac{1{,}063}{4{,}200}, \\dfrac{1{,}069}{4{,}200}, \\dfrac{1{,}089}{4{,}200}, \\text{ and } \\dfrac{1{,}125}{4{,}200}", "__seed__": "0554"}}, {"seed": 555, "data": {"p1_how_many": "13", "p1_a": "4.15", "p1_b": "4.16", "p1_numbers": "4.1505, 4.151, 4.1515, 4.152, 4.1525, 4.153, 4.1535, 4.154, 4.155, 4.156, 4.157, 4.158, and 4.159", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.151000000000001", "4.152", "4.1530000000000005", "4.154", "4.155", "4.156000000000001", "4.157", "4.158", "4.159000000000001"], "p1_2_xs": ["4.1505", "4.1515", "4.1525", "4.1535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{618}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{648}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{676}{4{,}200}, \\dfrac{681}{4{,}200}, \\text{ and } \\dfrac{689}{4{,}200}", "__seed__": "0555"}}, {"seed": 556, "data": {"p1_how_many": "11", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}507}{5{,}600}, \\dfrac{3{,}525}{5{,}600}, \\dfrac{3{,}526}{5{,}600}, \\dfrac{3{,}606}{5{,}600}, \\dfrac{3{,}737}{5{,}600}, \\dfrac{3{,}847}{5{,}600}, \\dfrac{3{,}881}{5{,}600}, \\dfrac{3{,}912}{5{,}600}, \\dfrac{3{,}919}{5{,}600}, \\text{ and } \\dfrac{3{,}987}{5{,}600}", "__seed__": "0556"}}, {"seed": 557, "data": {"p1_how_many": "10", "p1_a": "5.83", "p1_b": "5.84", "p1_numbers": "5.8305, 5.831, 5.832, 5.833, 5.834, 5.835, 5.836, 5.837, 5.838, and 5.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.831", "5.832", "5.833", "5.834", "5.835", "5.836", "5.837", "5.838", "5.839"], "p1_2_xs": ["5.8305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}586}{56{,}000}, \\dfrac{21{,}991}{56{,}000}, \\dfrac{22{,}019}{56{,}000}, \\dfrac{22{,}051}{56{,}000}, \\dfrac{22{,}360}{56{,}000}, \\dfrac{22{,}368}{56{,}000}, \\dfrac{22{,}809}{56{,}000}, \\dfrac{23{,}138}{56{,}000}, \\dfrac{23{,}603}{56{,}000}, \\text{ and } \\dfrac{23{,}885}{56{,}000}", "__seed__": "0557"}}, {"seed": 558, "data": {"p1_how_many": "11", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}028}{20{,}000}, \\dfrac{12{,}490}{20{,}000}, \\dfrac{13{,}560}{20{,}000}, \\dfrac{13{,}868}{20{,}000}, \\dfrac{14{,}433}{20{,}000}, \\dfrac{14{,}436}{20{,}000}, \\dfrac{14{,}520}{20{,}000}, \\dfrac{14{,}660}{20{,}000}, \\dfrac{14{,}682}{20{,}000}, \\text{ and } \\dfrac{14{,}883}{20{,}000}", "__seed__": "0558"}}, {"seed": 559, "data": {"p1_how_many": "12", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}001}{20{,}000}, \\dfrac{5{,}026}{20{,}000}, \\dfrac{5{,}039}{20{,}000}, \\dfrac{5{,}754}{20{,}000}, \\dfrac{6{,}389}{20{,}000}, \\dfrac{6{,}817}{20{,}000}, \\dfrac{6{,}829}{20{,}000}, \\dfrac{6{,}970}{20{,}000}, \\dfrac{7{,}231}{20{,}000}, \\dfrac{7{,}826}{20{,}000}, \\dfrac{7{,}848}{20{,}000}, \\text{ and } \\dfrac{7{,}954}{20{,}000}", "__seed__": "0559"}}, {"seed": 560, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}029}{35{,}000}, \\dfrac{14{,}073}{35{,}000}, \\dfrac{14{,}123}{35{,}000}, \\dfrac{14{,}151}{35{,}000}, \\dfrac{14{,}504}{35{,}000}, \\dfrac{14{,}542}{35{,}000}, \\dfrac{14{,}583}{35{,}000}, \\dfrac{14{,}726}{35{,}000}, \\dfrac{14{,}730}{35{,}000}, \\dfrac{14{,}788}{35{,}000}, \\dfrac{14{,}954}{35{,}000}, \\text{ and } \\dfrac{14{,}973}{35{,}000}", "__seed__": "0560"}}, {"seed": 561, "data": {"p1_how_many": "12", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}478}{42{,}000}, \\dfrac{7{,}504}{42{,}000}, \\dfrac{7{,}616}{42{,}000}, \\dfrac{7{,}837}{42{,}000}, \\dfrac{8{,}780}{42{,}000}, \\dfrac{10{,}378}{42{,}000}, \\dfrac{10{,}388}{42{,}000}, \\dfrac{11{,}038}{42{,}000}, \\dfrac{11{,}515}{42{,}000}, \\dfrac{11{,}549}{42{,}000}, \\text{ and } \\dfrac{11{,}756}{42{,}000}", "__seed__": "0561"}}, {"seed": 562, "data": {"p1_how_many": "12", "p1_a": "6.4", "p1_b": "6.5", "p1_numbers": "6.405, 6.41, 6.415, 6.42, 6.425, 6.43, 6.44, 6.45, 6.46, 6.47, 6.48, and 6.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.41", "6.42", "6.430000000000001", "6.44", "6.45", "6.46", "6.470000000000001", "6.48", "6.49"], "p1_2_xs": ["6.405", "6.415", "6.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, \\dfrac{243}{300}, \\dfrac{244}{300}, \\dfrac{245}{300}, \\dfrac{246}{300}, \\dfrac{247}{300}, \\dfrac{248}{300}, \\text{ and } \\dfrac{249}{300}", "__seed__": "0562"}}, {"seed": 563, "data": {"p1_how_many": "12", "p1_a": "8.14", "p1_b": "8.15", "p1_numbers": "8.1405, 8.141, 8.1415, 8.142, 8.1425, 8.143, 8.144, 8.145, 8.146, 8.147, 8.148, and 8.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.141", "8.142000000000001", "8.143", "8.144", "8.145000000000001", "8.146", "8.147", "8.148", "8.149000000000001"], "p1_2_xs": ["8.140500000000001", "8.1415", "8.142500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}426}{6{,}300}, \\dfrac{1{,}466}{6{,}300}, \\dfrac{1{,}499}{6{,}300}, \\dfrac{1{,}557}{6{,}300}, \\dfrac{1{,}563}{6{,}300}, \\dfrac{1{,}628}{6{,}300}, \\dfrac{1{,}644}{6{,}300}, \\dfrac{1{,}646}{6{,}300}, \\dfrac{1{,}793}{6{,}300}, \\text{ and } \\dfrac{1{,}798}{6{,}300}", "__seed__": "0563"}}, {"seed": 564, "data": {"p1_how_many": "13", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{612}{4{,}200}, \\dfrac{616}{4{,}200}, \\dfrac{620}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{629}{4{,}200}, \\dfrac{635}{4{,}200}, \\dfrac{644}{4{,}200}, \\dfrac{647}{4{,}200}, \\dfrac{653}{4{,}200}, \\text{ and } \\dfrac{680}{4{,}200}", "__seed__": "0564"}}, {"seed": 565, "data": {"p1_how_many": "12", "p1_a": "6.12", "p1_b": "6.13", "p1_numbers": "6.1205, 6.121, 6.1215, 6.122, 6.1225, 6.123, 6.124, 6.125, 6.126, 6.127, 6.128, and 6.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.121", "6.122", "6.123", "6.124", "6.125", "6.126", "6.127", "6.128", "6.1290000000000004"], "p1_2_xs": ["6.1205", "6.1215", "6.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{719}{4{,}200}, \\dfrac{893}{4{,}200}, \\dfrac{913}{4{,}200}, \\dfrac{939}{4{,}200}, \\dfrac{964}{4{,}200}, \\dfrac{1{,}000}{4{,}200}, \\dfrac{1{,}056}{4{,}200}, \\dfrac{1{,}097}{4{,}200}, \\dfrac{1{,}106}{4{,}200}, \\dfrac{1{,}115}{4{,}200}, \\text{ and } \\dfrac{1{,}189}{4{,}200}", "__seed__": "0565"}}, {"seed": 566, "data": {"p1_how_many": "10", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.52, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{795}{3{,}500}, \\dfrac{810}{3{,}500}, \\dfrac{822}{3{,}500}, \\dfrac{853}{3{,}500}, \\dfrac{854}{3{,}500}, \\dfrac{966}{3{,}500}, \\text{ and } \\dfrac{991}{3{,}500}", "__seed__": "0566"}}, {"seed": 567, "data": {"p1_how_many": "13", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.325, 8.33, 8.335, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001", "8.325000000000001", "8.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{500}{770}, \\dfrac{505}{770}, \\dfrac{518}{770}, \\dfrac{550}{770}, \\dfrac{557}{770}, \\dfrac{579}{770}, \\dfrac{599}{770}, \\text{ and } \\dfrac{600}{770}", "__seed__": "0567"}}, {"seed": 568, "data": {"p1_how_many": "13", "p1_a": "4.71", "p1_b": "4.72", "p1_numbers": "4.7105, 4.711, 4.7115, 4.712, 4.7125, 4.713, 4.7135, 4.714, 4.715, 4.716, 4.717, 4.718, and 4.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.711", "4.712", "4.713", "4.7139999999999995", "4.715", "4.716", "4.717", "4.718", "4.719"], "p1_2_xs": ["4.7105", "4.7115", "4.7124999999999995", "4.7135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{307}{1{,}200}, \\dfrac{309}{1{,}200}, \\dfrac{314}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{362}{1{,}200}, \\dfrac{368}{1{,}200}, \\dfrac{370}{1{,}200}, \\dfrac{374}{1{,}200}, \\dfrac{375}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0568"}}, {"seed": 569, "data": {"p1_how_many": "13", "p1_a": "3.12", "p1_b": "3.13", "p1_numbers": "3.1205, 3.121, 3.1215, 3.122, 3.1225, 3.123, 3.1235, 3.124, 3.125, 3.126, 3.127, 3.128, and 3.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.121", "3.122", "3.123", "3.124", "3.125", "3.126", "3.1270000000000002", "3.128", "3.129"], "p1_2_xs": ["3.1205000000000003", "3.1215", "3.1225", "3.1235000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{803}{1{,}200}, \\dfrac{828}{1{,}200}, \\dfrac{842}{1{,}200}, \\dfrac{844}{1{,}200}, \\dfrac{847}{1{,}200}, \\dfrac{849}{1{,}200}, \\dfrac{863}{1{,}200}, \\dfrac{875}{1{,}200}, \\dfrac{877}{1{,}200}, \\dfrac{882}{1{,}200}, \\text{ and } \\dfrac{889}{1{,}200}", "__seed__": "0569"}}, {"seed": 570, "data": {"p1_how_many": "14", "p1_a": "7.04", "p1_b": "7.05", "p1_numbers": "7.0405, 7.041, 7.0415, 7.042, 7.0425, 7.043, 7.0435, 7.044, 7.0445, 7.045, 7.046, 7.047, 7.048, and 7.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.041", "7.042", "7.043", "7.044", "7.045", "7.046", "7.047", "7.048", "7.049"], "p1_2_xs": ["7.0405", "7.0415", "7.0424999999999995", "7.0435", "7.044499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}052}{77{,}000}, \\dfrac{42{,}479}{77{,}000}, \\dfrac{42{,}694}{77{,}000}, \\dfrac{43{,}171}{77{,}000}, \\dfrac{44{,}397}{77{,}000}, \\dfrac{44{,}912}{77{,}000}, \\dfrac{48{,}293}{77{,}000}, \\dfrac{48{,}617}{77{,}000}, \\dfrac{49{,}973}{77{,}000}, \\dfrac{51{,}378}{77{,}000}, \\text{ and } \\dfrac{54{,}596}{77{,}000}", "__seed__": "0570"}}, {"seed": 571, "data": {"p1_how_many": "11", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{525}{2{,}000}, \\dfrac{568}{2{,}000}, \\dfrac{598}{2{,}000}, \\dfrac{617}{2{,}000}, \\dfrac{669}{2{,}000}, \\dfrac{745}{2{,}000}, \\text{ and } \\dfrac{792}{2{,}000}", "__seed__": "0571"}}, {"seed": 572, "data": {"p1_how_many": "12", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{74}{150}, \\dfrac{75}{150}, \\dfrac{87}{150}, \\dfrac{88}{150}, \\dfrac{89}{150}, \\dfrac{91}{150}, \\dfrac{92}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0572"}}, {"seed": 573, "data": {"p1_how_many": "10", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}505}{4{,}200}, \\dfrac{3{,}514}{4{,}200}, \\dfrac{3{,}518}{4{,}200}, \\dfrac{3{,}524}{4{,}200}, \\dfrac{3{,}527}{4{,}200}, \\dfrac{3{,}536}{4{,}200}, \\dfrac{3{,}542}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}567}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\dfrac{3{,}596}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0573"}}, {"seed": 574, "data": {"p1_how_many": "10", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}061}{20{,}000}, \\dfrac{12{,}266}{20{,}000}, \\dfrac{12{,}334}{20{,}000}, \\dfrac{12{,}693}{20{,}000}, \\dfrac{13{,}094}{20{,}000}, \\dfrac{13{,}140}{20{,}000}, \\dfrac{13{,}572}{20{,}000}, \\dfrac{14{,}423}{20{,}000}, \\dfrac{14{,}434}{20{,}000}, \\text{ and } \\dfrac{14{,}836}{20{,}000}", "__seed__": "0574"}}, {"seed": 575, "data": {"p1_how_many": "11", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}024}{42{,}000}, \\dfrac{35{,}050}{42{,}000}, \\dfrac{35{,}362}{42{,}000}, \\dfrac{35{,}545}{42{,}000}, \\dfrac{35{,}640}{42{,}000}, \\dfrac{35{,}682}{42{,}000}, \\dfrac{35{,}842}{42{,}000}, \\text{ and } \\dfrac{35{,}984}{42{,}000}", "__seed__": "0575"}}, {"seed": 576, "data": {"p1_how_many": "13", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{76}{420}, \\dfrac{77}{420}, \\dfrac{85}{420}, \\dfrac{93}{420}, \\dfrac{98}{420}, \\dfrac{99}{420}, \\dfrac{112}{420}, \\dfrac{115}{420}, \\text{ and } \\dfrac{119}{420}", "__seed__": "0576"}}, {"seed": 577, "data": {"p1_how_many": "12", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}257}{2{,}000}, \\dfrac{1{,}299}{2{,}000}, \\dfrac{1{,}301}{2{,}000}, \\dfrac{1{,}355}{2{,}000}, \\dfrac{1{,}367}{2{,}000}, \\dfrac{1{,}373}{2{,}000}, \\dfrac{1{,}449}{2{,}000}, \\text{ and } \\dfrac{1{,}464}{2{,}000}", "__seed__": "0577"}}, {"seed": 578, "data": {"p1_how_many": "13", "p1_a": "7.64", "p1_b": "7.65", "p1_numbers": "7.6405, 7.641, 7.6415, 7.642, 7.6425, 7.643, 7.6435, 7.644, 7.645, 7.646, 7.647, 7.648, and 7.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.641", "7.6419999999999995", "7.643", "7.643999999999999", "7.645", "7.646", "7.646999999999999", "7.648", "7.649"], "p1_2_xs": ["7.640499999999999", "7.6415", "7.642499999999999", "7.6434999999999995"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}202}{2{,}000}, \\dfrac{1{,}213}{2{,}000}, \\dfrac{1{,}336}{2{,}000}, \\dfrac{1{,}395}{2{,}000}, \\dfrac{1{,}404}{2{,}000}, \\dfrac{1{,}424}{2{,}000}, \\dfrac{1{,}462}{2{,}000}, \\text{ and } \\dfrac{1{,}485}{2{,}000}", "__seed__": "0578"}}, {"seed": 579, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{51}{300}, \\dfrac{52}{300}, \\dfrac{53}{300}, \\dfrac{54}{300}, \\dfrac{55}{300}, \\dfrac{56}{300}, \\dfrac{57}{300}, \\dfrac{58}{300}, \\text{ and } \\dfrac{59}{300}", "__seed__": "0579"}}, {"seed": 580, "data": {"p1_how_many": "14", "p1_a": "4.32", "p1_b": "4.33", "p1_numbers": "4.3205, 4.321, 4.3215, 4.322, 4.3225, 4.323, 4.3235, 4.324, 4.3245, 4.325, 4.326, 4.327, 4.328, and 4.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.321000000000001", "4.322", "4.323", "4.324", "4.325", "4.3260000000000005", "4.327", "4.328", "4.329000000000001"], "p1_2_xs": ["4.3205", "4.3215", "4.3225", "4.3235", "4.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{52}{200}, \\dfrac{57}{200}, \\dfrac{58}{200}, \\dfrac{72}{200}, \\dfrac{74}{200}, \\dfrac{75}{200}, \\dfrac{77}{200}, \\text{ and } \\dfrac{78}{200}", "__seed__": "0580"}}, {"seed": 581, "data": {"p1_how_many": "12", "p1_a": "9.12", "p1_b": "9.13", "p1_numbers": "9.1205, 9.121, 9.1215, 9.122, 9.1225, 9.123, 9.124, 9.125, 9.126, 9.127, 9.128, and 9.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.120999999999999", "9.122", "9.123", "9.123999999999999", "9.125", "9.126", "9.126999999999999", "9.127999999999998", "9.129"], "p1_2_xs": ["9.1205", "9.1215", "9.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{504}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{512}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{536}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{547}{1{,}500}, \\dfrac{548}{1{,}500}, \\dfrac{591}{1{,}500}, \\text{ and } \\dfrac{595}{1{,}500}", "__seed__": "0581"}}, {"seed": 582, "data": {"p1_how_many": "10", "p1_a": "4.02", "p1_b": "4.03", "p1_numbers": "4.0205, 4.021, 4.022, 4.023, 4.024, 4.025, 4.026, 4.027, 4.028, and 4.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.021", "4.021999999999999", "4.023", "4.023999999999999", "4.0249999999999995", "4.026", "4.026999999999999", "4.028", "4.029"], "p1_2_xs": ["4.020499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{45{,}174}{77{,}000}, \\dfrac{46{,}256}{77{,}000}, \\dfrac{46{,}808}{77{,}000}, \\dfrac{47{,}751}{77{,}000}, \\dfrac{47{,}963}{77{,}000}, \\dfrac{48{,}391}{77{,}000}, \\dfrac{49{,}502}{77{,}000}, \\dfrac{50{,}683}{77{,}000}, \\dfrac{51{,}258}{77{,}000}, \\dfrac{53{,}747}{77{,}000}, \\text{ and } \\dfrac{54{,}216}{77{,}000}", "__seed__": "0582"}}, {"seed": 583, "data": {"p1_how_many": "13", "p1_a": "4.95", "p1_b": "4.96", "p1_numbers": "4.9505, 4.951, 4.9515, 4.952, 4.9525, 4.953, 4.9535, 4.954, 4.955, 4.956, 4.957, 4.958, and 4.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.9510000000000005", "4.952", "4.953", "4.954", "4.955", "4.956", "4.957", "4.958", "4.9590000000000005"], "p1_2_xs": ["4.9505", "4.9515", "4.9525", "4.9535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}491}{12{,}000}, \\dfrac{3{,}500}{12{,}000}, \\dfrac{3{,}511}{12{,}000}, \\dfrac{3{,}522}{12{,}000}, \\dfrac{3{,}531}{12{,}000}, \\dfrac{3{,}647}{12{,}000}, \\dfrac{3{,}665}{12{,}000}, \\dfrac{3{,}673}{12{,}000}, \\dfrac{3{,}789}{12{,}000}, \\dfrac{3{,}858}{12{,}000}, \\dfrac{3{,}928}{12{,}000}, \\text{ and } \\dfrac{3{,}935}{12{,}000}", "__seed__": "0583"}}, {"seed": 584, "data": {"p1_how_many": "11", "p1_a": "7.67", "p1_b": "7.68", "p1_numbers": "7.6705, 7.671, 7.6715, 7.672, 7.673, 7.674, 7.675, 7.676, 7.677, 7.678, and 7.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.671", "7.672", "7.673", "7.6739999999999995", "7.675", "7.676", "7.677", "7.678", "7.679"], "p1_2_xs": ["7.6705", "7.6715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}069}{42{,}000}, \\dfrac{6{,}116}{42{,}000}, \\dfrac{6{,}231}{42{,}000}, \\dfrac{6{,}311}{42{,}000}, \\dfrac{6{,}585}{42{,}000}, \\dfrac{6{,}593}{42{,}000}, \\dfrac{6{,}655}{42{,}000}, \\dfrac{6{,}708}{42{,}000}, \\dfrac{6{,}782}{42{,}000}, \\text{ and } \\dfrac{6{,}903}{42{,}000}", "__seed__": "0584"}}, {"seed": 585, "data": {"p1_how_many": "11", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}003}{42{,}000}, \\dfrac{6{,}091}{42{,}000}, \\dfrac{6{,}191}{42{,}000}, \\dfrac{6{,}232}{42{,}000}, \\dfrac{6{,}489}{42{,}000}, \\dfrac{6{,}592}{42{,}000}, \\dfrac{6{,}697}{42{,}000}, \\dfrac{6{,}787}{42{,}000}, \\dfrac{6{,}874}{42{,}000}, \\dfrac{6{,}884}{42{,}000}, \\dfrac{6{,}934}{42{,}000}, \\text{ and } \\dfrac{6{,}960}{42{,}000}", "__seed__": "0585"}}, {"seed": 586, "data": {"p1_how_many": "13", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.635, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999", "4.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}035}{30{,}000}, \\dfrac{24{,}067}{30{,}000}, \\dfrac{24{,}125}{30{,}000}, \\dfrac{24{,}138}{30{,}000}, \\dfrac{24{,}182}{30{,}000}, \\dfrac{24{,}394}{30{,}000}, \\dfrac{24{,}536}{30{,}000}, \\dfrac{24{,}551}{30{,}000}, \\dfrac{24{,}613}{30{,}000}, \\dfrac{24{,}664}{30{,}000}, \\dfrac{24{,}786}{30{,}000}, \\text{ and } \\dfrac{24{,}830}{30{,}000}", "__seed__": "0586"}}, {"seed": 587, "data": {"p1_how_many": "14", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.545, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997", "3.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{606}{4{,}200}, \\dfrac{614}{4{,}200}, \\dfrac{629}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{651}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{672}{4{,}200}, \\dfrac{686}{4{,}200}, \\dfrac{690}{4{,}200}, \\dfrac{692}{4{,}200}, \\text{ and } \\dfrac{695}{4{,}200}", "__seed__": "0587"}}, {"seed": 588, "data": {"p1_how_many": "14", "p1_a": "7.94", "p1_b": "7.95", "p1_numbers": "7.9405, 7.941, 7.9415, 7.942, 7.9425, 7.943, 7.9435, 7.944, 7.9445, 7.945, 7.946, 7.947, 7.948, and 7.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.941000000000001", "7.942", "7.9430000000000005", "7.944", "7.945", "7.946000000000001", "7.947", "7.948", "7.949000000000001"], "p1_2_xs": ["7.9405", "7.9415000000000004", "7.9425", "7.9435", "7.9445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{504}{2{,}000}, \\dfrac{514}{2{,}000}, \\dfrac{528}{2{,}000}, \\dfrac{549}{2{,}000}, \\dfrac{564}{2{,}000}, \\dfrac{601}{2{,}000}, \\dfrac{753}{2{,}000}, \\dfrac{776}{2{,}000}, \\dfrac{781}{2{,}000}, \\text{ and } \\dfrac{791}{2{,}000}", "__seed__": "0588"}}, {"seed": 589, "data": {"p1_how_many": "12", "p1_a": "3.87", "p1_b": "3.88", "p1_numbers": "3.8705, 3.871, 3.8715, 3.872, 3.8725, 3.873, 3.874, 3.875, 3.876, 3.877, 3.878, and 3.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.871", "3.872", "3.873", "3.874", "3.875", "3.876", "3.8770000000000002", "3.878", "3.879"], "p1_2_xs": ["3.8705000000000003", "3.8715", "3.8725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}100}{56{,}000}, \\dfrac{35{,}269}{56{,}000}, \\dfrac{35{,}369}{56{,}000}, \\dfrac{35{,}975}{56{,}000}, \\dfrac{37{,}847}{56{,}000}, \\dfrac{38{,}101}{56{,}000}, \\dfrac{38{,}256}{56{,}000}, \\dfrac{39{,}015}{56{,}000}, \\dfrac{39{,}466}{56{,}000}, \\text{ and } \\dfrac{39{,}815}{56{,}000}", "__seed__": "0589"}}, {"seed": 590, "data": {"p1_how_many": "11", "p1_a": "6.75", "p1_b": "6.76", "p1_numbers": "6.7505, 6.751, 6.7515, 6.752, 6.753, 6.754, 6.755, 6.756, 6.757, 6.758, and 6.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.751", "6.752", "6.753", "6.754", "6.755", "6.756", "6.757", "6.758", "6.759"], "p1_2_xs": ["6.7505", "6.7515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{298}{630}, \\dfrac{305}{630}, \\dfrac{320}{630}, \\dfrac{336}{630}, \\dfrac{341}{630}, \\dfrac{345}{630}, \\dfrac{348}{630}, \\text{ and } \\dfrac{355}{630}", "__seed__": "0590"}}, {"seed": 591, "data": {"p1_how_many": "14", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.135, 8.14, 8.145, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125", "8.135", "8.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}244}{2{,}000}, \\dfrac{1{,}323}{2{,}000}, \\dfrac{1{,}324}{2{,}000}, \\dfrac{1{,}363}{2{,}000}, \\dfrac{1{,}383}{2{,}000}, \\dfrac{1{,}429}{2{,}000}, \\dfrac{1{,}448}{2{,}000}, \\text{ and } \\dfrac{1{,}459}{2{,}000}", "__seed__": "0591"}}, {"seed": 592, "data": {"p1_how_many": "10", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}557}{35{,}000}, \\dfrac{15{,}621}{35{,}000}, \\dfrac{17{,}112}{35{,}000}, \\dfrac{18{,}570}{35{,}000}, \\dfrac{18{,}571}{35{,}000}, \\dfrac{18{,}624}{35{,}000}, \\dfrac{18{,}712}{35{,}000}, \\text{ and } \\dfrac{20{,}771}{35{,}000}", "__seed__": "0592"}}, {"seed": 593, "data": {"p1_how_many": "10", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.72, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}519}{4{,}200}, \\dfrac{3{,}530}{4{,}200}, \\dfrac{3{,}541}{4{,}200}, \\dfrac{3{,}549}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}560}{4{,}200}, \\dfrac{3{,}565}{4{,}200}, \\dfrac{3{,}570}{4{,}200}, \\dfrac{3{,}577}{4{,}200}, \\dfrac{3{,}580}{4{,}200}, \\dfrac{3{,}589}{4{,}200}, \\text{ and } \\dfrac{3{,}597}{4{,}200}", "__seed__": "0593"}}, {"seed": 594, "data": {"p1_how_many": "10", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.02, 3.03, 3.04, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", 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numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{200}, \\dfrac{56}{200}, \\dfrac{57}{200}, \\dfrac{58}{200}, \\dfrac{65}{200}, \\dfrac{73}{200}, \\dfrac{74}{200}, \\text{ and } \\dfrac{78}{200}", "__seed__": "0595"}}, {"seed": 596, "data": {"p1_how_many": "10", "p1_a": "4.33", "p1_b": "4.34", "p1_numbers": "4.3305, 4.331, 4.332, 4.333, 4.334, 4.335, 4.336, 4.337, 4.338, and 4.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.331", "4.332", "4.333", "4.334", "4.335", "4.336", "4.337", "4.338", "4.339"], "p1_2_xs": ["4.3305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{533}{3{,}000}, \\dfrac{535}{3{,}000}, \\dfrac{544}{3{,}000}, \\dfrac{560}{3{,}000}, \\dfrac{561}{3{,}000}, \\dfrac{562}{3{,}000}, 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\\dfrac{34{,}035}{42{,}000}", "__seed__": "0605"}}, {"seed": 606, "data": {"p1_how_many": "12", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.2005, 6.201, 6.2015, 6.202, 6.2025, 6.203, 6.204, 6.205, 6.206, 6.207, 6.208, and 6.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.2010000000000005", "6.202", "6.203", "6.204", "6.205", "6.206", "6.207", "6.208", "6.2090000000000005"], "p1_2_xs": ["6.2005", "6.2015", "6.2025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}421}{3{,}500}, \\dfrac{1{,}439}{3{,}500}, \\dfrac{1{,}450}{3{,}500}, \\dfrac{1{,}454}{3{,}500}, \\dfrac{1{,}459}{3{,}500}, \\dfrac{1{,}464}{3{,}500}, \\dfrac{1{,}466}{3{,}500}, \\dfrac{1{,}486}{3{,}500}, \\dfrac{1{,}488}{3{,}500}, \\text{ and } \\dfrac{1{,}497}{3{,}500}", "__seed__": "0606"}}, {"seed": 607, "data": {"p1_how_many": 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"p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.161", "2.162", "2.1630000000000003", "2.164", "2.165", "2.166", "2.1670000000000003", "2.168", "2.169"], "p1_2_xs": ["2.1605000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}403}{3{,}500}, \\dfrac{1{,}411}{3{,}500}, \\dfrac{1{,}416}{3{,}500}, \\dfrac{1{,}417}{3{,}500}, \\dfrac{1{,}420}{3{,}500}, \\dfrac{1{,}429}{3{,}500}, \\dfrac{1{,}457}{3{,}500}, \\dfrac{1{,}458}{3{,}500}, \\dfrac{1{,}464}{3{,}500}, \\dfrac{1{,}466}{3{,}500}, \\dfrac{1{,}471}{3{,}500}, \\text{ and } \\dfrac{1{,}475}{3{,}500}", "__seed__": "0611"}}, {"seed": 612, "data": {"p1_how_many": "10", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}061}{3{,}500}, \\dfrac{1{,}063}{3{,}500}, \\dfrac{1{,}070}{3{,}500}, \\dfrac{1{,}106}{3{,}500}, \\dfrac{1{,}111}{3{,}500}, \\dfrac{1{,}120}{3{,}500}, \\dfrac{1{,}169}{3{,}500}, \\dfrac{1{,}230}{3{,}500}, \\dfrac{1{,}236}{3{,}500}, \\dfrac{1{,}270}{3{,}500}, \\text{ and } \\dfrac{1{,}368}{3{,}500}", "__seed__": "0612"}}, {"seed": 613, "data": {"p1_how_many": "14", "p1_a": "8.75", "p1_b": "8.76", "p1_numbers": "8.7505, 8.751, 8.7515, 8.752, 8.7525, 8.753, 8.7535, 8.754, 8.7545, 8.755, 8.756, 8.757, 8.758, and 8.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.751", "8.752", "8.753", "8.754", "8.755", 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additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}828}{5{,}600}, \\dfrac{4{,}833}{5{,}600}, \\dfrac{4{,}844}{5{,}600}, \\dfrac{4{,}845}{5{,}600}, \\dfrac{4{,}849}{5{,}600}, \\dfrac{4{,}850}{5{,}600}, \\dfrac{4{,}867}{5{,}600}, \\dfrac{4{,}868}{5{,}600}, \\dfrac{4{,}880}{5{,}600}, \\dfrac{4{,}881}{5{,}600}, \\text{ and } \\dfrac{4{,}892}{5{,}600}", "__seed__": "0614"}}, {"seed": 615, "data": {"p1_how_many": "11", "p1_a": "8.67", "p1_b": "8.68", "p1_numbers": "8.6705, 8.671, 8.6715, 8.672, 8.673, 8.674, 8.675, 8.676, 8.677, 8.678, and 8.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.671", "8.672", "8.673", "8.674", "8.675", "8.676", "8.677", "8.677999999999999", "8.679"], "p1_2_xs": ["8.6705", "8.6715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": 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"10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}046}{35{,}000}, \\dfrac{20{,}136}{35{,}000}, \\dfrac{20{,}302}{35{,}000}, \\dfrac{20{,}312}{35{,}000}, \\dfrac{20{,}319}{35{,}000}, \\dfrac{20{,}324}{35{,}000}, \\dfrac{20{,}502}{35{,}000}, \\dfrac{20{,}724}{35{,}000}, \\dfrac{20{,}824}{35{,}000}, \\text{ and } \\dfrac{20{,}916}{35{,}000}", "__seed__": "0616"}}, {"seed": 617, "data": {"p1_how_many": "11", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{612}{1{,}500}, \\dfrac{675}{1{,}500}, \\dfrac{699}{1{,}500}, \\dfrac{707}{1{,}500}, \\dfrac{861}{1{,}500}, \\dfrac{901}{1{,}500}, \\dfrac{906}{1{,}500}, \\dfrac{947}{1{,}500}, \\text{ and } \\dfrac{969}{1{,}500}", "__seed__": "0617"}}, {"seed": 618, "data": {"p1_how_many": "12", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.125, 9.13, 9.14, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}338}{20{,}000}, \\dfrac{15{,}379}{20{,}000}, \\dfrac{15{,}403}{20{,}000}, \\dfrac{15{,}643}{20{,}000}, \\dfrac{15{,}689}{20{,}000}, \\dfrac{15{,}780}{20{,}000}, \\text{ and } \\dfrac{15{,}885}{20{,}000}", "__seed__": "0618"}}, {"seed": 619, "data": {"p1_how_many": "13", "p1_a": "8.54", "p1_b": "8.55", "p1_numbers": "8.5405, 8.541, 8.5415, 8.542, 8.5425, 8.543, 8.5435, 8.544, 8.545, 8.546, 8.547, 8.548, and 8.549", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.540999999999999", "8.542", "8.543", "8.543999999999999", "8.545", "8.546", "8.546999999999999", "8.547999999999998", "8.549"], "p1_2_xs": ["8.5405", "8.5415", "8.5425", "8.5435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{614}{4{,}200}, \\dfrac{620}{4{,}200}, \\dfrac{634}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{645}{4{,}200}, \\dfrac{652}{4{,}200}, \\dfrac{653}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{687}{4{,}200}, \\dfrac{690}{4{,}200}, \\dfrac{695}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0619"}}, {"seed": 620, "data": {"p1_how_many": "11", "p1_a": "8.41", "p1_b": "8.42", "p1_numbers": "8.4105, 8.411, 8.4115, 8.412, 8.413, 8.414, 8.415, 8.416, 8.417, 8.418, and 8.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.411", "8.412", "8.413", "8.414", "8.415000000000001", "8.416", "8.417", "8.418", "8.419"], "p1_2_xs": ["8.4105", "8.4115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{610}{1{,}500}, \\dfrac{618}{1{,}500}, \\dfrac{627}{1{,}500}, \\dfrac{695}{1{,}500}, \\dfrac{716}{1{,}500}, \\dfrac{745}{1{,}500}, \\dfrac{754}{1{,}500}, \\dfrac{761}{1{,}500}, \\dfrac{787}{1{,}500}, \\dfrac{828}{1{,}500}, \\dfrac{991}{1{,}500}, \\text{ and } \\dfrac{994}{1{,}500}", "__seed__": "0620"}}, {"seed": 621, "data": {"p1_how_many": "13", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{710}{4{,}200}, \\dfrac{719}{4{,}200}, \\dfrac{720}{4{,}200}, \\dfrac{777}{4{,}200}, \\dfrac{836}{4{,}200}, \\dfrac{916}{4{,}200}, \\dfrac{929}{4{,}200}, \\dfrac{982}{4{,}200}, \\dfrac{1{,}134}{4{,}200}, \\text{ and } \\dfrac{1{,}168}{4{,}200}", "__seed__": "0621"}}, {"seed": 622, "data": {"p1_how_many": "14", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.535, 4.54, 4.545, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995", "4.535", "4.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}771}{42{,}000}, \\dfrac{31{,}263}{42{,}000}, \\dfrac{31{,}665}{42{,}000}, \\dfrac{31{,}742}{42{,}000}, \\dfrac{33{,}233}{42{,}000}, \\dfrac{33{,}348}{42{,}000}, \\dfrac{34{,}046}{42{,}000}, \\dfrac{34{,}105}{42{,}000}, \\dfrac{34{,}455}{42{,}000}, \\dfrac{34{,}456}{42{,}000}, \\dfrac{34{,}481}{42{,}000}, \\text{ and } \\dfrac{34{,}799}{42{,}000}", "__seed__": "0622"}}, {"seed": 623, "data": {"p1_how_many": "14", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.645, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635", "1.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{512}{3{,}000}, \\dfrac{518}{3{,}000}, \\dfrac{523}{3{,}000}, \\dfrac{524}{3{,}000}, \\dfrac{533}{3{,}000}, \\dfrac{545}{3{,}000}, \\dfrac{564}{3{,}000}, \\dfrac{566}{3{,}000}, \\text{ and } \\dfrac{578}{3{,}000}", "__seed__": "0623"}}, {"seed": 624, "data": {"p1_how_many": "14", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.445, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435", "9.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}087}{20{,}000}, \\dfrac{4{,}188}{20{,}000}, \\dfrac{4{,}223}{20{,}000}, \\dfrac{4{,}338}{20{,}000}, \\dfrac{4{,}459}{20{,}000}, \\dfrac{4{,}487}{20{,}000}, \\dfrac{4{,}528}{20{,}000}, \\dfrac{4{,}631}{20{,}000}, \\dfrac{4{,}850}{20{,}000}, \\text{ and } \\dfrac{4{,}956}{20{,}000}", "__seed__": "0624"}}, {"seed": 625, "data": {"p1_how_many": "12", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}151}{5{,}600}, \\dfrac{2{,}174}{5{,}600}, \\dfrac{2{,}196}{5{,}600}, \\dfrac{2{,}210}{5{,}600}, \\dfrac{2{,}229}{5{,}600}, \\dfrac{2{,}231}{5{,}600}, \\dfrac{2{,}232}{5{,}600}, \\dfrac{2{,}310}{5{,}600}, \\dfrac{2{,}346}{5{,}600}, \\dfrac{2{,}358}{5{,}600}, \\text{ and } \\dfrac{2{,}370}{5{,}600}", "__seed__": "0625"}}, {"seed": 626, "data": {"p1_how_many": "10", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{73}{150}, \\dfrac{74}{150}, \\dfrac{77}{150}, \\dfrac{81}{150}, \\dfrac{85}{150}, \\dfrac{87}{150}, \\dfrac{96}{150}, \\text{ and } \\dfrac{98}{150}", "__seed__": "0626"}}, {"seed": 627, "data": {"p1_how_many": "14", "p1_a": "4.81", "p1_b": "4.82", "p1_numbers": "4.8105, 4.811, 4.8115, 4.812, 4.8125, 4.813, 4.8135, 4.814, 4.8145, 4.815, 4.816, 4.817, 4.818, and 4.819", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.811", "4.811999999999999", "4.813", "4.813999999999999", "4.8149999999999995", "4.816", "4.816999999999999", "4.818", "4.819"], "p1_2_xs": ["4.810499999999999", "4.8115", "4.812499999999999", "4.8134999999999994", "4.814499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}291}{7{,}700}, \\dfrac{4{,}304}{7{,}700}, \\dfrac{4{,}589}{7{,}700}, \\dfrac{4{,}811}{7{,}700}, \\dfrac{4{,}833}{7{,}700}, \\dfrac{5{,}007}{7{,}700}, \\text{ and } \\dfrac{5{,}723}{7{,}700}", "__seed__": "0627"}}, {"seed": 628, "data": {"p1_how_many": "11", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{409}{2{,}000}, \\dfrac{410}{2{,}000}, \\dfrac{413}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{427}{2{,}000}, \\dfrac{429}{2{,}000}, \\dfrac{455}{2{,}000}, \\dfrac{459}{2{,}000}, \\dfrac{477}{2{,}000}, \\dfrac{486}{2{,}000}, \\dfrac{497}{2{,}000}, \\text{ and } \\dfrac{499}{2{,}000}", "__seed__": "0628"}}, {"seed": 629, "data": {"p1_how_many": "10", "p1_a": "1.53", "p1_b": "1.54", "p1_numbers": "1.5305, 1.531, 1.532, 1.533, 1.534, 1.535, 1.536, 1.537, 1.538, and 1.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.531", "1.532", "1.533", "1.534", "1.535", "1.536", "1.537", "1.538", "1.539"], "p1_2_xs": ["1.5305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{720}{5{,}600}, \\dfrac{723}{5{,}600}, \\dfrac{734}{5{,}600}, \\dfrac{748}{5{,}600}, \\dfrac{757}{5{,}600}, \\dfrac{764}{5{,}600}, \\dfrac{786}{5{,}600}, \\text{ and } \\dfrac{793}{5{,}600}", "__seed__": "0629"}}, {"seed": 630, "data": {"p1_how_many": "13", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 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the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0634"}}, {"seed": 635, "data": {"p1_how_many": "12", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}449}{6{,}300}, \\dfrac{1{,}471}{6{,}300}, \\dfrac{1{,}574}{6{,}300}, \\dfrac{1{,}583}{6{,}300}, \\dfrac{1{,}605}{6{,}300}, \\dfrac{1{,}688}{6{,}300}, \\dfrac{1{,}693}{6{,}300}, \\text{ and } \\dfrac{1{,}773}{6{,}300}", "__seed__": "0635"}}, {"seed": 636, "data": {"p1_how_many": "14", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.1005, 5.101, 5.1015, 5.102, 5.1025, 5.103, 5.1035, 5.104, 5.1045, 5.105, 5.106, 5.107, 5.108, and 5.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.101", "5.101999999999999", "5.103", "5.103999999999999", "5.1049999999999995", "5.106", "5.106999999999999", "5.108", "5.109"], "p1_2_xs": ["5.100499999999999", "5.1015", "5.102499999999999", "5.1034999999999995", "5.104499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{606}{4{,}200}, \\dfrac{623}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{657}{4{,}200}, 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6.23, 6.24, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205", "6.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}439}{42{,}000}, \\dfrac{30{,}807}{42{,}000}, \\dfrac{30{,}869}{42{,}000}, \\dfrac{30{,}965}{42{,}000}, \\dfrac{31{,}725}{42{,}000}, \\dfrac{31{,}815}{42{,}000}, \\dfrac{32{,}123}{42{,}000}, \\dfrac{32{,}185}{42{,}000}, \\dfrac{32{,}671}{42{,}000}, \\dfrac{32{,}737}{42{,}000}, \\text{ and } \\dfrac{34{,}340}{42{,}000}", "__seed__": "0639"}}, {"seed": 640, "data": {"p1_how_many": "14", "p1_a": "7.16", "p1_b": "7.17", "p1_numbers": "7.1605, 7.161, 7.1615, 7.162, 7.1625, 7.163, 7.1635, 7.164, 7.1645, 7.165, 7.166, 7.167, 7.168, and 7.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.1610000000000005", "7.162", "7.163", "7.164", "7.165", "7.166", "7.167", "7.168", "7.1690000000000005"], "p1_2_xs": ["7.1605", "7.1615", "7.1625", "7.1635", "7.164499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}075}{20{,}000}, \\dfrac{4{,}149}{20{,}000}, \\dfrac{4{,}269}{20{,}000}, \\dfrac{4{,}352}{20{,}000}, \\dfrac{4{,}399}{20{,}000}, \\dfrac{4{,}631}{20{,}000}, \\dfrac{4{,}794}{20{,}000}, \\dfrac{4{,}886}{20{,}000}, \\text{ and } \\dfrac{4{,}970}{20{,}000}", "__seed__": "0640"}}, {"seed": 641, "data": {"p1_how_many": "13", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.535, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995", "6.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{123}{200}, \\dfrac{130}{200}, \\dfrac{133}{200}, \\dfrac{135}{200}, \\dfrac{136}{200}, \\dfrac{143}{200}, \\dfrac{146}{200}, \\text{ and } \\dfrac{147}{200}", "__seed__": "0641"}}, {"seed": 642, "data": {"p1_how_many": "13", "p1_a": "5.8", "p1_b": "5.9", "p1_numbers": "5.8005, 5.801, 5.8015, 5.802, 5.8025, 5.803, 5.8035, 5.804, 5.805, 5.806, 5.807, 5.808, and 5.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.801", "5.802", "5.803", "5.803999999999999", "5.805", "5.806", "5.8069999999999995", "5.808", "5.809"], "p1_2_xs": ["5.8004999999999995", "5.8015", "5.802499999999999", "5.8035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}405}{3{,}000}, \\dfrac{2{,}444}{3{,}000}, \\dfrac{2{,}460}{3{,}000}, \\dfrac{2{,}466}{3{,}000}, \\dfrac{2{,}471}{3{,}000}, \\dfrac{2{,}479}{3{,}000}, \\dfrac{2{,}484}{3{,}000}, \\dfrac{2{,}491}{3{,}000}, \\text{ and } \\dfrac{2{,}498}{3{,}000}", "__seed__": "0642"}}, {"seed": 643, "data": {"p1_how_many": "13", "p1_a": "4.25", "p1_b": "4.26", "p1_numbers": "4.2505, 4.251, 4.2515, 4.252, 4.2525, 4.253, 4.2535, 4.254, 4.255, 4.256, 4.257, 4.258, and 4.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.251", "4.252", "4.253", "4.254", "4.255", "4.256", "4.257", "4.258", "4.259"], "p1_2_xs": ["4.2505", "4.2515", "4.2524999999999995", "4.2535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}213}{12{,}000}, \\dfrac{3{,}440}{12{,}000}, \\dfrac{3{,}448}{12{,}000}, \\dfrac{3{,}455}{12{,}000}, \\dfrac{3{,}656}{12{,}000}, \\dfrac{3{,}865}{12{,}000}, \\dfrac{3{,}899}{12{,}000}, \\text{ and } \\dfrac{3{,}974}{12{,}000}", "__seed__": "0643"}}, {"seed": 644, "data": {"p1_how_many": "11", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.215, 6.22, 6.23, 6.24, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205", "6.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}219}{2{,}000}, \\dfrac{1{,}275}{2{,}000}, \\dfrac{1{,}279}{2{,}000}, \\dfrac{1{,}340}{2{,}000}, \\dfrac{1{,}341}{2{,}000}, \\dfrac{1{,}353}{2{,}000}, \\dfrac{1{,}411}{2{,}000}, \\dfrac{1{,}448}{2{,}000}, \\dfrac{1{,}454}{2{,}000}, \\text{ and } \\dfrac{1{,}497}{2{,}000}", "__seed__": "0644"}}, {"seed": 645, "data": {"p1_how_many": "10", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.02, 9.03, 9.04, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}434}{63{,}000}, \\dfrac{29{,}295}{63{,}000}, \\dfrac{31{,}429}{63{,}000}, \\dfrac{31{,}455}{63{,}000}, \\dfrac{32{,}604}{63{,}000}, \\dfrac{32{,}777}{63{,}000}, \\dfrac{33{,}316}{63{,}000}, \\dfrac{33{,}761}{63{,}000}, \\dfrac{34{,}296}{63{,}000}, \\dfrac{34{,}313}{63{,}000}, \\dfrac{34{,}567}{63{,}000}, \\text{ and } \\dfrac{35{,}141}{63{,}000}", "__seed__": "0645"}}, {"seed": 646, "data": {"p1_how_many": "13", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.335, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999", "7.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}299}{42{,}000}, \\dfrac{35{,}331}{42{,}000}, \\dfrac{35{,}372}{42{,}000}, \\dfrac{35{,}448}{42{,}000}, \\dfrac{35{,}638}{42{,}000}, \\dfrac{35{,}672}{42{,}000}, \\text{ and } \\dfrac{35{,}858}{42{,}000}", "__seed__": "0646"}}, {"seed": 647, "data": {"p1_how_many": "12", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.705, 5.71, 5.715, 5.72, 5.725, 5.73, 5.74, 5.75, 5.76, 5.77, 5.78, and 5.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.71", "5.72", "5.73", "5.74", "5.75", "5.76", "5.7700000000000005", "5.78", "5.79"], "p1_2_xs": ["5.705", "5.715", "5.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}102}{30{,}000}, \\dfrac{24{,}114}{30{,}000}, \\dfrac{24{,}148}{30{,}000}, \\dfrac{24{,}343}{30{,}000}, \\dfrac{24{,}434}{30{,}000}, \\dfrac{24{,}480}{30{,}000}, \\dfrac{24{,}517}{30{,}000}, \\dfrac{24{,}604}{30{,}000}, \\text{ and } \\dfrac{24{,}626}{30{,}000}", "__seed__": "0647"}}, {"seed": 648, "data": {"p1_how_many": "11", "p1_a": "8.03", "p1_b": "8.04", "p1_numbers": "8.0305, 8.031, 8.0315, 8.032, 8.033, 8.034, 8.035, 8.036, 8.037, 8.038, and 8.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.030999999999999", "8.032", "8.033", "8.033999999999999", "8.035", "8.036", "8.036999999999999", "8.037999999999998", "8.039"], "p1_2_xs": ["8.0305", "8.0315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}238}{56{,}000}, \\dfrac{16{,}807}{56{,}000}, \\dfrac{16{,}946}{56{,}000}, \\dfrac{16{,}979}{56{,}000}, \\dfrac{17{,}095}{56{,}000}, \\dfrac{18{,}208}{56{,}000}, \\dfrac{19{,}237}{56{,}000}, \\dfrac{20{,}063}{56{,}000}, \\text{ and } \\dfrac{20{,}426}{56{,}000}", "__seed__": "0648"}}, {"seed": 649, "data": {"p1_how_many": "14", "p1_a": "6.34", "p1_b": "6.35", "p1_numbers": "6.3405, 6.341, 6.3415, 6.342, 6.3425, 6.343, 6.3435, 6.344, 6.3445, 6.345, 6.346, 6.347, 6.348, and 6.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.341", "6.342", "6.343", "6.343999999999999", "6.345", "6.346", "6.3469999999999995", "6.348", "6.349"], "p1_2_xs": ["6.3405", "6.3415", "6.342499999999999", "6.3435", "6.344499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}021}{12{,}000}, \\dfrac{8{,}197}{12{,}000}, \\dfrac{8{,}358}{12{,}000}, \\dfrac{8{,}400}{12{,}000}, \\dfrac{8{,}520}{12{,}000}, \\dfrac{8{,}626}{12{,}000}, \\dfrac{8{,}743}{12{,}000}, \\dfrac{8{,}764}{12{,}000}, \\dfrac{8{,}895}{12{,}000}, \\dfrac{8{,}910}{12{,}000}, \\text{ and } \\dfrac{8{,}976}{12{,}000}", "__seed__": "0649"}}, {"seed": 650, "data": {"p1_how_many": "14", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.135, 8.14, 8.145, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125", "8.135", "8.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{97}{630}, \\dfrac{104}{630}, \\dfrac{106}{630}, \\dfrac{110}{630}, \\dfrac{111}{630}, \\dfrac{117}{630}, \\dfrac{126}{630}, \\dfrac{129}{630}, \\text{ and } \\dfrac{136}{630}", "__seed__": "0650"}}, {"seed": 651, "data": {"p1_how_many": "10", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.705, 5.71, 5.72, 5.73, 5.74, 5.75, 5.76, 5.77, 5.78, and 5.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.71", "5.72", "5.73", "5.74", "5.75", "5.76", "5.7700000000000005", "5.78", "5.79"], "p1_2_xs": ["5.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}706}{6{,}300}, \\dfrac{2{,}712}{6{,}300}, \\dfrac{2{,}720}{6{,}300}, \\dfrac{2{,}736}{6{,}300}, \\dfrac{2{,}755}{6{,}300}, \\dfrac{2{,}767}{6{,}300}, \\text{ and } \\dfrac{2{,}781}{6{,}300}", "__seed__": "0651"}}, {"seed": 652, "data": {"p1_how_many": "11", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}005}{42{,}000}, \\dfrac{6{,}062}{42{,}000}, \\dfrac{6{,}169}{42{,}000}, \\dfrac{6{,}283}{42{,}000}, \\dfrac{6{,}328}{42{,}000}, \\dfrac{6{,}382}{42{,}000}, \\dfrac{6{,}520}{42{,}000}, \\dfrac{6{,}809}{42{,}000}, \\text{ and } \\dfrac{6{,}920}{42{,}000}", "__seed__": "0652"}}, {"seed": 653, "data": {"p1_how_many": "10", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}536}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}560}{4{,}200}, \\dfrac{3{,}575}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0653"}}, {"seed": 654, "data": 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"data": {"p1_how_many": "10", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.72, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{78}{420}, \\dfrac{83}{420}, \\dfrac{87}{420}, \\dfrac{106}{420}, \\dfrac{110}{420}, \\dfrac{111}{420}, \\text{ and } \\dfrac{115}{420}", "__seed__": "0655"}}, {"seed": 656, "data": {"p1_how_many": "12", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}134}{35{,}000}, \\dfrac{14{,}197}{35{,}000}, \\dfrac{14{,}615}{35{,}000}, \\dfrac{14{,}679}{35{,}000}, \\dfrac{14{,}709}{35{,}000}, \\dfrac{14{,}788}{35{,}000}, \\text{ and } \\dfrac{14{,}937}{35{,}000}", "__seed__": "0656"}}, {"seed": 657, "data": {"p1_how_many": "14", "p1_a": "4.67", "p1_b": "4.68", "p1_numbers": "4.6705, 4.671, 4.6715, 4.672, 4.6725, 4.673, 4.6735, 4.674, 4.6745, 4.675, 4.676, 4.677, 4.678, and 4.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.671", "4.672", "4.673", "4.6739999999999995", "4.675", "4.676", "4.677", "4.678", "4.679"], "p1_2_xs": ["4.6705", "4.6715", "4.672499999999999", "4.6735", "4.674499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}804}{6{,}300}, \\dfrac{2{,}810}{6{,}300}, \\dfrac{2{,}872}{6{,}300}, \\dfrac{2{,}945}{6{,}300}, \\dfrac{3{,}119}{6{,}300}, \\dfrac{3{,}151}{6{,}300}, \\dfrac{3{,}278}{6{,}300}, \\dfrac{3{,}352}{6{,}300}, \\dfrac{3{,}371}{6{,}300}, \\dfrac{3{,}403}{6{,}300}, \\dfrac{3{,}458}{6{,}300}, \\text{ and } \\dfrac{3{,}524}{6{,}300}", "__seed__": "0657"}}, {"seed": 658, "data": {"p1_how_many": "12", "p1_a": "7.06", "p1_b": "7.07", "p1_numbers": "7.0605, 7.061, 7.0615, 7.062, 7.0625, 7.063, 7.064, 7.065, 7.066, 7.067, 7.068, and 7.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.061", "7.061999999999999", "7.063", "7.063999999999999", "7.0649999999999995", "7.066", "7.066999999999999", "7.068", "7.069"], "p1_2_xs": ["7.060499999999999", "7.0615", "7.062499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{150}, \\dfrac{52}{150}, \\dfrac{53}{150}, \\dfrac{54}{150}, \\dfrac{55}{150}, \\dfrac{57}{150}, \\dfrac{58}{150}, \\text{ and } \\dfrac{59}{150}", "__seed__": "0658"}}, {"seed": 659, "data": {"p1_how_many": "11", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}031}{3{,}500}, \\dfrac{2{,}060}{3{,}500}, \\dfrac{2{,}107}{3{,}500}, \\dfrac{2{,}163}{3{,}500}, \\dfrac{2{,}166}{3{,}500}, \\dfrac{2{,}169}{3{,}500}, \\dfrac{2{,}316}{3{,}500}, \\dfrac{2{,}503}{3{,}500}, \\dfrac{2{,}660}{3{,}500}, \\dfrac{2{,}685}{3{,}500}, \\text{ and } \\dfrac{2{,}730}{3{,}500}", "__seed__": "0659"}}, {"seed": 660, "data": {"p1_how_many": "13", "p1_a": "8.67", "p1_b": "8.68", "p1_numbers": "8.6705, 8.671, 8.6715, 8.672, 8.6725, 8.673, 8.6735, 8.674, 8.675, 8.676, 8.677, 8.678, and 8.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.671", "8.672", "8.673", "8.674", "8.675", "8.676", "8.677", "8.677999999999999", "8.679"], "p1_2_xs": ["8.6705", "8.6715", "8.672500000000001", "8.6735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}863}{6{,}300}, \\dfrac{2{,}946}{6{,}300}, \\dfrac{2{,}961}{6{,}300}, \\dfrac{2{,}991}{6{,}300}, \\dfrac{3{,}038}{6{,}300}, \\dfrac{3{,}137}{6{,}300}, \\dfrac{3{,}194}{6{,}300}, \\dfrac{3{,}336}{6{,}300}, \\dfrac{3{,}350}{6{,}300}, \\dfrac{3{,}354}{6{,}300}, \\dfrac{3{,}387}{6{,}300}, \\text{ and } \\dfrac{3{,}499}{6{,}300}", "__seed__": "0660"}}, {"seed": 661, "data": {"p1_how_many": "11", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{31{,}324}{42{,}000}, \\dfrac{31{,}452}{42{,}000}, \\dfrac{31{,}721}{42{,}000}, \\dfrac{31{,}829}{42{,}000}, \\dfrac{32{,}110}{42{,}000}, \\dfrac{32{,}383}{42{,}000}, \\dfrac{32{,}984}{42{,}000}, \\dfrac{33{,}121}{42{,}000}, \\dfrac{33{,}692}{42{,}000}, \\dfrac{33{,}940}{42{,}000}, \\dfrac{33{,}972}{42{,}000}, \\text{ and } \\dfrac{34{,}308}{42{,}000}", "__seed__": "0661"}}, {"seed": 662, "data": {"p1_how_many": "11", "p1_a": "8.91", "p1_b": "8.92", "p1_numbers": "8.9105, 8.911, 8.9115, 8.912, 8.913, 8.914, 8.915, 8.916, 8.917, 8.918, and 8.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.911", "8.912", "8.913", "8.914", "8.915000000000001", "8.916", "8.917", "8.918", "8.919"], "p1_2_xs": ["8.9105", "8.9115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}498}{6{,}300}, \\dfrac{1{,}599}{6{,}300}, \\dfrac{1{,}607}{6{,}300}, \\dfrac{1{,}619}{6{,}300}, \\dfrac{1{,}640}{6{,}300}, \\dfrac{1{,}690}{6{,}300}, \\dfrac{1{,}731}{6{,}300}, \\text{ and } \\dfrac{1{,}732}{6{,}300}", "__seed__": "0662"}}, {"seed": 663, "data": {"p1_how_many": "14", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.345, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315", "1.325", "1.335", "1.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{502}{3{,}000}, \\dfrac{515}{3{,}000}, \\dfrac{534}{3{,}000}, \\dfrac{536}{3{,}000}, \\dfrac{539}{3{,}000}, \\dfrac{546}{3{,}000}, \\dfrac{559}{3{,}000}, \\dfrac{567}{3{,}000}, \\text{ and } \\dfrac{590}{3{,}000}", "__seed__": "0663"}}, {"seed": 664, "data": {"p1_how_many": "10", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{162}{560}, \\dfrac{174}{560}, \\dfrac{179}{560}, \\dfrac{205}{560}, \\dfrac{206}{560}, \\dfrac{207}{560}, \\text{ and } \\dfrac{209}{560}", "__seed__": "0664"}}, {"seed": 665, "data": {"p1_how_many": "13", "p1_a": "4.71", "p1_b": "4.72", "p1_numbers": "4.7105, 4.711, 4.7115, 4.712, 4.7125, 4.713, 4.7135, 4.714, 4.715, 4.716, 4.717, 4.718, and 4.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.711", "4.712", "4.713", "4.7139999999999995", "4.715", "4.716", "4.717", "4.718", "4.719"], "p1_2_xs": ["4.7105", "4.7115", "4.7124999999999995", "4.7135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}033}{56{,}000}, \\dfrac{16{,}087}{56{,}000}, \\dfrac{17{,}070}{56{,}000}, \\dfrac{17{,}333}{56{,}000}, \\dfrac{17{,}661}{56{,}000}, \\dfrac{18{,}633}{56{,}000}, \\dfrac{19{,}058}{56{,}000}, \\dfrac{19{,}225}{56{,}000}, \\dfrac{19{,}675}{56{,}000}, \\dfrac{20{,}017}{56{,}000}, \\dfrac{20{,}247}{56{,}000}, \\text{ and } \\dfrac{20{,}359}{56{,}000}", "__seed__": "0665"}}, {"seed": 666, "data": {"p1_how_many": "11", "p1_a": "4.0", "p1_b": "4.1", "p1_numbers": "4.005, 4.01, 4.015, 4.02, 4.03, 4.04, 4.05, 4.06, 4.07, 4.08, and 4.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.01", "4.02", "4.03", "4.04", "4.05", "4.06", "4.07", "4.08", "4.09"], "p1_2_xs": ["4.005", "4.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{31}{120}, \\dfrac{32}{120}, \\dfrac{33}{120}, \\dfrac{35}{120}, \\dfrac{36}{120}, \\dfrac{37}{120}, \\dfrac{38}{120}, \\text{ and } \\dfrac{39}{120}", "__seed__": "0666"}}, {"seed": 667, "data": {"p1_how_many": "12", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}091}{35{,}000}, \\dfrac{7{,}196}{35{,}000}, \\dfrac{7{,}211}{35{,}000}, \\dfrac{7{,}429}{35{,}000}, \\dfrac{7{,}552}{35{,}000}, \\dfrac{7{,}769}{35{,}000}, \\dfrac{8{,}357}{35{,}000}, \\dfrac{8{,}786}{35{,}000}, \\dfrac{9{,}102}{35{,}000}, \\text{ and } \\dfrac{9{,}160}{35{,}000}", "__seed__": "0667"}}, {"seed": 668, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{21{,}002}{35{,}000}, \\dfrac{21{,}273}{35{,}000}, \\dfrac{21{,}347}{35{,}000}, \\dfrac{21{,}617}{35{,}000}, \\dfrac{21{,}925}{35{,}000}, \\dfrac{22{,}181}{35{,}000}, \\dfrac{22{,}844}{35{,}000}, \\dfrac{23{,}106}{35{,}000}, \\dfrac{25{,}376}{35{,}000}, \\dfrac{26{,}323}{35{,}000}, \\dfrac{26{,}336}{35{,}000}, \\text{ and } \\dfrac{27{,}480}{35{,}000}", "__seed__": "0668"}}, {"seed": 669, "data": {"p1_how_many": "14", "p1_a": "8.8", "p1_b": "8.9", "p1_numbers": "8.8005, 8.801, 8.8015, 8.802, 8.8025, 8.803, 8.8035, 8.804, 8.8045, 8.805, 8.806, 8.807, 8.808, and 8.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.801", "8.802000000000001", "8.803", "8.804", "8.805000000000001", "8.806000000000001", "8.807", "8.808", "8.809000000000001"], "p1_2_xs": ["8.800500000000001", "8.8015", "8.802500000000002", "8.803500000000001", "8.8045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}015}{4{,}200}, \\dfrac{3{,}193}{4{,}200}, \\dfrac{3{,}230}{4{,}200}, \\dfrac{3{,}276}{4{,}200}, \\dfrac{3{,}324}{4{,}200}, \\dfrac{3{,}341}{4{,}200}, \\dfrac{3{,}368}{4{,}200}, \\dfrac{3{,}374}{4{,}200}, \\dfrac{3{,}403}{4{,}200}, \\dfrac{3{,}419}{4{,}200}, \\dfrac{3{,}490}{4{,}200}, \\text{ and } \\dfrac{3{,}493}{4{,}200}", "__seed__": "0669"}}, {"seed": 670, "data": {"p1_how_many": "11", "p1_a": "8.66", "p1_b": "8.67", "p1_numbers": "8.6605, 8.661, 8.6615, 8.662, 8.663, 8.664, 8.665, 8.666, 8.667, 8.668, and 8.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.661", "8.662", "8.663", "8.664", "8.665000000000001", "8.666", "8.667", "8.668", "8.669"], "p1_2_xs": ["8.6605", "8.6615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}038}{3{,}500}, \\dfrac{1{,}050}{3{,}500}, \\dfrac{1{,}052}{3{,}500}, \\dfrac{1{,}089}{3{,}500}, \\dfrac{1{,}161}{3{,}500}, \\dfrac{1{,}186}{3{,}500}, \\dfrac{1{,}244}{3{,}500}, \\dfrac{1{,}245}{3{,}500}, \\dfrac{1{,}284}{3{,}500}, \\dfrac{1{,}309}{3{,}500}, \\dfrac{1{,}324}{3{,}500}, \\text{ and } \\dfrac{1{,}396}{3{,}500}", "__seed__": "0670"}}, {"seed": 671, "data": {"p1_how_many": "11", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.03, 3.04, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{502}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{547}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{565}{1{,}500}, \\dfrac{585}{1{,}500}, \\text{ and } \\dfrac{591}{1{,}500}", "__seed__": "0671"}}, {"seed": 672, "data": {"p1_how_many": "14", "p1_a": "5.55", "p1_b": "5.56", "p1_numbers": "5.5505, 5.551, 5.5515, 5.552, 5.5525, 5.553, 5.5535, 5.554, 5.5545, 5.555, 5.556, 5.557, 5.558, and 5.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.551", "5.552", "5.553", "5.553999999999999", "5.555", "5.556", "5.5569999999999995", "5.558", "5.559"], "p1_2_xs": ["5.5504999999999995", "5.5515", "5.552499999999999", "5.5535", "5.554499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}119}{20{,}000}, \\dfrac{15{,}335}{20{,}000}, \\dfrac{15{,}466}{20{,}000}, \\dfrac{15{,}470}{20{,}000}, \\dfrac{15{,}492}{20{,}000}, \\dfrac{15{,}581}{20{,}000}, \\dfrac{15{,}649}{20{,}000}, \\dfrac{15{,}796}{20{,}000}, \\dfrac{15{,}983}{20{,}000}, \\text{ and } \\dfrac{15{,}985}{20{,}000}", "__seed__": "0672"}}, {"seed": 673, "data": {"p1_how_many": "12", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}015}{3{,}500}, \\dfrac{1{,}049}{3{,}500}, \\dfrac{1{,}055}{3{,}500}, \\dfrac{1{,}072}{3{,}500}, \\dfrac{1{,}090}{3{,}500}, \\dfrac{1{,}148}{3{,}500}, \\dfrac{1{,}154}{3{,}500}, \\dfrac{1{,}219}{3{,}500}, \\dfrac{1{,}262}{3{,}500}, \\dfrac{1{,}351}{3{,}500}, \\text{ and } \\dfrac{1{,}368}{3{,}500}", "__seed__": "0673"}}, {"seed": 674, "data": {"p1_how_many": "12", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.625, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998", "2.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{620}{4{,}200}, \\dfrac{622}{4{,}200}, \\dfrac{627}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{643}{4{,}200}, \\dfrac{661}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{680}{4{,}200}, \\text{ and } \\dfrac{682}{4{,}200}", "__seed__": "0674"}}, {"seed": 675, "data": {"p1_how_many": "12", "p1_a": "2.2", "p1_b": "2.3", "p1_numbers": "2.205, 2.21, 2.215, 2.22, 2.225, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, and 2.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.21", "2.22", "2.23", "2.24", "2.25", "2.2600000000000002", "2.27", "2.2800000000000002", "2.29"], "p1_2_xs": ["2.205", "2.215", "2.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{31{,}308}{42{,}000}, \\dfrac{31{,}375}{42{,}000}, \\dfrac{32{,}177}{42{,}000}, \\dfrac{32{,}219}{42{,}000}, \\dfrac{32{,}262}{42{,}000}, \\dfrac{32{,}690}{42{,}000}, \\dfrac{33{,}164}{42{,}000}, \\dfrac{33{,}562}{42{,}000}, \\dfrac{33{,}825}{42{,}000}, \\text{ and } \\dfrac{34{,}307}{42{,}000}", "__seed__": "0675"}}, {"seed": 676, "data": {"p1_how_many": "12", "p1_a": "3.01", "p1_b": "3.02", "p1_numbers": "3.0105, 3.011, 3.0115, 3.012, 3.0125, 3.013, 3.014, 3.015, 3.016, 3.017, 3.018, and 3.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.0109999999999997", "3.0119999999999996", "3.013", "3.014", "3.0149999999999997", "3.0159999999999996", "3.017", "3.018", "3.0189999999999997"], "p1_2_xs": ["3.0105", "3.0115", "3.0124999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}149}{15{,}000}, \\dfrac{5{,}233}{15{,}000}, \\dfrac{5{,}264}{15{,}000}, \\dfrac{5{,}323}{15{,}000}, \\dfrac{5{,}342}{15{,}000}, \\dfrac{5{,}595}{15{,}000}, \\dfrac{5{,}630}{15{,}000}, \\dfrac{5{,}706}{15{,}000}, \\dfrac{5{,}784}{15{,}000}, \\dfrac{5{,}805}{15{,}000}, \\text{ and } \\dfrac{5{,}816}{15{,}000}", "__seed__": "0676"}}, {"seed": 677, "data": {"p1_how_many": "13", "p1_a": "9.94", "p1_b": "9.95", "p1_numbers": "9.9405, 9.941, 9.9415, 9.942, 9.9425, 9.943, 9.9435, 9.944, 9.945, 9.946, 9.947, 9.948, and 9.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.940999999999999", "9.942", "9.943", "9.943999999999999", "9.945", "9.946", "9.947", "9.947999999999999", "9.949"], "p1_2_xs": ["9.9405", "9.9415", "9.9425", "9.9435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{285}{630}, \\dfrac{299}{630}, \\dfrac{304}{630}, \\dfrac{314}{630}, \\dfrac{330}{630}, \\dfrac{337}{630}, \\dfrac{341}{630}, \\dfrac{344}{630}, \\text{ and } \\dfrac{351}{630}", "__seed__": "0677"}}, {"seed": 678, "data": {"p1_how_many": "13", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.735, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725", "8.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{403}{2{,}000}, \\dfrac{417}{2{,}000}, \\dfrac{422}{2{,}000}, \\dfrac{430}{2{,}000}, \\dfrac{447}{2{,}000}, \\dfrac{448}{2{,}000}, \\dfrac{450}{2{,}000}, \\dfrac{470}{2{,}000}, \\dfrac{484}{2{,}000}, \\dfrac{490}{2{,}000}, \\dfrac{493}{2{,}000}, \\text{ and } \\dfrac{495}{2{,}000}", "__seed__": "0678"}}, {"seed": 679, "data": {"p1_how_many": "14", "p1_a": "3.56", "p1_b": "3.57", "p1_numbers": "3.5605, 3.561, 3.5615, 3.562, 3.5625, 3.563, 3.5635, 3.564, 3.5645, 3.565, 3.566, 3.567, 3.568, and 3.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.561", "3.562", "3.563", "3.564", "3.565", "3.566", "3.567", "3.568", "3.569"], "p1_2_xs": ["3.5605", "3.5615", "3.5625", "3.5635000000000003", "3.5645000000000002"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}246}{2{,}000}, \\dfrac{1{,}257}{2{,}000}, \\dfrac{1{,}268}{2{,}000}, \\dfrac{1{,}270}{2{,}000}, \\dfrac{1{,}317}{2{,}000}, \\dfrac{1{,}318}{2{,}000}, \\dfrac{1{,}340}{2{,}000}, \\dfrac{1{,}384}{2{,}000}, \\dfrac{1{,}453}{2{,}000}, \\text{ and } \\dfrac{1{,}463}{2{,}000}", "__seed__": "0679"}}, {"seed": 680, "data": {"p1_how_many": "11", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}413}{7{,}700}, \\dfrac{4{,}590}{7{,}700}, \\dfrac{4{,}848}{7{,}700}, \\dfrac{4{,}854}{7{,}700}, \\dfrac{5{,}318}{7{,}700}, \\dfrac{5{,}488}{7{,}700}, \\dfrac{5{,}502}{7{,}700}, \\dfrac{5{,}866}{7{,}700}, \\dfrac{6{,}210}{7{,}700}, \\dfrac{6{,}388}{7{,}700}, \\dfrac{6{,}397}{7{,}700}, \\text{ and } \\dfrac{6{,}515}{7{,}700}", "__seed__": "0680"}}, {"seed": 681, "data": {"p1_how_many": "10", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.22, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers 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"p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.561", "6.561999999999999", "6.563", "6.563999999999999", "6.5649999999999995", "6.566", "6.566999999999999", "6.568", "6.569"], "p1_2_xs": ["6.560499999999999", "6.5615", "6.562499999999999", "6.5634999999999994", "6.564499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0690"}}, {"seed": 691, "data": {"p1_how_many": "10", "p1_a": "4.37", "p1_b": "4.38", "p1_numbers": "4.3705, 4.371, 4.372, 4.373, 4.374, 4.375, 4.376, 4.377, 4.378, and 4.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.371", "4.372", "4.373", "4.374", "4.375", "4.376", "4.377", "4.378", 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"p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}063}{56{,}000}, \\dfrac{17{,}061}{56{,}000}, \\dfrac{17{,}374}{56{,}000}, \\dfrac{18{,}068}{56{,}000}, \\dfrac{18{,}802}{56{,}000}, \\dfrac{19{,}176}{56{,}000}, \\dfrac{19{,}320}{56{,}000}, \\text{ and } \\dfrac{20{,}591}{56{,}000}", "__seed__": "0692"}}, {"seed": 693, "data": {"p1_how_many": "12", "p1_a": "3.26", "p1_b": "3.27", "p1_numbers": "3.2605, 3.261, 3.2615, 3.262, 3.2625, 3.263, 3.264, 3.265, 3.266, 3.267, 3.268, and 3.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.2609999999999997", "3.2619999999999996", "3.263", "3.264", "3.2649999999999997", "3.2659999999999996", "3.267", "3.268", "3.2689999999999997"], "p1_2_xs": ["3.2605", "3.2615", "3.2624999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}071}{15{,}000}, \\dfrac{5{,}152}{15{,}000}, \\dfrac{5{,}245}{15{,}000}, \\dfrac{5{,}287}{15{,}000}, \\dfrac{5{,}443}{15{,}000}, \\dfrac{5{,}562}{15{,}000}, \\dfrac{5{,}586}{15{,}000}, \\dfrac{5{,}598}{15{,}000}, \\dfrac{5{,}642}{15{,}000}, \\dfrac{5{,}826}{15{,}000}, \\text{ and } \\dfrac{5{,}846}{15{,}000}", "__seed__": "0693"}}, {"seed": 694, "data": {"p1_how_many": "14", "p1_a": "1.73", "p1_b": "1.74", "p1_numbers": "1.7305, 1.731, 1.7315, 1.732, 1.7325, 1.733, 1.7335, 1.734, 1.7345, 1.735, 1.736, 1.737, 1.738, and 1.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.7309999999999999", "1.732", "1.7329999999999999", "1.734", "1.7349999999999999", "1.736", "1.7369999999999999", "1.738", "1.7389999999999999"], "p1_2_xs": ["1.7305", "1.7314999999999998", "1.7325", "1.7334999999999998", "1.7345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}196}{35{,}000}, \\dfrac{20{,}813}{35{,}000}, \\dfrac{21{,}191}{35{,}000}, \\dfrac{22{,}386}{35{,}000}, \\dfrac{23{,}069}{35{,}000}, \\dfrac{23{,}880}{35{,}000}, \\dfrac{23{,}895}{35{,}000}, \\dfrac{25{,}169}{35{,}000}, \\dfrac{25{,}812}{35{,}000}, \\dfrac{26{,}172}{35{,}000}, \\dfrac{26{,}465}{35{,}000}, \\text{ and } \\dfrac{27{,}521}{35{,}000}", "__seed__": "0694"}}, {"seed": 695, "data": {"p1_how_many": "14", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.025, 6.03, 6.035, 6.04, 6.045, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015", "6.0249999999999995", "6.035", "6.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}250}{5{,}600}, \\dfrac{3{,}315}{5{,}600}, \\dfrac{3{,}317}{5{,}600}, \\dfrac{3{,}344}{5{,}600}, \\dfrac{3{,}433}{5{,}600}, \\dfrac{3{,}452}{5{,}600}, \\dfrac{3{,}473}{5{,}600}, \\text{ and } \\dfrac{3{,}481}{5{,}600}", "__seed__": "0695"}}, {"seed": 696, "data": {"p1_how_many": "12", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.74, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}025}{15{,}000}, \\dfrac{5{,}181}{15{,}000}, \\dfrac{5{,}414}{15{,}000}, \\dfrac{5{,}665}{15{,}000}, \\dfrac{5{,}674}{15{,}000}, \\dfrac{5{,}695}{15{,}000}, \\dfrac{5{,}701}{15{,}000}, \\dfrac{5{,}753}{15{,}000}, \\dfrac{5{,}806}{15{,}000}, \\text{ and } \\dfrac{5{,}872}{15{,}000}", "__seed__": "0696"}}, {"seed": 697, "data": {"p1_how_many": "14", "p1_a": "4.05", "p1_b": "4.06", "p1_numbers": "4.0505, 4.051, 4.0515, 4.052, 4.0525, 4.053, 4.0535, 4.054, 4.0545, 4.055, 4.056, 4.057, 4.058, and 4.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.051", "4.052", "4.053", "4.053999999999999", "4.055", "4.056", "4.0569999999999995", "4.058", "4.059"], "p1_2_xs": ["4.0504999999999995", "4.0515", "4.052499999999999", "4.0535", "4.054499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}821}{5{,}600}, \\dfrac{4{,}829}{5{,}600}, \\dfrac{4{,}845}{5{,}600}, \\dfrac{4{,}847}{5{,}600}, \\dfrac{4{,}863}{5{,}600}, \\dfrac{4{,}867}{5{,}600}, \\dfrac{4{,}875}{5{,}600}, \\dfrac{4{,}886}{5{,}600}, \\dfrac{4{,}893}{5{,}600}, \\dfrac{4{,}894}{5{,}600}, \\text{ and } \\dfrac{4{,}896}{5{,}600}", "__seed__": "0697"}}, {"seed": 698, "data": {"p1_how_many": "14", "p1_a": "9.24", "p1_b": "9.25", "p1_numbers": "9.2405, 9.241, 9.2415, 9.242, 9.2425, 9.243, 9.2435, 9.244, 9.2445, 9.245, 9.246, 9.247, 9.248, and 9.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.241", "9.242", "9.243", "9.244", "9.245000000000001", "9.246", "9.247", "9.248", "9.249"], "p1_2_xs": ["9.2405", "9.2415", "9.242500000000001", "9.243500000000001", "9.2445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{324}{1{,}200}, \\dfrac{334}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{371}{1{,}200}, \\dfrac{387}{1{,}200}, \\dfrac{390}{1{,}200}, \\text{ and } \\dfrac{397}{1{,}200}", "__seed__": "0698"}}, {"seed": 699, "data": {"p1_how_many": "12", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.725, 4.73, 4.74, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715", "4.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}256}{3{,}500}, \\dfrac{2{,}272}{3{,}500}, \\dfrac{2{,}302}{3{,}500}, \\dfrac{2{,}383}{3{,}500}, \\dfrac{2{,}469}{3{,}500}, \\dfrac{2{,}584}{3{,}500}, \\dfrac{2{,}655}{3{,}500}, \\text{ and } \\dfrac{2{,}725}{3{,}500}", "__seed__": "0699"}}, {"seed": 700, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}067}{42{,}000}, \\dfrac{35{,}071}{42{,}000}, \\dfrac{35{,}166}{42{,}000}, \\dfrac{35{,}169}{42{,}000}, \\dfrac{35{,}265}{42{,}000}, \\dfrac{35{,}270}{42{,}000}, \\dfrac{35{,}423}{42{,}000}, \\dfrac{35{,}501}{42{,}000}, \\dfrac{35{,}587}{42{,}000}, \\dfrac{35{,}706}{42{,}000}, \\dfrac{35{,}936}{42{,}000}, \\text{ and } \\dfrac{35{,}957}{42{,}000}", "__seed__": "0700"}}, {"seed": 701, "data": {"p1_how_many": "11", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.43, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}038}{30{,}000}, \\dfrac{24{,}076}{30{,}000}, \\dfrac{24{,}304}{30{,}000}, \\dfrac{24{,}330}{30{,}000}, \\dfrac{24{,}595}{30{,}000}, \\dfrac{24{,}632}{30{,}000}, \\dfrac{24{,}719}{30{,}000}, \\dfrac{24{,}720}{30{,}000}, \\dfrac{24{,}842}{30{,}000}, \\dfrac{24{,}863}{30{,}000}, \\text{ and } \\dfrac{24{,}987}{30{,}000}", "__seed__": "0701"}}, {"seed": 702, "data": {"p1_how_many": "10", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.52, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{312}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{353}{1{,}200}, \\dfrac{358}{1{,}200}, \\dfrac{372}{1{,}200}, \\dfrac{393}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0702"}}, {"seed": 703, "data": {"p1_how_many": "13", "p1_a": "8.23", "p1_b": "8.24", "p1_numbers": "8.2305, 8.231, 8.2315, 8.232, 8.2325, 8.233, 8.2335, 8.234, 8.235, 8.236, 8.237, 8.238, and 8.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.231", "8.232000000000001", "8.233", "8.234", "8.235000000000001", "8.236", "8.237", "8.238", "8.239"], "p1_2_xs": ["8.230500000000001", "8.2315", "8.232500000000002", "8.233500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}136}{42{,}000}, \\dfrac{35{,}235}{42{,}000}, \\dfrac{35{,}263}{42{,}000}, \\dfrac{35{,}374}{42{,}000}, \\dfrac{35{,}384}{42{,}000}, \\dfrac{35{,}440}{42{,}000}, \\dfrac{35{,}513}{42{,}000}, \\dfrac{35{,}569}{42{,}000}, \\text{ and } \\dfrac{35{,}988}{42{,}000}", "__seed__": "0703"}}, {"seed": 704, "data": {"p1_how_many": "14", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.625, 5.63, 5.635, 5.64, 5.645, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999", "5.635", "5.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0704"}}, {"seed": 705, "data": {"p1_how_many": "12", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.2005, 8.201, 8.2015, 8.202, 8.2025, 8.203, 8.204, 8.205, 8.206, 8.207, 8.208, and 8.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.200999999999999", "8.202", "8.203", "8.203999999999999", "8.205", "8.206", "8.206999999999999", "8.207999999999998", "8.209"], "p1_2_xs": ["8.2005", "8.2015", "8.2025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{762}{3{,}500}, \\dfrac{828}{3{,}500}, \\dfrac{831}{3{,}500}, \\dfrac{876}{3{,}500}, \\dfrac{882}{3{,}500}, \\dfrac{904}{3{,}500}, \\dfrac{937}{3{,}500}, \\dfrac{972}{3{,}500}, \\text{ and } \\dfrac{994}{3{,}500}", "__seed__": "0705"}}, {"seed": 706, "data": {"p1_how_many": "12", "p1_a": "7.71", "p1_b": "7.72", "p1_numbers": "7.7105, 7.711, 7.7115, 7.712, 7.7125, 7.713, 7.714, 7.715, 7.716, 7.717, 7.718, and 7.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.711", "7.712", "7.713", "7.7139999999999995", "7.715", "7.716", "7.717", "7.718", "7.719"], "p1_2_xs": ["7.7105", "7.7115", "7.7124999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}052}{20{,}000}, \\dfrac{15{,}261}{20{,}000}, \\dfrac{15{,}452}{20{,}000}, \\dfrac{15{,}549}{20{,}000}, \\dfrac{15{,}650}{20{,}000}, \\dfrac{15{,}675}{20{,}000}, \\dfrac{15{,}706}{20{,}000}, \\dfrac{15{,}804}{20{,}000}, \\dfrac{15{,}840}{20{,}000}, \\text{ and } \\dfrac{15{,}850}{20{,}000}", "__seed__": "0706"}}, {"seed": 707, "data": {"p1_how_many": "14", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.735, 9.74, 9.745, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725", "9.735", "9.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{143}{630}, \\dfrac{145}{630}, \\dfrac{146}{630}, \\dfrac{147}{630}, \\dfrac{152}{630}, \\dfrac{153}{630}, \\dfrac{155}{630}, \\dfrac{170}{630}, \\text{ and } \\dfrac{178}{630}", "__seed__": "0707"}}, {"seed": 708, "data": {"p1_how_many": "14", "p1_a": "3.51", "p1_b": "3.52", "p1_numbers": "3.5105, 3.511, 3.5115, 3.512, 3.5125, 3.513, 3.5135, 3.514, 3.5145, 3.515, 3.516, 3.517, 3.518, and 3.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.5109999999999997", "3.5119999999999996", "3.513", "3.514", "3.5149999999999997", "3.5159999999999996", "3.517", "3.518", "3.5189999999999997"], "p1_2_xs": ["3.5105", "3.5115", "3.5124999999999997", "3.5135", "3.5145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}530}{56{,}000}, \\dfrac{16{,}580}{56{,}000}, \\dfrac{16{,}654}{56{,}000}, \\dfrac{16{,}923}{56{,}000}, \\dfrac{16{,}950}{56{,}000}, \\dfrac{17{,}361}{56{,}000}, \\dfrac{18{,}505}{56{,}000}, \\dfrac{19{,}744}{56{,}000}, \\dfrac{19{,}965}{56{,}000}, \\dfrac{20{,}451}{56{,}000}, \\text{ and } \\dfrac{20{,}560}{56{,}000}", "__seed__": "0708"}}, {"seed": 709, "data": {"p1_how_many": "14", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.335, 2.34, 2.345, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997", "2.3349999999999995", "2.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}526}{20{,}000}, \\dfrac{12{,}641}{20{,}000}, \\dfrac{13{,}230}{20{,}000}, \\dfrac{13{,}296}{20{,}000}, \\dfrac{13{,}500}{20{,}000}, \\dfrac{13{,}652}{20{,}000}, \\dfrac{13{,}695}{20{,}000}, \\dfrac{13{,}943}{20{,}000}, \\dfrac{14{,}341}{20{,}000}, \\text{ and } \\dfrac{14{,}671}{20{,}000}", "__seed__": "0709"}}, {"seed": 710, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}414}{3{,}000}, \\dfrac{2{,}415}{3{,}000}, \\dfrac{2{,}442}{3{,}000}, \\dfrac{2{,}445}{3{,}000}, \\dfrac{2{,}446}{3{,}000}, \\dfrac{2{,}454}{3{,}000}, \\dfrac{2{,}457}{3{,}000}, \\dfrac{2{,}475}{3{,}000}, \\dfrac{2{,}479}{3{,}000}, \\dfrac{2{,}482}{3{,}000}, \\text{ and } \\dfrac{2{,}483}{3{,}000}", "__seed__": "0710"}}, {"seed": 711, "data": {"p1_how_many": "11", "p1_a": "6.1", "p1_b": "6.2", "p1_numbers": "6.105, 6.11, 6.115, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17, 6.18, and 6.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.109999999999999", "6.119999999999999", "6.13", "6.14", "6.1499999999999995", "6.159999999999999", "6.17", "6.18", "6.1899999999999995"], "p1_2_xs": ["6.1049999999999995", "6.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{103}{350}, \\dfrac{104}{350}, \\dfrac{105}{350}, \\dfrac{113}{350}, \\dfrac{123}{350}, \\dfrac{135}{350}, \\dfrac{136}{350}, \\text{ and } \\dfrac{138}{350}", "__seed__": "0711"}}, {"seed": 712, "data": {"p1_how_many": "14", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.145, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135", "4.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}007}{3{,}500}, \\dfrac{1{,}033}{3{,}500}, \\dfrac{1{,}038}{3{,}500}, \\dfrac{1{,}044}{3{,}500}, \\dfrac{1{,}071}{3{,}500}, \\dfrac{1{,}160}{3{,}500}, \\text{ and } \\dfrac{1{,}209}{3{,}500}", "__seed__": "0712"}}, {"seed": 713, "data": {"p1_how_many": "14", "p1_a": "8.93", "p1_b": "8.94", "p1_numbers": "8.9305, 8.931, 8.9315, 8.932, 8.9325, 8.933, 8.9335, 8.934, 8.9345, 8.935, 8.936, 8.937, 8.938, and 8.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.931", "8.932", "8.933", "8.934", "8.935", "8.936", "8.937", "8.937999999999999", "8.939"], "p1_2_xs": ["8.9305", "8.9315", "8.932500000000001", "8.9335", "8.9345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{424}{2{,}000}, \\dfrac{426}{2{,}000}, \\dfrac{432}{2{,}000}, \\dfrac{433}{2{,}000}, \\dfrac{437}{2{,}000}, \\dfrac{460}{2{,}000}, \\dfrac{468}{2{,}000}, \\dfrac{482}{2{,}000}, \\dfrac{493}{2{,}000}, \\text{ and } \\dfrac{495}{2{,}000}", "__seed__": "0713"}}, {"seed": 714, "data": {"p1_how_many": "10", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{157}{630}, \\dfrac{161}{630}, \\dfrac{164}{630}, \\dfrac{166}{630}, \\dfrac{167}{630}, \\dfrac{170}{630}, \\text{ and } \\dfrac{174}{630}", "__seed__": "0714"}}, {"seed": 715, "data": {"p1_how_many": "11", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.73, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{16{,}152}{35{,}000}, \\dfrac{16{,}197}{35{,}000}, \\dfrac{16{,}302}{35{,}000}, \\dfrac{16{,}870}{35{,}000}, \\dfrac{16{,}972}{35{,}000}, \\dfrac{17{,}156}{35{,}000}, \\dfrac{17{,}474}{35{,}000}, \\dfrac{17{,}592}{35{,}000}, \\text{ and } \\dfrac{20{,}575}{35{,}000}", "__seed__": "0715"}}, {"seed": 716, "data": {"p1_how_many": "11", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}182}{35{,}000}, \\dfrac{7{,}352}{35{,}000}, \\dfrac{7{,}728}{35{,}000}, \\dfrac{7{,}768}{35{,}000}, \\dfrac{7{,}864}{35{,}000}, \\dfrac{8{,}466}{35{,}000}, \\dfrac{8{,}494}{35{,}000}, \\dfrac{8{,}836}{35{,}000}, \\dfrac{8{,}873}{35{,}000}, \\text{ and } \\dfrac{9{,}522}{35{,}000}", "__seed__": "0716"}}, {"seed": 717, "data": {"p1_how_many": "12", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{305}{1{,}200}, \\dfrac{327}{1{,}200}, \\dfrac{329}{1{,}200}, \\dfrac{346}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{369}{1{,}200}, \\text{ and } \\dfrac{374}{1{,}200}", "__seed__": "0717"}}, {"seed": 718, "data": {"p1_how_many": "11", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}544}{5{,}600}, \\dfrac{3{,}595}{5{,}600}, \\dfrac{3{,}609}{5{,}600}, \\dfrac{3{,}666}{5{,}600}, \\dfrac{3{,}713}{5{,}600}, \\dfrac{3{,}739}{5{,}600}, \\dfrac{3{,}839}{5{,}600}, \\dfrac{3{,}879}{5{,}600}, \\dfrac{3{,}907}{5{,}600}, \\dfrac{3{,}917}{5{,}600}, \\dfrac{3{,}931}{5{,}600}, \\text{ and } \\dfrac{3{,}933}{5{,}600}", "__seed__": "0718"}}, {"seed": 719, "data": {"p1_how_many": "13", "p1_a": "7.86", "p1_b": "7.87", "p1_numbers": "7.8605, 7.861, 7.8615, 7.862, 7.8625, 7.863, 7.8635, 7.864, 7.865, 7.866, 7.867, 7.868, and 7.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.861000000000001", "7.862", "7.863", "7.864", "7.865", "7.8660000000000005", "7.867", "7.868", "7.869000000000001"], "p1_2_xs": ["7.8605", "7.8615", "7.8625", "7.8635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}918}{20{,}000}, \\dfrac{6{,}064}{20{,}000}, \\dfrac{6{,}287}{20{,}000}, \\dfrac{6{,}751}{20{,}000}, \\dfrac{6{,}965}{20{,}000}, \\dfrac{7{,}396}{20{,}000}, \\dfrac{7{,}496}{20{,}000}, \\dfrac{7{,}735}{20{,}000}, \\dfrac{7{,}867}{20{,}000}, \\text{ and } \\dfrac{7{,}883}{20{,}000}", "__seed__": "0719"}}, {"seed": 720, "data": {"p1_how_many": "13", "p1_a": "2.96", "p1_b": "2.97", "p1_numbers": "2.9605, 2.961, 2.9615, 2.962, 2.9625, 2.963, 2.9635, 2.964, 2.965, 2.966, 2.967, 2.968, and 2.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.961", "2.9619999999999997", "2.963", "2.964", "2.965", "2.9659999999999997", "2.967", "2.968", "2.969"], "p1_2_xs": ["2.9605", "2.9615", "2.9625", "2.9635000000000002"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}117}{20{,}000}, \\dfrac{4{,}183}{20{,}000}, \\dfrac{4{,}368}{20{,}000}, \\dfrac{4{,}614}{20{,}000}, \\dfrac{4{,}674}{20{,}000}, \\dfrac{4{,}712}{20{,}000}, \\dfrac{4{,}831}{20{,}000}, \\text{ and } \\dfrac{4{,}837}{20{,}000}", "__seed__": "0720"}}, {"seed": 721, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{73}{420}, \\dfrac{80}{420}, \\dfrac{81}{420}, \\dfrac{86}{420}, \\dfrac{93}{420}, \\dfrac{97}{420}, \\text{ and } \\dfrac{105}{420}", "__seed__": "0721"}}, {"seed": 722, "data": {"p1_how_many": "10", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.42, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{618}{4{,}200}, \\dfrac{623}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{644}{4{,}200}, \\dfrac{646}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{666}{4{,}200}, \\dfrac{681}{4{,}200}, \\dfrac{696}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0722"}}, {"seed": 723, "data": {"p1_how_many": "14", "p1_a": "9.32", "p1_b": "9.33", "p1_numbers": "9.3205, 9.321, 9.3215, 9.322, 9.3225, 9.323, 9.3235, 9.324, 9.3245, 9.325, 9.326, 9.327, 9.328, and 9.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.321", "9.322000000000001", "9.323", "9.324", "9.325000000000001", "9.326", "9.327", "9.328", "9.329"], "p1_2_xs": ["9.320500000000001", "9.3215", "9.322500000000002", "9.323500000000001", "9.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{7{,}132}{56{,}000}, \\dfrac{7{,}311}{56{,}000}, \\dfrac{7{,}334}{56{,}000}, \\dfrac{7{,}596}{56{,}000}, \\dfrac{7{,}643}{56{,}000}, \\dfrac{7{,}660}{56{,}000}, \\dfrac{7{,}696}{56{,}000}, \\dfrac{7{,}816}{56{,}000}, \\dfrac{7{,}861}{56{,}000}, \\text{ and } \\dfrac{7{,}882}{56{,}000}", "__seed__": "0723"}}, {"seed": 724, "data": {"p1_how_many": "12", "p1_a": "5.01", "p1_b": "5.02", "p1_numbers": "5.0105, 5.011, 5.0115, 5.012, 5.0125, 5.013, 5.014, 5.015, 5.016, 5.017, 5.018, and 5.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.011", "5.012", "5.013", "5.013999999999999", "5.015", "5.016", "5.0169999999999995", "5.018", "5.019"], "p1_2_xs": ["5.0104999999999995", "5.0115", "5.012499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}120}{12{,}000}, \\dfrac{8{,}146}{12{,}000}, \\dfrac{8{,}516}{12{,}000}, \\dfrac{8{,}588}{12{,}000}, \\dfrac{8{,}831}{12{,}000}, \\dfrac{8{,}940}{12{,}000}, \\text{ and } \\dfrac{8{,}973}{12{,}000}", "__seed__": "0724"}}, {"seed": 725, "data": {"p1_how_many": "12", "p1_a": "3.51", "p1_b": "3.52", "p1_numbers": "3.5105, 3.511, 3.5115, 3.512, 3.5125, 3.513, 3.514, 3.515, 3.516, 3.517, 3.518, and 3.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.5109999999999997", "3.5119999999999996", "3.513", "3.514", "3.5149999999999997", "3.5159999999999996", "3.517", "3.518", "3.5189999999999997"], "p1_2_xs": ["3.5105", "3.5115", "3.5124999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0725"}}, {"seed": 726, "data": {"p1_how_many": "13", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315", "1.325", "1.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}335}{42{,}000}, \\dfrac{7{,}874}{42{,}000}, \\dfrac{7{,}923}{42{,}000}, \\dfrac{9{,}014}{42{,}000}, \\dfrac{9{,}311}{42{,}000}, \\dfrac{9{,}785}{42{,}000}, \\dfrac{10{,}109}{42{,}000}, \\dfrac{10{,}809}{42{,}000}, \\dfrac{11{,}152}{42{,}000}, \\dfrac{11{,}531}{42{,}000}, \\dfrac{11{,}550}{42{,}000}, \\text{ and } \\dfrac{11{,}602}{42{,}000}", "__seed__": "0726"}}, {"seed": 727, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{604}{4{,}200}, \\dfrac{605}{4{,}200}, \\dfrac{620}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{641}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{664}{4{,}200}, \\dfrac{666}{4{,}200}, \\dfrac{668}{4{,}200}, \\text{ and } \\dfrac{676}{4{,}200}", "__seed__": "0727"}}, {"seed": 728, "data": {"p1_how_many": "12", "p1_a": "7.57", "p1_b": "7.58", "p1_numbers": "7.5705, 7.571, 7.5715, 7.572, 7.5725, 7.573, 7.574, 7.575, 7.576, 7.577, 7.578, and 7.579", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.571000000000001", "7.572", "7.573", "7.574", "7.575", "7.5760000000000005", "7.577", "7.578", "7.579000000000001"], "p1_2_xs": ["7.5705", "7.5715", "7.5725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0728"}}, {"seed": 729, "data": {"p1_how_many": "13", "p1_a": "6.74", "p1_b": "6.75", "p1_numbers": "6.7405, 6.741, 6.7415, 6.742, 6.7425, 6.743, 6.7435, 6.744, 6.745, 6.746, 6.747, 6.748, and 6.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.7410000000000005", "6.742", "6.743", "6.744", "6.745", "6.746", "6.747", "6.748", "6.7490000000000006"], "p1_2_xs": ["6.7405", "6.7415", "6.7425", "6.7435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{751}{4{,}200}, \\dfrac{788}{4{,}200}, \\dfrac{807}{4{,}200}, \\dfrac{893}{4{,}200}, \\dfrac{926}{4{,}200}, \\dfrac{951}{4{,}200}, \\dfrac{963}{4{,}200}, \\dfrac{999}{4{,}200}, \\dfrac{1{,}103}{4{,}200}, \\text{ and } \\dfrac{1{,}145}{4{,}200}", "__seed__": "0729"}}, {"seed": 730, "data": {"p1_how_many": "11", "p1_a": "9.13", "p1_b": "9.14", "p1_numbers": "9.1305, 9.131, 9.1315, 9.132, 9.133, 9.134, 9.135, 9.136, 9.137, 9.138, and 9.139", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.131", "9.132000000000001", "9.133000000000001", "9.134", "9.135000000000002", "9.136000000000001", "9.137", "9.138", "9.139000000000001"], "p1_2_xs": ["9.130500000000001", "9.1315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{733}{4{,}200}, \\dfrac{769}{4{,}200}, \\dfrac{775}{4{,}200}, \\dfrac{841}{4{,}200}, \\dfrac{847}{4{,}200}, \\dfrac{855}{4{,}200}, \\dfrac{912}{4{,}200}, \\dfrac{1{,}004}{4{,}200}, \\dfrac{1{,}018}{4{,}200}, \\dfrac{1{,}019}{4{,}200}, \\text{ and } \\dfrac{1{,}171}{4{,}200}", "__seed__": "0730"}}, {"seed": 731, "data": {"p1_how_many": "10", "p1_a": "6.22", "p1_b": "6.23", "p1_numbers": "6.2205, 6.221, 6.222, 6.223, 6.224, 6.225, 6.226, 6.227, 6.228, and 6.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.221", "6.2219999999999995", "6.223", "6.223999999999999", "6.225", "6.226", "6.226999999999999", "6.228", "6.229"], "p1_2_xs": ["6.2204999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}175}{42{,}000}, \\dfrac{35{,}229}{42{,}000}, \\dfrac{35{,}343}{42{,}000}, \\dfrac{35{,}391}{42{,}000}, \\dfrac{35{,}512}{42{,}000}, \\dfrac{35{,}870}{42{,}000}, \\text{ and } \\dfrac{35{,}882}{42{,}000}", "__seed__": "0731"}}, {"seed": 732, "data": {"p1_how_many": "10", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}232}{35{,}000}, \\dfrac{10{,}332}{35{,}000}, \\dfrac{10{,}580}{35{,}000}, \\dfrac{10{,}797}{35{,}000}, \\dfrac{11{,}008}{35{,}000}, \\dfrac{11{,}561}{35{,}000}, \\dfrac{11{,}631}{35{,}000}, \\dfrac{11{,}664}{35{,}000}, \\dfrac{11{,}823}{35{,}000}, \\dfrac{11{,}958}{35{,}000}, \\text{ and } \\dfrac{13{,}455}{35{,}000}", "__seed__": "0732"}}, {"seed": 733, "data": {"p1_how_many": "13", "p1_a": "9.06", "p1_b": "9.07", "p1_numbers": "9.0605, 9.061, 9.0615, 9.062, 9.0625, 9.063, 9.0635, 9.064, 9.065, 9.066, 9.067, 9.068, and 9.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.061", "9.062000000000001", "9.063", "9.064", "9.065000000000001", "9.066", "9.067", "9.068", "9.069"], "p1_2_xs": ["9.060500000000001", "9.0615", "9.062500000000002", "9.063500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}830}{6{,}300}, \\dfrac{2{,}912}{6{,}300}, \\dfrac{2{,}930}{6{,}300}, \\dfrac{3{,}224}{6{,}300}, \\dfrac{3{,}279}{6{,}300}, \\dfrac{3{,}330}{6{,}300}, \\dfrac{3{,}356}{6{,}300}, \\dfrac{3{,}402}{6{,}300}, \\dfrac{3{,}477}{6{,}300}, \\dfrac{3{,}530}{6{,}300}, \\text{ and } \\dfrac{3{,}596}{6{,}300}", "__seed__": "0733"}}, {"seed": 734, "data": {"p1_how_many": "13", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.035, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995", "7.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{71}{350}, \\dfrac{75}{350}, \\dfrac{76}{350}, \\dfrac{86}{350}, \\dfrac{88}{350}, \\dfrac{89}{350}, \\dfrac{95}{350}, \\text{ and } \\dfrac{97}{350}", "__seed__": "0734"}}, {"seed": 735, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{502}{1{,}500}, \\dfrac{510}{1{,}500}, \\dfrac{522}{1{,}500}, \\dfrac{523}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{568}{1{,}500}, \\text{ and } \\dfrac{594}{1{,}500}", "__seed__": "0735"}}, {"seed": 736, "data": {"p1_how_many": "14", "p1_a": "3.96", "p1_b": "3.97", "p1_numbers": "3.9605, 3.961, 3.9615, 3.962, 3.9625, 3.963, 3.9635, 3.964, 3.9645, 3.965, 3.966, 3.967, 3.968, and 3.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.961", "3.9619999999999997", "3.963", "3.964", "3.965", "3.9659999999999997", "3.967", "3.968", "3.969"], "p1_2_xs": ["3.9605", "3.9615", "3.9625", "3.9635000000000002", "3.9645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}047}{4{,}200}, \\dfrac{3{,}074}{4{,}200}, \\dfrac{3{,}120}{4{,}200}, \\dfrac{3{,}122}{4{,}200}, \\dfrac{3{,}149}{4{,}200}, \\dfrac{3{,}227}{4{,}200}, \\dfrac{3{,}234}{4{,}200}, \\dfrac{3{,}290}{4{,}200}, \\dfrac{3{,}353}{4{,}200}, \\dfrac{3{,}416}{4{,}200}, \\text{ and } \\dfrac{3{,}496}{4{,}200}", "__seed__": "0736"}}, {"seed": 737, "data": {"p1_how_many": "13", "p1_a": "2.34", "p1_b": "2.35", "p1_numbers": "2.3405, 2.341, 2.3415, 2.342, 2.3425, 2.343, 2.3435, 2.344, 2.345, 2.346, 2.347, 2.348, and 2.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3409999999999997", "2.3419999999999996", "2.343", "2.344", "2.3449999999999998", "2.3459999999999996", "2.347", "2.348", "2.3489999999999998"], "p1_2_xs": ["2.3405", "2.3415", "2.3425", "2.3435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{511}{2{,}000}, \\dfrac{542}{2{,}000}, \\dfrac{555}{2{,}000}, \\dfrac{601}{2{,}000}, \\dfrac{632}{2{,}000}, \\dfrac{640}{2{,}000}, \\dfrac{657}{2{,}000}, \\dfrac{724}{2{,}000}, \\dfrac{746}{2{,}000}, \\text{ and } \\dfrac{749}{2{,}000}", "__seed__": "0737"}}, {"seed": 738, "data": {"p1_how_many": "14", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.3005, 6.301, 6.3015, 6.302, 6.3025, 6.303, 6.3035, 6.304, 6.3045, 6.305, 6.306, 6.307, 6.308, and 6.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.301", "6.302", "6.303", "6.303999999999999", "6.305", "6.306", "6.3069999999999995", "6.308", "6.309"], "p1_2_xs": ["6.3004999999999995", "6.3015", "6.302499999999999", "6.3035", "6.304499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{508}{3{,}000}, \\dfrac{532}{3{,}000}, \\dfrac{538}{3{,}000}, \\dfrac{542}{3{,}000}, \\dfrac{550}{3{,}000}, \\dfrac{556}{3{,}000}, \\dfrac{558}{3{,}000}, \\dfrac{561}{3{,}000}, \\dfrac{568}{3{,}000}, \\dfrac{579}{3{,}000}, \\text{ and } \\dfrac{581}{3{,}000}", "__seed__": "0738"}}, {"seed": 739, "data": {"p1_how_many": "14", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.545, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997", "3.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}510}{6{,}300}, \\dfrac{1{,}540}{6{,}300}, \\dfrac{1{,}581}{6{,}300}, \\dfrac{1{,}685}{6{,}300}, \\dfrac{1{,}708}{6{,}300}, \\dfrac{1{,}748}{6{,}300}, \\text{ and } \\dfrac{1{,}770}{6{,}300}", "__seed__": "0739"}}, {"seed": 740, "data": {"p1_how_many": "11", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}068}{42{,}000}, \\dfrac{35{,}263}{42{,}000}, \\dfrac{35{,}385}{42{,}000}, \\dfrac{35{,}398}{42{,}000}, \\dfrac{35{,}443}{42{,}000}, \\dfrac{35{,}458}{42{,}000}, \\text{ and } \\dfrac{35{,}703}{42{,}000}", "__seed__": "0740"}}, {"seed": 741, "data": {"p1_how_many": "14", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135", "2.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0741"}}, {"seed": 742, "data": {"p1_how_many": "14", "p1_a": "1.65", "p1_b": "1.66", "p1_numbers": "1.6505, 1.651, 1.6515, 1.652, 1.6525, 1.653, 1.6535, 1.654, 1.6545, 1.655, 1.656, 1.657, 1.658, and 1.659", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.6509999999999998", "1.652", "1.6529999999999998", "1.654", "1.6549999999999998", "1.656", "1.6569999999999998", "1.658", "1.6589999999999998"], "p1_2_xs": ["1.6504999999999999", "1.6514999999999997", "1.6524999999999999", "1.6534999999999997", "1.6544999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}419}{3{,}000}, \\dfrac{2{,}432}{3{,}000}, \\dfrac{2{,}446}{3{,}000}, \\dfrac{2{,}447}{3{,}000}, \\dfrac{2{,}450}{3{,}000}, \\dfrac{2{,}457}{3{,}000}, \\dfrac{2{,}464}{3{,}000}, \\dfrac{2{,}475}{3{,}000}, \\dfrac{2{,}476}{3{,}000}, \\dfrac{2{,}486}{3{,}000}, \\dfrac{2{,}493}{3{,}000}, \\text{ and } \\dfrac{2{,}494}{3{,}000}", "__seed__": "0742"}}, {"seed": 743, "data": {"p1_how_many": "10", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}160}{35{,}000}, \\dfrac{20{,}306}{35{,}000}, \\dfrac{20{,}472}{35{,}000}, \\dfrac{20{,}560}{35{,}000}, \\dfrac{20{,}573}{35{,}000}, \\dfrac{20{,}746}{35{,}000}, \\dfrac{20{,}813}{35{,}000}, \\dfrac{20{,}879}{35{,}000}, \\dfrac{20{,}923}{35{,}000}, \\dfrac{20{,}925}{35{,}000}, \\text{ and } \\dfrac{20{,}995}{35{,}000}", "__seed__": "0743"}}, {"seed": 744, "data": {"p1_how_many": "12", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.7005, 5.701, 5.7015, 5.702, 5.7025, 5.703, 5.704, 5.705, 5.706, 5.707, 5.708, and 5.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7010000000000005", "5.702", "5.703", "5.704", "5.705", "5.706", "5.707", "5.708", "5.7090000000000005"], "p1_2_xs": ["5.7005", "5.7015", "5.7025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}113}{56{,}000}, \\dfrac{33{,}446}{56{,}000}, \\dfrac{33{,}553}{56{,}000}, \\dfrac{33{,}844}{56{,}000}, \\dfrac{34{,}004}{56{,}000}, \\dfrac{34{,}098}{56{,}000}, \\dfrac{34{,}573}{56{,}000}, \\text{ and } \\dfrac{34{,}771}{56{,}000}", "__seed__": "0744"}}, {"seed": 745, "data": {"p1_how_many": "12", "p1_a": "9.53", "p1_b": "9.54", "p1_numbers": "9.5305, 9.531, 9.5315, 9.532, 9.5325, 9.533, 9.534, 9.535, 9.536, 9.537, 9.538, and 9.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.530999999999999", "9.532", "9.533", "9.533999999999999", "9.535", "9.536", "9.536999999999999", "9.537999999999998", "9.539"], "p1_2_xs": ["9.5305", "9.5315", "9.5325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}002}{20{,}000}, \\dfrac{15{,}014}{20{,}000}, \\dfrac{15{,}055}{20{,}000}, \\dfrac{15{,}092}{20{,}000}, \\dfrac{15{,}103}{20{,}000}, \\dfrac{15{,}126}{20{,}000}, \\dfrac{15{,}143}{20{,}000}, \\dfrac{15{,}248}{20{,}000}, \\dfrac{15{,}363}{20{,}000}, \\dfrac{15{,}385}{20{,}000}, \\text{ and } \\dfrac{15{,}964}{20{,}000}", "__seed__": "0745"}}, {"seed": 746, "data": {"p1_how_many": "13", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.425, 5.43, 5.435, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415", "5.425", "5.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{635}{1{,}500}, \\dfrac{659}{1{,}500}, \\dfrac{677}{1{,}500}, \\dfrac{709}{1{,}500}, \\dfrac{757}{1{,}500}, \\dfrac{844}{1{,}500}, \\dfrac{859}{1{,}500}, \\dfrac{923}{1{,}500}, \\text{ and } \\dfrac{930}{1{,}500}", "__seed__": "0746"}}, {"seed": 747, "data": {"p1_how_many": "11", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}392}{35{,}000}, \\dfrac{15{,}416}{35{,}000}, \\dfrac{15{,}587}{35{,}000}, \\dfrac{15{,}620}{35{,}000}, \\dfrac{15{,}829}{35{,}000}, \\dfrac{16{,}149}{35{,}000}, \\dfrac{16{,}900}{35{,}000}, \\dfrac{17{,}302}{35{,}000}, \\dfrac{19{,}210}{35{,}000}, \\text{ and } \\dfrac{19{,}620}{35{,}000}", "__seed__": "0747"}}, {"seed": 748, "data": {"p1_how_many": "11", "p1_a": "9.62", "p1_b": "9.63", "p1_numbers": "9.6205, 9.621, 9.6215, 9.622, 9.623, 9.624, 9.625, 9.626, 9.627, 9.628, and 9.629", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.620999999999999", "9.622", "9.623", "9.623999999999999", "9.625", "9.626", "9.626999999999999", "9.627999999999998", "9.629"], "p1_2_xs": ["9.6205", "9.6215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{710}{5{,}600}, \\dfrac{713}{5{,}600}, \\dfrac{724}{5{,}600}, \\dfrac{730}{5{,}600}, \\dfrac{740}{5{,}600}, \\dfrac{755}{5{,}600}, \\dfrac{757}{5{,}600}, \\dfrac{759}{5{,}600}, \\dfrac{785}{5{,}600}, \\dfrac{788}{5{,}600}, \\text{ and } \\dfrac{798}{5{,}600}", "__seed__": "0748"}}, {"seed": 749, "data": {"p1_how_many": "13", "p1_a": "4.43", "p1_b": "4.44", "p1_numbers": "4.4305, 4.431, 4.4315, 4.432, 4.4325, 4.433, 4.4335, 4.434, 4.435, 4.436, 4.437, 4.438, and 4.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.431", "4.4319999999999995", "4.433", "4.433999999999999", "4.435", "4.436", "4.436999999999999", "4.438", "4.439"], "p1_2_xs": ["4.430499999999999", "4.4315", "4.432499999999999", "4.4334999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}513}{4{,}200}, \\dfrac{3{,}531}{4{,}200}, \\dfrac{3{,}534}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}536}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}554}{4{,}200}, \\dfrac{3{,}568}{4{,}200}, \\dfrac{3{,}582}{4{,}200}, \\text{ and } \\dfrac{3{,}594}{4{,}200}", "__seed__": "0749"}}, {"seed": 750, "data": {"p1_how_many": "13", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}211}{2{,}000}, \\dfrac{1{,}246}{2{,}000}, \\dfrac{1{,}414}{2{,}000}, \\dfrac{1{,}417}{2{,}000}, \\dfrac{1{,}424}{2{,}000}, \\dfrac{1{,}429}{2{,}000}, \\dfrac{1{,}459}{2{,}000}, \\text{ and } \\dfrac{1{,}460}{2{,}000}", "__seed__": "0750"}}, {"seed": 751, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}130}{15{,}000}, \\dfrac{5{,}211}{15{,}000}, \\dfrac{5{,}264}{15{,}000}, \\dfrac{5{,}287}{15{,}000}, \\dfrac{5{,}348}{15{,}000}, \\dfrac{5{,}370}{15{,}000}, \\dfrac{5{,}388}{15{,}000}, \\dfrac{5{,}543}{15{,}000}, \\dfrac{5{,}738}{15{,}000}, \\dfrac{5{,}825}{15{,}000}, \\dfrac{5{,}937}{15{,}000}, \\text{ and } \\dfrac{5{,}996}{15{,}000}", "__seed__": "0751"}}, {"seed": 752, "data": {"p1_how_many": "11", "p1_a": "8.06", "p1_b": "8.07", "p1_numbers": "8.0605, 8.061, 8.0615, 8.062, 8.063, 8.064, 8.065, 8.066, 8.067, 8.068, and 8.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.061", "8.062000000000001", "8.063", "8.064", "8.065000000000001", "8.066", "8.067", "8.068", "8.069"], "p1_2_xs": ["8.060500000000001", "8.0615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{934}{6{,}300}, \\dfrac{1{,}045}{6{,}300}, \\dfrac{1{,}076}{6{,}300}, \\dfrac{1{,}089}{6{,}300}, \\dfrac{1{,}202}{6{,}300}, \\dfrac{1{,}244}{6{,}300}, \\dfrac{1{,}254}{6{,}300}, \\dfrac{1{,}257}{6{,}300}, \\dfrac{1{,}313}{6{,}300}, \\dfrac{1{,}319}{6{,}300}, \\dfrac{1{,}346}{6{,}300}, \\text{ and } \\dfrac{1{,}398}{6{,}300}", "__seed__": "0752"}}, {"seed": 753, "data": {"p1_how_many": "13", "p1_a": "2.45", "p1_b": "2.46", "p1_numbers": "2.4505, 2.451, 2.4515, 2.452, 2.4525, 2.453, 2.4535, 2.454, 2.455, 2.456, 2.457, 2.458, and 2.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.451", "2.452", "2.4530000000000003", "2.454", "2.455", "2.456", "2.4570000000000003", "2.458", "2.459"], "p1_2_xs": ["2.4505000000000003", "2.4515000000000002", "2.4525", "2.4535000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0753"}}, {"seed": 754, "data": {"p1_how_many": "13", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}305}{12{,}000}, \\dfrac{3{,}516}{12{,}000}, \\dfrac{3{,}634}{12{,}000}, \\dfrac{3{,}738}{12{,}000}, \\dfrac{3{,}775}{12{,}000}, \\dfrac{3{,}865}{12{,}000}, \\text{ and } \\dfrac{3{,}888}{12{,}000}", "__seed__": "0754"}}, {"seed": 755, "data": {"p1_how_many": "11", "p1_a": "2.21", "p1_b": "2.22", "p1_numbers": "2.2105, 2.211, 2.2115, 2.212, 2.213, 2.214, 2.215, 2.216, 2.217, 2.218, and 2.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.211", "2.2119999999999997", "2.213", "2.214", "2.215", "2.2159999999999997", "2.217", "2.218", "2.219"], "p1_2_xs": ["2.2105", "2.2115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{608}{1{,}500}, \\dfrac{664}{1{,}500}, \\dfrac{761}{1{,}500}, \\dfrac{865}{1{,}500}, \\dfrac{916}{1{,}500}, \\dfrac{973}{1{,}500}, \\text{ and } \\dfrac{977}{1{,}500}", "__seed__": "0755"}}, {"seed": 756, "data": {"p1_how_many": "13", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725", "7.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}071}{63{,}000}, \\dfrac{27{,}198}{63{,}000}, \\dfrac{27{,}302}{63{,}000}, \\dfrac{27{,}335}{63{,}000}, \\dfrac{27{,}351}{63{,}000}, \\dfrac{27{,}398}{63{,}000}, \\dfrac{27{,}447}{63{,}000}, \\text{ and } \\dfrac{27{,}506}{63{,}000}", "__seed__": "0756"}}, {"seed": 757, "data": {"p1_how_many": "13", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}507}{5{,}600}, \\dfrac{3{,}675}{5{,}600}, \\dfrac{3{,}751}{5{,}600}, \\dfrac{3{,}787}{5{,}600}, \\dfrac{3{,}800}{5{,}600}, \\dfrac{3{,}805}{5{,}600}, \\dfrac{3{,}825}{5{,}600}, \\dfrac{3{,}831}{5{,}600}, \\dfrac{3{,}870}{5{,}600}, \\text{ and } \\dfrac{3{,}958}{5{,}600}", "__seed__": "0757"}}, {"seed": 758, "data": {"p1_how_many": "13", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.125, 1.13, 1.135, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115", "1.125", "1.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{295}{630}, \\dfrac{307}{630}, \\dfrac{309}{630}, \\dfrac{310}{630}, \\dfrac{337}{630}, \\dfrac{346}{630}, \\dfrac{353}{630}, \\text{ and } \\dfrac{359}{630}", "__seed__": "0758"}}, {"seed": 759, "data": {"p1_how_many": "12", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.025, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015", "1.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}406}{3{,}500}, \\dfrac{1{,}412}{3{,}500}, \\dfrac{1{,}427}{3{,}500}, \\dfrac{1{,}436}{3{,}500}, \\dfrac{1{,}440}{3{,}500}, \\dfrac{1{,}442}{3{,}500}, \\dfrac{1{,}446}{3{,}500}, \\dfrac{1{,}450}{3{,}500}, \\dfrac{1{,}461}{3{,}500}, \\dfrac{1{,}465}{3{,}500}, \\dfrac{1{,}493}{3{,}500}, \\text{ and } \\dfrac{1{,}497}{3{,}500}", "__seed__": "0759"}}, {"seed": 760, "data": {"p1_how_many": "13", "p1_a": "3.64", "p1_b": "3.65", "p1_numbers": "3.6405, 3.641, 3.6415, 3.642, 3.6425, 3.643, 3.6435, 3.644, 3.645, 3.646, 3.647, 3.648, and 3.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.641", "3.642", "3.6430000000000002", "3.644", "3.645", "3.646", "3.6470000000000002", "3.648", "3.649"], "p1_2_xs": ["3.6405000000000003", "3.6415", "3.6425", "3.6435000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}231}{2{,}000}, \\dfrac{1{,}303}{2{,}000}, \\dfrac{1{,}312}{2{,}000}, \\dfrac{1{,}339}{2{,}000}, \\dfrac{1{,}392}{2{,}000}, \\dfrac{1{,}394}{2{,}000}, \\dfrac{1{,}405}{2{,}000}, \\dfrac{1{,}410}{2{,}000}, \\text{ and } \\dfrac{1{,}413}{2{,}000}", "__seed__": "0760"}}, {"seed": 761, "data": {"p1_how_many": "14", "p1_a": "4.07", "p1_b": "4.08", "p1_numbers": "4.0705, 4.071, 4.0715, 4.072, 4.0725, 4.073, 4.0735, 4.074, 4.0745, 4.075, 4.076, 4.077, 4.078, and 4.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.071000000000001", "4.072", "4.073", "4.074", "4.075", "4.0760000000000005", "4.077", "4.078", "4.079000000000001"], "p1_2_xs": ["4.0705", "4.0715", "4.0725", "4.0735", "4.0745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}092}{42{,}000}, \\dfrac{35{,}133}{42{,}000}, \\dfrac{35{,}456}{42{,}000}, \\dfrac{35{,}521}{42{,}000}, \\dfrac{35{,}569}{42{,}000}, \\dfrac{35{,}570}{42{,}000}, \\dfrac{35{,}642}{42{,}000}, \\dfrac{35{,}662}{42{,}000}, \\dfrac{35{,}673}{42{,}000}, \\dfrac{35{,}754}{42{,}000}, \\dfrac{35{,}916}{42{,}000}, \\text{ and } \\dfrac{35{,}953}{42{,}000}", "__seed__": "0761"}}, {"seed": 762, "data": {"p1_how_many": "11", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.73, 4.74, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{517}{2{,}000}, \\dfrac{557}{2{,}000}, \\dfrac{594}{2{,}000}, \\dfrac{612}{2{,}000}, \\dfrac{632}{2{,}000}, \\dfrac{661}{2{,}000}, \\dfrac{678}{2{,}000}, \\dfrac{687}{2{,}000}, \\dfrac{694}{2{,}000}, \\text{ and } \\dfrac{772}{2{,}000}", "__seed__": "0762"}}, {"seed": 763, "data": {"p1_how_many": "13", "p1_a": "2.76", "p1_b": "2.77", "p1_numbers": "2.7605, 2.761, 2.7615, 2.762, 2.7625, 2.763, 2.7635, 2.764, 2.765, 2.766, 2.767, 2.768, and 2.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.7609999999999997", "2.7619999999999996", "2.763", "2.764", "2.7649999999999997", "2.7659999999999996", "2.767", "2.768", "2.7689999999999997"], "p1_2_xs": ["2.7605", "2.7615", "2.7624999999999997", "2.7635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{304}{1{,}200}, \\dfrac{327}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{337}{1{,}200}, \\dfrac{346}{1{,}200}, \\dfrac{348}{1{,}200}, \\dfrac{355}{1{,}200}, \\dfrac{365}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{373}{1{,}200}, \\dfrac{393}{1{,}200}, \\text{ and } \\dfrac{398}{1{,}200}", "__seed__": "0763"}}, {"seed": 764, "data": {"p1_how_many": "10", "p1_a": "8.43", "p1_b": "8.44", "p1_numbers": "8.4305, 8.431, 8.432, 8.433, 8.434, 8.435, 8.436, 8.437, 8.438, and 8.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.431", "8.432", "8.433", "8.434", "8.435", "8.436", "8.437", "8.437999999999999", "8.439"], "p1_2_xs": ["8.4305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}025}{12{,}000}, \\dfrac{3{,}107}{12{,}000}, \\dfrac{3{,}121}{12{,}000}, \\dfrac{3{,}252}{12{,}000}, \\dfrac{3{,}411}{12{,}000}, \\dfrac{3{,}428}{12{,}000}, \\dfrac{3{,}527}{12{,}000}, \\dfrac{3{,}584}{12{,}000}, \\text{ and } \\dfrac{3{,}725}{12{,}000}", "__seed__": "0764"}}, {"seed": 765, "data": {"p1_how_many": "11", "p1_a": "1.87", "p1_b": "1.88", "p1_numbers": "1.8705, 1.871, 1.8715, 1.872, 1.873, 1.874, 1.875, 1.876, 1.877, 1.878, and 1.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.871", "1.872", "1.873", "1.874", "1.875", "1.8760000000000001", "1.877", "1.8780000000000001", "1.879"], "p1_2_xs": ["1.8705", "1.8715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}403}{3{,}500}, \\dfrac{1{,}406}{3{,}500}, \\dfrac{1{,}407}{3{,}500}, \\dfrac{1{,}421}{3{,}500}, \\dfrac{1{,}424}{3{,}500}, \\dfrac{1{,}425}{3{,}500}, \\dfrac{1{,}445}{3{,}500}, \\dfrac{1{,}458}{3{,}500}, \\dfrac{1{,}461}{3{,}500}, \\dfrac{1{,}465}{3{,}500}, \\dfrac{1{,}477}{3{,}500}, \\text{ and } \\dfrac{1{,}498}{3{,}500}", "__seed__": "0765"}}, {"seed": 766, "data": {"p1_how_many": "11", "p1_a": "5.86", "p1_b": "5.87", "p1_numbers": "5.8605, 5.861, 5.8615, 5.862, 5.863, 5.864, 5.865, 5.866, 5.867, 5.868, and 5.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.861000000000001", "5.862", "5.863", "5.864", "5.865", "5.8660000000000005", "5.867", "5.868", "5.869000000000001"], "p1_2_xs": ["5.8605", "5.8615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}009}{3{,}500}, \\dfrac{2{,}090}{3{,}500}, \\dfrac{2{,}190}{3{,}500}, \\dfrac{2{,}301}{3{,}500}, \\dfrac{2{,}315}{3{,}500}, \\dfrac{2{,}399}{3{,}500}, \\dfrac{2{,}673}{3{,}500}, \\dfrac{2{,}713}{3{,}500}, \\text{ and } \\dfrac{2{,}777}{3{,}500}", "__seed__": "0766"}}, {"seed": 767, "data": {"p1_how_many": "10", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}146}{20{,}000}, \\dfrac{5{,}510}{20{,}000}, \\dfrac{5{,}870}{20{,}000}, \\dfrac{5{,}903}{20{,}000}, \\dfrac{6{,}013}{20{,}000}, \\dfrac{6{,}118}{20{,}000}, \\dfrac{6{,}737}{20{,}000}, \\dfrac{7{,}157}{20{,}000}, \\dfrac{7{,}525}{20{,}000}, \\dfrac{7{,}562}{20{,}000}, \\text{ and } \\dfrac{7{,}962}{20{,}000}", "__seed__": "0767"}}, {"seed": 768, "data": {"p1_how_many": "13", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.135, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125", "3.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}026}{42{,}000}, \\dfrac{6{,}057}{42{,}000}, \\dfrac{6{,}309}{42{,}000}, \\dfrac{6{,}396}{42{,}000}, \\dfrac{6{,}582}{42{,}000}, \\dfrac{6{,}674}{42{,}000}, \\dfrac{6{,}762}{42{,}000}, \\dfrac{6{,}778}{42{,}000}, \\dfrac{6{,}810}{42{,}000}, \\dfrac{6{,}857}{42{,}000}, \\text{ and } \\dfrac{6{,}935}{42{,}000}", "__seed__": "0768"}}, {"seed": 769, "data": {"p1_how_many": "12", "p1_a": "8.26", "p1_b": "8.27", "p1_numbers": "8.2605, 8.261, 8.2615, 8.262, 8.2625, 8.263, 8.264, 8.265, 8.266, 8.267, 8.268, and 8.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.261", "8.262", "8.263", "8.264", "8.265", "8.266", "8.267", "8.267999999999999", "8.269"], "p1_2_xs": ["8.2605", "8.2615", "8.262500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0769"}}, {"seed": 770, "data": {"p1_how_many": "11", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{516}{2{,}000}, \\dfrac{593}{2{,}000}, \\dfrac{637}{2{,}000}, \\dfrac{643}{2{,}000}, \\dfrac{669}{2{,}000}, \\dfrac{699}{2{,}000}, \\dfrac{701}{2{,}000}, \\dfrac{714}{2{,}000}, \\dfrac{754}{2{,}000}, \\dfrac{755}{2{,}000}, \\text{ and } \\dfrac{784}{2{,}000}", "__seed__": "0770"}}, {"seed": 771, "data": {"p1_how_many": "13", "p1_a": "3.44", "p1_b": "3.45", "p1_numbers": "3.4405, 3.441, 3.4415, 3.442, 3.4425, 3.443, 3.4435, 3.444, 3.445, 3.446, 3.447, 3.448, and 3.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.441", "3.4419999999999997", "3.443", "3.444", "3.445", "3.4459999999999997", "3.447", "3.448", "3.449"], "p1_2_xs": ["3.4405", "3.4415", "3.4425", "3.4435000000000002"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{22{,}431}{35{,}000}, \\dfrac{22{,}906}{35{,}000}, \\dfrac{23{,}468}{35{,}000}, \\dfrac{23{,}765}{35{,}000}, \\dfrac{25{,}507}{35{,}000}, \\dfrac{26{,}118}{35{,}000}, \\dfrac{26{,}325}{35{,}000}, \\dfrac{27{,}208}{35{,}000}, \\text{ and } \\dfrac{27{,}430}{35{,}000}", "__seed__": "0771"}}, {"seed": 772, "data": {"p1_how_many": "13", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.735, 3.74, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725", "3.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}430}{6{,}300}, \\dfrac{1{,}441}{6{,}300}, \\dfrac{1{,}507}{6{,}300}, \\dfrac{1{,}523}{6{,}300}, \\dfrac{1{,}636}{6{,}300}, \\dfrac{1{,}702}{6{,}300}, \\dfrac{1{,}720}{6{,}300}, \\dfrac{1{,}758}{6{,}300}, \\dfrac{1{,}778}{6{,}300}, \\text{ and } \\dfrac{1{,}781}{6{,}300}", "__seed__": "0772"}}, {"seed": 773, "data": {"p1_how_many": "10", "p1_a": "5.87", "p1_b": "5.88", "p1_numbers": "5.8705, 5.871, 5.872, 5.873, 5.874, 5.875, 5.876, 5.877, 5.878, and 5.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.871", "5.872", "5.873", "5.874", "5.875", "5.876", "5.877", "5.878", "5.8790000000000004"], "p1_2_xs": ["5.8705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{809}{1{,}200}, \\dfrac{818}{1{,}200}, \\dfrac{822}{1{,}200}, \\dfrac{826}{1{,}200}, \\dfrac{840}{1{,}200}, \\dfrac{870}{1{,}200}, \\text{ and } \\dfrac{898}{1{,}200}", "__seed__": "0773"}}, {"seed": 774, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}195}{12{,}000}, \\dfrac{3{,}222}{12{,}000}, \\dfrac{3{,}291}{12{,}000}, \\dfrac{3{,}316}{12{,}000}, \\dfrac{3{,}345}{12{,}000}, \\dfrac{3{,}415}{12{,}000}, \\dfrac{3{,}498}{12{,}000}, \\text{ and } \\dfrac{3{,}716}{12{,}000}", "__seed__": "0774"}}, {"seed": 775, "data": {"p1_how_many": "14", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.415, 3.42, 3.425, 3.43, 3.435, 3.44, 3.445, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996", "3.425", "3.4349999999999996", "3.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{603}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{645}{4{,}200}, \\dfrac{653}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{662}{4{,}200}, \\text{ and } \\dfrac{686}{4{,}200}", "__seed__": "0775"}}, {"seed": 776, "data": {"p1_how_many": "13", "p1_a": "9.6", "p1_b": "9.7", "p1_numbers": "9.605, 9.61, 9.615, 9.62, 9.625, 9.63, 9.635, 9.64, 9.65, 9.66, 9.67, 9.68, and 9.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.61", "9.62", "9.629999999999999", "9.639999999999999", "9.65", "9.66", "9.67", "9.68", "9.69"], "p1_2_xs": ["9.605", "9.615", "9.625", "9.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{728}{4{,}200}, \\dfrac{742}{4{,}200}, \\dfrac{785}{4{,}200}, \\dfrac{909}{4{,}200}, \\dfrac{944}{4{,}200}, \\dfrac{1{,}020}{4{,}200}, \\dfrac{1{,}034}{4{,}200}, \\dfrac{1{,}037}{4{,}200}, \\dfrac{1{,}048}{4{,}200}, \\text{ and } \\dfrac{1{,}070}{4{,}200}", "__seed__": "0776"}}, {"seed": 777, "data": {"p1_how_many": "13", "p1_a": "5.21", "p1_b": "5.22", "p1_numbers": "5.2105, 5.211, 5.2115, 5.212, 5.2125, 5.213, 5.2135, 5.214, 5.215, 5.216, 5.217, 5.218, and 5.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.211", "5.212", "5.213", "5.2139999999999995", "5.215", "5.216", "5.217", "5.218", "5.219"], "p1_2_xs": ["5.2105", "5.2115", "5.2124999999999995", "5.2135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}093}{35{,}000}, \\dfrac{20{,}177}{35{,}000}, \\dfrac{20{,}987}{35{,}000}, \\dfrac{22{,}382}{35{,}000}, \\dfrac{23{,}404}{35{,}000}, \\dfrac{24{,}069}{35{,}000}, \\dfrac{24{,}934}{35{,}000}, \\dfrac{24{,}956}{35{,}000}, \\dfrac{25{,}887}{35{,}000}, \\dfrac{26{,}326}{35{,}000}, \\text{ and } \\dfrac{27{,}511}{35{,}000}", "__seed__": "0777"}}, {"seed": 778, "data": {"p1_how_many": "10", "p1_a": "6.71", "p1_b": "6.72", "p1_numbers": "6.7105, 6.711, 6.712, 6.713, 6.714, 6.715, 6.716, 6.717, 6.718, and 6.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.711", "6.712", "6.713", "6.7139999999999995", "6.715", "6.716", "6.717", "6.718", "6.719"], "p1_2_xs": ["6.7105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}016}{42{,}000}, \\dfrac{7{,}587}{42{,}000}, \\dfrac{8{,}288}{42{,}000}, \\dfrac{8{,}944}{42{,}000}, \\dfrac{9{,}217}{42{,}000}, \\dfrac{10{,}983}{42{,}000}, \\dfrac{11{,}334}{42{,}000}, \\text{ and } \\dfrac{11{,}829}{42{,}000}", "__seed__": "0778"}}, {"seed": 779, "data": {"p1_how_many": "14", "p1_a": "7.27", "p1_b": "7.28", "p1_numbers": "7.2705, 7.271, 7.2715, 7.272, 7.2725, 7.273, 7.2735, 7.274, 7.2745, 7.275, 7.276, 7.277, 7.278, and 7.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.271", "7.271999999999999", "7.273", "7.273999999999999", "7.2749999999999995", "7.276", "7.276999999999999", "7.278", "7.279"], "p1_2_xs": ["7.270499999999999", "7.2715", "7.272499999999999", "7.273499999999999", "7.274499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}372}{15{,}000}, \\dfrac{7{,}412}{15{,}000}, \\dfrac{7{,}662}{15{,}000}, \\dfrac{7{,}772}{15{,}000}, \\dfrac{7{,}885}{15{,}000}, \\dfrac{9{,}046}{15{,}000}, \\text{ and } \\dfrac{9{,}409}{15{,}000}", "__seed__": "0779"}}, {"seed": 780, "data": {"p1_how_many": "10", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{123}{200}, \\dfrac{128}{200}, \\dfrac{133}{200}, \\dfrac{135}{200}, \\dfrac{139}{200}, \\dfrac{145}{200}, \\text{ and } \\dfrac{148}{200}", "__seed__": "0780"}}, {"seed": 781, "data": {"p1_how_many": "11", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}958}{6{,}300}, \\dfrac{3{,}000}{6{,}300}, \\dfrac{3{,}032}{6{,}300}, \\dfrac{3{,}087}{6{,}300}, \\dfrac{3{,}318}{6{,}300}, \\dfrac{3{,}433}{6{,}300}, \\text{ and } \\dfrac{3{,}516}{6{,}300}", "__seed__": "0781"}}, {"seed": 782, "data": {"p1_how_many": "11", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{53}{200}, \\dfrac{55}{200}, \\dfrac{56}{200}, \\dfrac{61}{200}, \\dfrac{65}{200}, \\dfrac{72}{200}, \\dfrac{74}{200}, \\dfrac{75}{200}, \\text{ and } \\dfrac{76}{200}", "__seed__": "0782"}}, {"seed": 783, "data": {"p1_how_many": "13", "p1_a": "4.86", "p1_b": "4.87", "p1_numbers": "4.8605, 4.861, 4.8615, 4.862, 4.8625, 4.863, 4.8635, 4.864, 4.865, 4.866, 4.867, 4.868, and 4.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.861000000000001", "4.862", "4.863", "4.864", "4.865", "4.8660000000000005", "4.867", "4.868", "4.869000000000001"], "p1_2_xs": ["4.8605", "4.8615", "4.8625", "4.8635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{531}{2{,}000}, \\dfrac{543}{2{,}000}, \\dfrac{550}{2{,}000}, \\dfrac{558}{2{,}000}, \\dfrac{562}{2{,}000}, \\dfrac{568}{2{,}000}, \\dfrac{604}{2{,}000}, \\dfrac{730}{2{,}000}, \\dfrac{734}{2{,}000}, \\dfrac{743}{2{,}000}, \\text{ and } \\dfrac{747}{2{,}000}", "__seed__": "0783"}}, {"seed": 784, "data": {"p1_how_many": "14", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.215, 1.22, 1.225, 1.23, 1.235, 1.24, 1.245, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998", "1.2149999999999999", "1.2249999999999999", "1.2349999999999999", "1.2449999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}261}{12{,}000}, \\dfrac{8{,}329}{12{,}000}, \\dfrac{8{,}519}{12{,}000}, \\dfrac{8{,}574}{12{,}000}, \\dfrac{8{,}592}{12{,}000}, \\dfrac{8{,}632}{12{,}000}, \\dfrac{8{,}646}{12{,}000}, \\dfrac{8{,}784}{12{,}000}, \\dfrac{8{,}823}{12{,}000}, \\dfrac{8{,}857}{12{,}000}, \\dfrac{8{,}900}{12{,}000}, \\text{ and } \\dfrac{8{,}993}{12{,}000}", "__seed__": "0784"}}, {"seed": 785, "data": {"p1_how_many": "13", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.015, 8.02, 8.025, 8.03, 8.035, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005", "8.015", "8.025", "8.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}034}{77{,}000}, \\dfrac{42{,}063}{77{,}000}, \\dfrac{42{,}129}{77{,}000}, \\dfrac{44{,}411}{77{,}000}, \\dfrac{48{,}457}{77{,}000}, \\dfrac{49{,}080}{77{,}000}, \\dfrac{49{,}214}{77{,}000}, \\text{ and } \\dfrac{54{,}791}{77{,}000}", "__seed__": "0785"}}, {"seed": 786, "data": {"p1_how_many": "11", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.1005, 5.101, 5.1015, 5.102, 5.103, 5.104, 5.105, 5.106, 5.107, 5.108, and 5.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.101", "5.101999999999999", "5.103", "5.103999999999999", "5.1049999999999995", "5.106", "5.106999999999999", "5.108", "5.109"], "p1_2_xs": ["5.100499999999999", "5.1015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{331}{560}, \\dfrac{335}{560}, \\dfrac{339}{560}, \\dfrac{341}{560}, \\dfrac{343}{560}, \\dfrac{344}{560}, \\text{ and } \\dfrac{348}{560}", "__seed__": "0786"}}, {"seed": 787, "data": {"p1_how_many": "12", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.425, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001", "8.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}187}{3{,}500}, \\dfrac{2{,}205}{3{,}500}, \\dfrac{2{,}260}{3{,}500}, \\dfrac{2{,}261}{3{,}500}, \\dfrac{2{,}440}{3{,}500}, \\dfrac{2{,}464}{3{,}500}, \\dfrac{2{,}540}{3{,}500}, \\dfrac{2{,}545}{3{,}500}, \\dfrac{2{,}631}{3{,}500}, \\text{ and } \\dfrac{2{,}653}{3{,}500}", "__seed__": "0787"}}, {"seed": 788, "data": {"p1_how_many": "12", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.215, 1.22, 1.225, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998", "1.2149999999999999", "1.2249999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}214}{7{,}700}, \\dfrac{4{,}289}{7{,}700}, \\dfrac{4{,}476}{7{,}700}, \\dfrac{4{,}521}{7{,}700}, \\dfrac{4{,}586}{7{,}700}, \\dfrac{4{,}783}{7{,}700}, \\dfrac{4{,}880}{7{,}700}, \\dfrac{5{,}003}{7{,}700}, \\dfrac{5{,}025}{7{,}700}, \\dfrac{5{,}036}{7{,}700}, \\text{ and } \\dfrac{5{,}454}{7{,}700}", "__seed__": "0788"}}, {"seed": 789, "data": {"p1_how_many": "14", "p1_a": "4.91", "p1_b": "4.92", "p1_numbers": "4.9105, 4.911, 4.9115, 4.912, 4.9125, 4.913, 4.9135, 4.914, 4.9145, 4.915, 4.916, 4.917, 4.918, and 4.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.9110000000000005", "4.912", "4.913", "4.914", "4.915", "4.916", "4.917", "4.918", "4.9190000000000005"], "p1_2_xs": ["4.9105", "4.9115", "4.9125", "4.9135", "4.914499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{501}{3{,}000}, \\dfrac{519}{3{,}000}, \\dfrac{528}{3{,}000}, \\dfrac{530}{3{,}000}, \\dfrac{542}{3{,}000}, \\dfrac{547}{3{,}000}, \\dfrac{566}{3{,}000}, \\dfrac{570}{3{,}000}, \\dfrac{587}{3{,}000}, \\dfrac{590}{3{,}000}, \\dfrac{593}{3{,}000}, \\text{ and } \\dfrac{596}{3{,}000}", "__seed__": "0789"}}, {"seed": 790, "data": {"p1_how_many": "13", "p1_a": "5.87", "p1_b": "5.88", "p1_numbers": "5.8705, 5.871, 5.8715, 5.872, 5.8725, 5.873, 5.8735, 5.874, 5.875, 5.876, 5.877, 5.878, and 5.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.871", "5.872", "5.873", "5.874", "5.875", "5.876", "5.877", "5.878", "5.8790000000000004"], "p1_2_xs": ["5.8705", "5.8715", "5.8725", "5.8735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{506}{3{,}000}, \\dfrac{554}{3{,}000}, \\dfrac{555}{3{,}000}, \\dfrac{576}{3{,}000}, \\dfrac{586}{3{,}000}, \\dfrac{590}{3{,}000}, \\text{ and } \\dfrac{591}{3{,}000}", "__seed__": "0790"}}, {"seed": 791, "data": {"p1_how_many": "14", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.445, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998", "1.4449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}116}{20{,}000}, \\dfrac{4{,}240}{20{,}000}, \\dfrac{4{,}249}{20{,}000}, \\dfrac{4{,}266}{20{,}000}, \\dfrac{4{,}292}{20{,}000}, \\dfrac{4{,}316}{20{,}000}, \\dfrac{4{,}550}{20{,}000}, \\dfrac{4{,}591}{20{,}000}, \\dfrac{4{,}713}{20{,}000}, \\dfrac{4{,}729}{20{,}000}, \\text{ and } \\dfrac{4{,}796}{20{,}000}", "__seed__": "0791"}}, {"seed": 792, "data": {"p1_how_many": "14", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.535, 4.54, 4.545, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995", "4.535", "4.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{621}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{644}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{665}{4{,}200}, \\dfrac{688}{4{,}200}, \\dfrac{698}{4{,}200}, \\text{ and } \\dfrac{699}{4{,}200}", "__seed__": "0792"}}, {"seed": 793, "data": {"p1_how_many": "14", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.0005, 9.001, 9.0015, 9.002, 9.0025, 9.003, 9.0035, 9.004, 9.0045, 9.005, 9.006, 9.007, 9.008, and 9.009", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.001", "9.002", "9.003", "9.004", "9.005", "9.006", "9.007", "9.008", "9.009"], "p1_2_xs": ["9.0005", "9.0015", "9.002500000000001", "9.0035", "9.0045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{32}{120}, \\dfrac{33}{120}, \\dfrac{34}{120}, \\dfrac{35}{120}, \\dfrac{36}{120}, \\dfrac{37}{120}, \\text{ and } \\dfrac{38}{120}", "__seed__": "0793"}}, {"seed": 794, "data": {"p1_how_many": "11", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.43, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{413}{2{,}000}, \\dfrac{433}{2{,}000}, \\dfrac{437}{2{,}000}, \\dfrac{448}{2{,}000}, \\dfrac{451}{2{,}000}, \\dfrac{456}{2{,}000}, \\dfrac{464}{2{,}000}, \\dfrac{465}{2{,}000}, \\dfrac{480}{2{,}000}, \\dfrac{492}{2{,}000}, \\dfrac{493}{2{,}000}, \\text{ and } \\dfrac{499}{2{,}000}", "__seed__": "0794"}}, {"seed": 795, "data": {"p1_how_many": "11", "p1_a": "6.1", "p1_b": "6.2", "p1_numbers": "6.105, 6.11, 6.115, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17, 6.18, and 6.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.109999999999999", "6.119999999999999", "6.13", "6.14", "6.1499999999999995", "6.159999999999999", "6.17", "6.18", "6.1899999999999995"], "p1_2_xs": ["6.1049999999999995", "6.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{407}{2{,}000}, \\dfrac{411}{2{,}000}, \\dfrac{415}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{423}{2{,}000}, \\dfrac{438}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{464}{2{,}000}, \\dfrac{466}{2{,}000}, \\dfrac{472}{2{,}000}, \\dfrac{483}{2{,}000}, \\text{ and } \\dfrac{484}{2{,}000}", "__seed__": "0795"}}, {"seed": 796, "data": {"p1_how_many": "10", "p1_a": "8.84", "p1_b": "8.85", "p1_numbers": "8.8405, 8.841, 8.842, 8.843, 8.844, 8.845, 8.846, 8.847, 8.848, and 8.849", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.841", "8.842", "8.843", "8.844", "8.845", "8.846", "8.847", "8.847999999999999", "8.849"], "p1_2_xs": ["8.8405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{320}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{334}{1{,}200}, \\dfrac{363}{1{,}200}, \\dfrac{369}{1{,}200}, \\dfrac{386}{1{,}200}, \\dfrac{387}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0796"}}, {"seed": 797, "data": {"p1_how_many": "11", "p1_a": "3.92", "p1_b": "3.93", "p1_numbers": "3.9205, 3.921, 3.9215, 3.922, 3.923, 3.924, 3.925, 3.926, 3.927, 3.928, and 3.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.921", "3.9219999999999997", "3.923", "3.924", "3.925", "3.9259999999999997", "3.927", "3.928", "3.929"], "p1_2_xs": ["3.9205", "3.9215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}033}{12{,}000}, \\dfrac{8{,}078}{12{,}000}, \\dfrac{8{,}313}{12{,}000}, \\dfrac{8{,}388}{12{,}000}, \\dfrac{8{,}431}{12{,}000}, \\dfrac{8{,}509}{12{,}000}, \\dfrac{8{,}616}{12{,}000}, \\dfrac{8{,}739}{12{,}000}, \\dfrac{8{,}794}{12{,}000}, \\dfrac{8{,}829}{12{,}000}, \\dfrac{8{,}868}{12{,}000}, \\text{ and } \\dfrac{8{,}905}{12{,}000}", "__seed__": "0797"}}, {"seed": 798, "data": {"p1_how_many": "13", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.735, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725", "8.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0798"}}, {"seed": 799, "data": {"p1_how_many": "12", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{928}{6{,}300}, \\dfrac{998}{6{,}300}, \\dfrac{1{,}107}{6{,}300}, \\dfrac{1{,}165}{6{,}300}, \\dfrac{1{,}291}{6{,}300}, \\dfrac{1{,}351}{6{,}300}, \\text{ and } \\dfrac{1{,}360}{6{,}300}", "__seed__": "0799"}}, {"seed": 800, "data": {"p1_how_many": "14", "p1_a": "5.72", "p1_b": "5.73", "p1_numbers": "5.7205, 5.721, 5.7215, 5.722, 5.7225, 5.723, 5.7235, 5.724, 5.7245, 5.725, 5.726, 5.727, 5.728, and 5.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.721", "5.7219999999999995", "5.723", "5.723999999999999", "5.725", "5.726", "5.726999999999999", "5.728", "5.729"], "p1_2_xs": ["5.7204999999999995", "5.7215", "5.722499999999999", "5.7235", "5.724499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}067}{15{,}000}, \\dfrac{6{,}122}{15{,}000}, \\dfrac{6{,}384}{15{,}000}, \\dfrac{7{,}251}{15{,}000}, \\dfrac{7{,}951}{15{,}000}, \\dfrac{7{,}990}{15{,}000}, \\dfrac{8{,}189}{15{,}000}, \\dfrac{8{,}261}{15{,}000}, \\dfrac{9{,}219}{15{,}000}, \\text{ and } \\dfrac{9{,}526}{15{,}000}", "__seed__": "0800"}}, {"seed": 801, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}775}{77{,}000}, \\dfrac{44{,}956}{77{,}000}, \\dfrac{46{,}803}{77{,}000}, \\dfrac{46{,}877}{77{,}000}, \\dfrac{47{,}749}{77{,}000}, \\dfrac{49{,}413}{77{,}000}, \\dfrac{49{,}696}{77{,}000}, \\text{ and } \\dfrac{52{,}104}{77{,}000}", "__seed__": "0801"}}, {"seed": 802, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{432}{770}, \\dfrac{446}{770}, \\dfrac{457}{770}, \\dfrac{493}{770}, \\dfrac{507}{770}, \\dfrac{508}{770}, \\dfrac{511}{770}, \\text{ and } \\dfrac{539}{770}", "__seed__": "0802"}}, {"seed": 803, "data": {"p1_how_many": "12", "p1_a": "4.26", "p1_b": "4.27", "p1_numbers": "4.2605, 4.261, 4.2615, 4.262, 4.2625, 4.263, 4.264, 4.265, 4.266, 4.267, 4.268, and 4.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.261", "4.262", "4.263", "4.263999999999999", "4.265", "4.266", "4.2669999999999995", "4.268", "4.269"], "p1_2_xs": ["4.2604999999999995", "4.2615", "4.262499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}106}{20{,}000}, \\dfrac{4{,}135}{20{,}000}, \\dfrac{4{,}326}{20{,}000}, \\dfrac{4{,}360}{20{,}000}, \\dfrac{4{,}509}{20{,}000}, \\dfrac{4{,}806}{20{,}000}, \\text{ and } \\dfrac{4{,}853}{20{,}000}", "__seed__": "0803"}}, {"seed": 804, "data": {"p1_how_many": "11", "p1_a": "9.31", "p1_b": "9.32", "p1_numbers": "9.3105, 9.311, 9.3115, 9.312, 9.313, 9.314, 9.315, 9.316, 9.317, 9.318, and 9.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.311", "9.312000000000001", "9.313", "9.314", "9.315000000000001", "9.316", "9.317", "9.318", "9.319"], "p1_2_xs": ["9.310500000000001", "9.3115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{351}{560}, \\dfrac{353}{560}, \\dfrac{360}{560}, \\dfrac{373}{560}, \\dfrac{377}{560}, \\dfrac{385}{560}, \\dfrac{396}{560}, \\text{ and } \\dfrac{397}{560}", "__seed__": "0804"}}, {"seed": 805, "data": {"p1_how_many": "14", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.535, 6.54, 6.545, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995", "6.535", "6.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{713}{4{,}200}, \\dfrac{731}{4{,}200}, \\dfrac{746}{4{,}200}, \\dfrac{858}{4{,}200}, \\dfrac{910}{4{,}200}, \\dfrac{959}{4{,}200}, \\dfrac{990}{4{,}200}, \\dfrac{1{,}010}{4{,}200}, \\dfrac{1{,}015}{4{,}200}, \\dfrac{1{,}032}{4{,}200}, \\dfrac{1{,}054}{4{,}200}, \\text{ and } \\dfrac{1{,}149}{4{,}200}", "__seed__": "0805"}}, {"seed": 806, "data": {"p1_how_many": "14", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.515, 8.52, 8.525, 8.53, 8.535, 8.54, 8.545, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505", "8.515", "8.525", "8.535", "8.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{810}{1{,}200}, \\dfrac{818}{1{,}200}, \\dfrac{822}{1{,}200}, \\dfrac{829}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{883}{1{,}200}, \\dfrac{884}{1{,}200}, \\dfrac{890}{1{,}200}, \\text{ and } \\dfrac{895}{1{,}200}", "__seed__": "0806"}}, {"seed": 807, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}004}{35{,}000}, \\dfrac{20{,}356}{35{,}000}, \\dfrac{20{,}530}{35{,}000}, \\dfrac{20{,}654}{35{,}000}, \\dfrac{20{,}730}{35{,}000}, \\dfrac{20{,}756}{35{,}000}, \\dfrac{20{,}866}{35{,}000}, \\dfrac{20{,}926}{35{,}000}, \\text{ and } \\dfrac{20{,}969}{35{,}000}", "__seed__": "0807"}}, {"seed": 808, "data": {"p1_how_many": "10", "p1_a": "3.82", "p1_b": "3.83", "p1_numbers": "3.8205, 3.821, 3.822, 3.823, 3.824, 3.825, 3.826, 3.827, 3.828, and 3.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.8209999999999997", "3.8219999999999996", "3.823", "3.824", "3.8249999999999997", "3.8259999999999996", "3.827", "3.828", "3.8289999999999997"], "p1_2_xs": ["3.8205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}331}{15{,}000}, \\dfrac{6{,}409}{15{,}000}, \\dfrac{7{,}026}{15{,}000}, \\dfrac{8{,}264}{15{,}000}, \\dfrac{8{,}334}{15{,}000}, \\dfrac{8{,}752}{15{,}000}, \\dfrac{8{,}938}{15{,}000}, \\dfrac{9{,}220}{15{,}000}, \\dfrac{9{,}253}{15{,}000}, \\dfrac{9{,}625}{15{,}000}, \\text{ and } \\dfrac{9{,}908}{15{,}000}", "__seed__": "0808"}}, {"seed": 809, "data": {"p1_how_many": "10", "p1_a": "2.91", "p1_b": "2.92", "p1_numbers": "2.9105, 2.911, 2.912, 2.913, 2.914, 2.915, 2.916, 2.917, 2.918, and 2.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.911", "2.912", "2.9130000000000003", "2.914", "2.915", "2.916", "2.9170000000000003", "2.918", "2.919"], "p1_2_xs": ["2.9105000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{48}{200}", "__seed__": "0809"}}, {"seed": 810, "data": {"p1_how_many": "10", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{804}{1{,}200}, \\dfrac{809}{1{,}200}, \\dfrac{813}{1{,}200}, \\dfrac{821}{1{,}200}, \\dfrac{839}{1{,}200}, \\dfrac{841}{1{,}200}, \\dfrac{848}{1{,}200}, \\dfrac{852}{1{,}200}, \\dfrac{857}{1{,}200}, \\dfrac{861}{1{,}200}, \\dfrac{874}{1{,}200}, \\text{ and } \\dfrac{893}{1{,}200}", "__seed__": "0810"}}, {"seed": 811, "data": {"p1_how_many": "14", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.015, 9.02, 9.025, 9.03, 9.035, 9.04, 9.045, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005", "9.015", "9.025", "9.035", "9.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}188}{12{,}000}, \\dfrac{3{,}211}{12{,}000}, \\dfrac{3{,}462}{12{,}000}, \\dfrac{3{,}593}{12{,}000}, \\dfrac{3{,}619}{12{,}000}, \\dfrac{3{,}875}{12{,}000}, \\dfrac{3{,}940}{12{,}000}, \\text{ and } \\dfrac{3{,}983}{12{,}000}", "__seed__": "0811"}}, {"seed": 812, "data": {"p1_how_many": "10", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.02, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{307}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{332}{1{,}200}, \\dfrac{345}{1{,}200}, \\dfrac{361}{1{,}200}, \\dfrac{378}{1{,}200}, \\dfrac{380}{1{,}200}, \\dfrac{382}{1{,}200}, \\dfrac{391}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0812"}}, {"seed": 813, "data": {"p1_how_many": "10", "p1_a": "3.66", "p1_b": "3.67", "p1_numbers": "3.6605, 3.661, 3.662, 3.663, 3.664, 3.665, 3.666, 3.667, 3.668, and 3.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.661", "3.662", "3.6630000000000003", "3.664", "3.665", "3.666", "3.6670000000000003", "3.668", "3.669"], "p1_2_xs": ["3.6605000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}103}{35{,}000}, \\dfrac{20{,}190}{35{,}000}, \\dfrac{20{,}212}{35{,}000}, \\dfrac{20{,}477}{35{,}000}, \\dfrac{20{,}504}{35{,}000}, \\dfrac{20{,}801}{35{,}000}, \\text{ and } \\dfrac{20{,}863}{35{,}000}", "__seed__": "0813"}}, {"seed": 814, "data": {"p1_how_many": "11", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}028}{20{,}000}, \\dfrac{5{,}781}{20{,}000}, \\dfrac{5{,}976}{20{,}000}, \\dfrac{6{,}376}{20{,}000}, \\dfrac{6{,}760}{20{,}000}, \\dfrac{6{,}931}{20{,}000}, \\text{ and } \\dfrac{7{,}004}{20{,}000}", "__seed__": "0814"}}, {"seed": 815, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{43{,}005}{77{,}000}, \\dfrac{45{,}928}{77{,}000}, \\dfrac{48{,}373}{77{,}000}, \\dfrac{48{,}445}{77{,}000}, \\dfrac{49{,}386}{77{,}000}, \\dfrac{49{,}892}{77{,}000}, \\dfrac{50{,}794}{77{,}000}, \\text{ and } \\dfrac{53{,}268}{77{,}000}", "__seed__": "0815"}}, {"seed": 816, "data": {"p1_how_many": "12", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}043}{12{,}000}, \\dfrac{3{,}196}{12{,}000}, \\dfrac{3{,}203}{12{,}000}, \\dfrac{3{,}342}{12{,}000}, \\dfrac{3{,}346}{12{,}000}, \\dfrac{3{,}580}{12{,}000}, \\dfrac{3{,}674}{12{,}000}, \\dfrac{3{,}763}{12{,}000}, \\dfrac{3{,}810}{12{,}000}, \\dfrac{3{,}858}{12{,}000}, \\text{ and } \\dfrac{3{,}889}{12{,}000}", "__seed__": "0816"}}, {"seed": 817, "data": {"p1_how_many": "14", "p1_a": "6.05", "p1_b": "6.06", "p1_numbers": "6.0505, 6.051, 6.0515, 6.052, 6.0525, 6.053, 6.0535, 6.054, 6.0545, 6.055, 6.056, 6.057, 6.058, and 6.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.051", "6.052", "6.053", "6.053999999999999", "6.055", "6.056", "6.0569999999999995", "6.058", "6.059"], "p1_2_xs": ["6.0504999999999995", "6.0515", "6.052499999999999", "6.0535", "6.054499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}318}{56{,}000}, \\dfrac{32{,}512}{56{,}000}, \\dfrac{32{,}590}{56{,}000}, \\dfrac{32{,}940}{56{,}000}, \\dfrac{33{,}358}{56{,}000}, \\dfrac{33{,}482}{56{,}000}, \\dfrac{33{,}722}{56{,}000}, \\dfrac{33{,}871}{56{,}000}, \\dfrac{33{,}888}{56{,}000}, \\dfrac{33{,}953}{56{,}000}, \\text{ and } \\dfrac{34{,}619}{56{,}000}", "__seed__": "0817"}}, {"seed": 818, "data": {"p1_how_many": "11", "p1_a": "8.26", "p1_b": "8.27", "p1_numbers": "8.2605, 8.261, 8.2615, 8.262, 8.263, 8.264, 8.265, 8.266, 8.267, 8.268, and 8.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.261", "8.262", "8.263", "8.264", "8.265", "8.266", "8.267", "8.267999999999999", "8.269"], "p1_2_xs": ["8.2605", "8.2615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}137}{35{,}000}, \\dfrac{14{,}157}{35{,}000}, \\dfrac{14{,}193}{35{,}000}, \\dfrac{14{,}412}{35{,}000}, \\dfrac{14{,}414}{35{,}000}, \\dfrac{14{,}522}{35{,}000}, \\text{ and } \\dfrac{14{,}762}{35{,}000}", "__seed__": "0818"}}, {"seed": 819, "data": {"p1_how_many": "14", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.325, 9.33, 9.335, 9.34, 9.345, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001", "9.325000000000001", "9.335", "9.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}467}{42{,}000}, \\dfrac{30{,}764}{42{,}000}, \\dfrac{31{,}700}{42{,}000}, \\dfrac{32{,}150}{42{,}000}, \\dfrac{32{,}864}{42{,}000}, \\dfrac{33{,}017}{42{,}000}, \\dfrac{33{,}954}{42{,}000}, \\text{ and } \\dfrac{34{,}435}{42{,}000}", "__seed__": "0819"}}, {"seed": 820, "data": {"p1_how_many": "10", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.52, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}525}{42{,}000}, \\dfrac{31{,}708}{42{,}000}, \\dfrac{31{,}796}{42{,}000}, \\dfrac{33{,}263}{42{,}000}, \\dfrac{33{,}546}{42{,}000}, \\dfrac{34{,}610}{42{,}000}, \\text{ and } \\dfrac{34{,}994}{42{,}000}", "__seed__": "0820"}}, {"seed": 821, "data": {"p1_how_many": "10", "p1_a": "5.92", "p1_b": "5.93", "p1_numbers": "5.9205, 5.921, 5.922, 5.923, 5.924, 5.925, 5.926, 5.927, 5.928, and 5.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.921", "5.922", "5.923", "5.9239999999999995", "5.925", "5.926", "5.927", "5.928", "5.929"], "p1_2_xs": ["5.9205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0821"}}, {"seed": 822, "data": {"p1_how_many": "13", "p1_a": "2.85", "p1_b": "2.86", "p1_numbers": "2.8505, 2.851, 2.8515, 2.852, 2.8525, 2.853, 2.8535, 2.854, 2.855, 2.856, 2.857, 2.858, and 2.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.851", "2.852", "2.853", "2.854", "2.855", "2.856", "2.857", "2.858", "2.859"], "p1_2_xs": ["2.8505000000000003", "2.8515", "2.8525", "2.8535000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}159}{20{,}000}, \\dfrac{12{,}216}{20{,}000}, \\dfrac{12{,}442}{20{,}000}, \\dfrac{12{,}852}{20{,}000}, \\dfrac{13{,}143}{20{,}000}, \\dfrac{13{,}273}{20{,}000}, \\dfrac{13{,}963}{20{,}000}, \\dfrac{14{,}534}{20{,}000}, \\text{ and } \\dfrac{14{,}546}{20{,}000}", "__seed__": "0822"}}, {"seed": 823, "data": {"p1_how_many": "12", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}311}{15{,}000}, \\dfrac{5{,}413}{15{,}000}, \\dfrac{5{,}537}{15{,}000}, \\dfrac{5{,}542}{15{,}000}, \\dfrac{5{,}560}{15{,}000}, \\dfrac{5{,}637}{15{,}000}, \\dfrac{5{,}707}{15{,}000}, \\dfrac{5{,}838}{15{,}000}, \\text{ and } \\dfrac{5{,}990}{15{,}000}", "__seed__": "0823"}}, {"seed": 824, "data": {"p1_how_many": "12", "p1_a": "4.44", "p1_b": "4.45", "p1_numbers": "4.4405, 4.441, 4.4415, 4.442, 4.4425, 4.443, 4.444, 4.445, 4.446, 4.447, 4.448, and 4.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.441000000000001", "4.442", "4.4430000000000005", "4.444", "4.445", "4.446000000000001", "4.447", "4.448", "4.449000000000001"], "p1_2_xs": ["4.4405", "4.4415000000000004", "4.4425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}044}{20{,}000}, \\dfrac{5{,}264}{20{,}000}, \\dfrac{6{,}105}{20{,}000}, \\dfrac{6{,}228}{20{,}000}, \\dfrac{6{,}566}{20{,}000}, \\dfrac{6{,}721}{20{,}000}, \\dfrac{6{,}785}{20{,}000}, \\text{ and } \\dfrac{7{,}484}{20{,}000}", "__seed__": "0824"}}, {"seed": 825, "data": {"p1_how_many": "11", "p1_a": "9.23", "p1_b": "9.24", "p1_numbers": "9.2305, 9.231, 9.2315, 9.232, 9.233, 9.234, 9.235, 9.236, 9.237, 9.238, and 9.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.231", "9.232000000000001", "9.233", "9.234", "9.235000000000001", "9.236", "9.237", "9.238", "9.239"], "p1_2_xs": ["9.230500000000001", "9.2315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}809}{5{,}600}, \\dfrac{4{,}817}{5{,}600}, \\dfrac{4{,}827}{5{,}600}, \\dfrac{4{,}844}{5{,}600}, \\dfrac{4{,}845}{5{,}600}, \\dfrac{4{,}865}{5{,}600}, \\dfrac{4{,}878}{5{,}600}, \\dfrac{4{,}882}{5{,}600}, \\dfrac{4{,}884}{5{,}600}, \\text{ and } \\dfrac{4{,}889}{5{,}600}", "__seed__": "0825"}}, {"seed": 826, "data": {"p1_how_many": "11", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{402}{2{,}000}, \\dfrac{407}{2{,}000}, \\dfrac{412}{2{,}000}, \\dfrac{417}{2{,}000}, \\dfrac{432}{2{,}000}, \\dfrac{438}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{457}{2{,}000}, \\dfrac{468}{2{,}000}, \\dfrac{482}{2{,}000}, \\dfrac{488}{2{,}000}, \\text{ and } \\dfrac{491}{2{,}000}", "__seed__": "0826"}}, {"seed": 827, "data": {"p1_how_many": "11", "p1_a": "9.14", "p1_b": "9.15", "p1_numbers": "9.1405, 9.141, 9.1415, 9.142, 9.143, 9.144, 9.145, 9.146, 9.147, 9.148, and 9.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.141", "9.142000000000001", "9.143", "9.144", "9.145000000000001", "9.146", "9.147", "9.148", "9.149000000000001"], "p1_2_xs": ["9.140500000000001", "9.1415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}100}{42{,}000}, \\dfrac{7{,}526}{42{,}000}, \\dfrac{7{,}665}{42{,}000}, \\dfrac{8{,}492}{42{,}000}, \\dfrac{8{,}742}{42{,}000}, \\dfrac{8{,}801}{42{,}000}, \\dfrac{8{,}850}{42{,}000}, \\dfrac{11{,}102}{42{,}000}, \\dfrac{11{,}342}{42{,}000}, \\text{ and } \\dfrac{11{,}399}{42{,}000}", "__seed__": "0827"}}, {"seed": 828, "data": {"p1_how_many": "10", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.42, 9.43, 9.44, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}387}{42{,}000}, \\dfrac{7{,}468}{42{,}000}, \\dfrac{8{,}833}{42{,}000}, \\dfrac{8{,}939}{42{,}000}, \\dfrac{9{,}293}{42{,}000}, \\dfrac{9{,}553}{42{,}000}, \\dfrac{9{,}671}{42{,}000}, \\text{ and } \\dfrac{11{,}796}{42{,}000}", "__seed__": "0828"}}, {"seed": 829, "data": {"p1_how_many": "12", "p1_a": "4.77", "p1_b": "4.78", "p1_numbers": "4.7705, 4.771, 4.7715, 4.772, 4.7725, 4.773, 4.774, 4.775, 4.776, 4.777, 4.778, and 4.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.771", "4.771999999999999", "4.773", "4.773999999999999", "4.7749999999999995", "4.776", "4.776999999999999", "4.778", "4.779"], "p1_2_xs": ["4.770499999999999", "4.7715", "4.772499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{716}{3{,}500}, \\dfrac{822}{3{,}500}, \\dfrac{870}{3{,}500}, \\dfrac{883}{3{,}500}, \\dfrac{977}{3{,}500}, \\dfrac{996}{3{,}500}, \\dfrac{997}{3{,}500}, \\text{ and } \\dfrac{999}{3{,}500}", "__seed__": "0829"}}, {"seed": 830, "data": {"p1_how_many": "11", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.73, 4.74, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{602}{4{,}200}, \\dfrac{603}{4{,}200}, \\dfrac{633}{4{,}200}, \\dfrac{634}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{674}{4{,}200}, \\dfrac{675}{4{,}200}, \\dfrac{684}{4{,}200}, \\dfrac{691}{4{,}200}, \\text{ and } \\dfrac{699}{4{,}200}", "__seed__": "0830"}}, {"seed": 831, "data": {"p1_how_many": "11", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.6005, 8.601, 8.6015, 8.602, 8.603, 8.604, 8.605, 8.606, 8.607, 8.608, and 8.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.600999999999999", "8.602", "8.603", "8.604", "8.605", "8.606", "8.607", "8.607999999999999", "8.609"], "p1_2_xs": ["8.6005", "8.6015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}003}{12{,}000}, \\dfrac{8{,}043}{12{,}000}, \\dfrac{8{,}213}{12{,}000}, \\dfrac{8{,}300}{12{,}000}, \\dfrac{8{,}530}{12{,}000}, \\dfrac{8{,}653}{12{,}000}, \\dfrac{8{,}674}{12{,}000}, \\dfrac{8{,}749}{12{,}000}, \\dfrac{8{,}763}{12{,}000}, \\dfrac{8{,}833}{12{,}000}, \\text{ and } \\dfrac{8{,}933}{12{,}000}", "__seed__": "0831"}}, {"seed": 832, "data": {"p1_how_many": "14", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.515, 8.52, 8.525, 8.53, 8.535, 8.54, 8.545, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505", "8.515", "8.525", "8.535", "8.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}505}{2{,}000}, \\dfrac{1{,}508}{2{,}000}, \\dfrac{1{,}519}{2{,}000}, \\dfrac{1{,}522}{2{,}000}, \\dfrac{1{,}527}{2{,}000}, \\dfrac{1{,}534}{2{,}000}, \\dfrac{1{,}544}{2{,}000}, \\dfrac{1{,}551}{2{,}000}, \\dfrac{1{,}557}{2{,}000}, \\dfrac{1{,}571}{2{,}000}, \\dfrac{1{,}577}{2{,}000}, \\text{ and } \\dfrac{1{,}595}{2{,}000}", "__seed__": "0832"}}, {"seed": 833, "data": {"p1_how_many": "13", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}508}{4{,}200}, \\dfrac{3{,}515}{4{,}200}, \\dfrac{3{,}524}{4{,}200}, \\dfrac{3{,}547}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}558}{4{,}200}, \\dfrac{3{,}563}{4{,}200}, \\dfrac{3{,}590}{4{,}200}, \\text{ and } \\dfrac{3{,}592}{4{,}200}", "__seed__": "0833"}}, {"seed": 834, "data": {"p1_how_many": "11", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}707}{6{,}300}, \\dfrac{2{,}709}{6{,}300}, \\dfrac{2{,}717}{6{,}300}, \\dfrac{2{,}719}{6{,}300}, \\dfrac{2{,}728}{6{,}300}, \\dfrac{2{,}735}{6{,}300}, \\dfrac{2{,}747}{6{,}300}, \\dfrac{2{,}776}{6{,}300}, \\text{ and } \\dfrac{2{,}791}{6{,}300}", "__seed__": "0834"}}, {"seed": 835, "data": {"p1_how_many": "11", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}415}{56{,}000}, \\dfrac{36{,}686}{56{,}000}, \\dfrac{36{,}826}{56{,}000}, \\dfrac{38{,}031}{56{,}000}, \\dfrac{38{,}523}{56{,}000}, \\dfrac{39{,}117}{56{,}000}, \\dfrac{39{,}216}{56{,}000}, \\dfrac{39{,}471}{56{,}000}, \\dfrac{39{,}558}{56{,}000}, \\text{ and } \\dfrac{39{,}716}{56{,}000}", "__seed__": "0835"}}, {"seed": 836, "data": {"p1_how_many": "11", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{22{,}023}{35{,}000}, \\dfrac{22{,}124}{35{,}000}, \\dfrac{22{,}440}{35{,}000}, \\dfrac{22{,}883}{35{,}000}, \\dfrac{23{,}034}{35{,}000}, \\dfrac{23{,}726}{35{,}000}, \\dfrac{25{,}084}{35{,}000}, \\text{ and } \\dfrac{25{,}907}{35{,}000}", "__seed__": "0836"}}, {"seed": 837, "data": {"p1_how_many": "12", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}454}{35{,}000}, \\dfrac{7{,}652}{35{,}000}, \\dfrac{8{,}679}{35{,}000}, \\dfrac{9{,}204}{35{,}000}, \\dfrac{9{,}311}{35{,}000}, \\dfrac{9{,}332}{35{,}000}, \\dfrac{9{,}439}{35{,}000}, \\dfrac{9{,}605}{35{,}000}, \\text{ and } \\dfrac{9{,}709}{35{,}000}", "__seed__": "0837"}}, {"seed": 838, "data": {"p1_how_many": "13", "p1_a": "2.81", "p1_b": "2.82", "p1_numbers": "2.8105, 2.811, 2.8115, 2.812, 2.8125, 2.813, 2.8135, 2.814, 2.815, 2.816, 2.817, 2.818, and 2.819", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.811", "2.812", "2.813", "2.814", "2.815", "2.816", "2.817", "2.818", "2.819"], "p1_2_xs": ["2.8105", "2.8115", "2.8125", "2.8135000000000003"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{624}{4{,}200}, \\dfrac{627}{4{,}200}, \\dfrac{633}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{664}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0838"}}, {"seed": 839, "data": {"p1_how_many": "10", "p1_a": "9.72", "p1_b": "9.73", "p1_numbers": "9.7205, 9.721, 9.722, 9.723, 9.724, 9.725, 9.726, 9.727, 9.728, and 9.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.721", "9.722000000000001", "9.723", "9.724", "9.725000000000001", "9.726", "9.727", "9.728", "9.729000000000001"], "p1_2_xs": ["9.720500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}144}{42{,}000}, \\dfrac{7{,}364}{42{,}000}, \\dfrac{7{,}479}{42{,}000}, \\dfrac{8{,}037}{42{,}000}, \\dfrac{8{,}132}{42{,}000}, \\dfrac{8{,}306}{42{,}000}, \\dfrac{9{,}190}{42{,}000}, \\dfrac{10{,}866}{42{,}000}, \\dfrac{11{,}185}{42{,}000}, \\dfrac{11{,}307}{42{,}000}, \\dfrac{11{,}322}{42{,}000}, \\text{ and } \\dfrac{11{,}697}{42{,}000}", "__seed__": "0839"}}, {"seed": 840, "data": {"p1_how_many": "10", "p1_a": "9.06", "p1_b": "9.07", "p1_numbers": "9.0605, 9.061, 9.062, 9.063, 9.064, 9.065, 9.066, 9.067, 9.068, and 9.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.061", "9.062000000000001", "9.063", "9.064", "9.065000000000001", "9.066", "9.067", "9.068", "9.069"], "p1_2_xs": ["9.060500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0840"}}, {"seed": 841, "data": {"p1_how_many": "11", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}410}{3{,}500}, \\dfrac{1{,}415}{3{,}500}, \\dfrac{1{,}424}{3{,}500}, \\dfrac{1{,}440}{3{,}500}, \\dfrac{1{,}452}{3{,}500}, \\dfrac{1{,}453}{3{,}500}, \\dfrac{1{,}456}{3{,}500}, \\dfrac{1{,}468}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}476}{3{,}500}, \\text{ and } \\dfrac{1{,}491}{3{,}500}", "__seed__": "0841"}}, {"seed": 842, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}051}{63{,}000}, \\dfrac{27{,}226}{63{,}000}, \\dfrac{27{,}229}{63{,}000}, \\dfrac{27{,}322}{63{,}000}, \\dfrac{27{,}381}{63{,}000}, \\dfrac{27{,}506}{63{,}000}, \\dfrac{27{,}537}{63{,}000}, \\dfrac{27{,}625}{63{,}000}, \\dfrac{27{,}628}{63{,}000}, \\dfrac{27{,}693}{63{,}000}, \\dfrac{27{,}823}{63{,}000}, \\text{ and } \\dfrac{27{,}986}{63{,}000}", "__seed__": "0842"}}, {"seed": 843, "data": {"p1_how_many": "14", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.325, 3.33, 3.335, 3.34, 3.345, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995", "3.3249999999999997", "3.3349999999999995", "3.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}242}{5{,}600}, \\dfrac{3{,}244}{5{,}600}, \\dfrac{3{,}271}{5{,}600}, \\dfrac{3{,}304}{5{,}600}, \\dfrac{3{,}352}{5{,}600}, \\dfrac{3{,}371}{5{,}600}, \\dfrac{3{,}373}{5{,}600}, \\text{ and } \\dfrac{3{,}400}{5{,}600}", "__seed__": "0843"}}, {"seed": 844, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}025}{3{,}500}, \\dfrac{1{,}050}{3{,}500}, \\dfrac{1{,}146}{3{,}500}, \\dfrac{1{,}159}{3{,}500}, \\dfrac{1{,}193}{3{,}500}, \\dfrac{1{,}208}{3{,}500}, \\dfrac{1{,}225}{3{,}500}, \\dfrac{1{,}248}{3{,}500}, \\dfrac{1{,}255}{3{,}500}, \\text{ and } \\dfrac{1{,}332}{3{,}500}", "__seed__": "0844"}}, {"seed": 845, "data": {"p1_how_many": "10", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{602}{4{,}200}, \\dfrac{603}{4{,}200}, \\dfrac{604}{4{,}200}, \\dfrac{641}{4{,}200}, \\dfrac{647}{4{,}200}, \\dfrac{654}{4{,}200}, \\dfrac{657}{4{,}200}, \\dfrac{664}{4{,}200}, \\dfrac{673}{4{,}200}, \\dfrac{692}{4{,}200}, \\dfrac{694}{4{,}200}, \\text{ and } \\dfrac{698}{4{,}200}", "__seed__": "0845"}}, {"seed": 846, "data": {"p1_how_many": "10", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{207}{350}, \\dfrac{210}{350}, \\dfrac{211}{350}, \\dfrac{216}{350}, \\dfrac{230}{350}, \\dfrac{232}{350}, \\dfrac{235}{350}, \\text{ and } \\dfrac{263}{350}", "__seed__": "0846"}}, {"seed": 847, "data": {"p1_how_many": "12", "p1_a": "4.21", "p1_b": "4.22", "p1_numbers": "4.2105, 4.211, 4.2115, 4.212, 4.2125, 4.213, 4.214, 4.215, 4.216, 4.217, 4.218, and 4.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.211", "4.212", "4.213", "4.2139999999999995", "4.215", "4.216", "4.217", "4.218", "4.219"], "p1_2_xs": ["4.2105", "4.2115", "4.2124999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}123}{35{,}000}, \\dfrac{20{,}173}{35{,}000}, \\dfrac{20{,}253}{35{,}000}, \\dfrac{20{,}316}{35{,}000}, \\dfrac{20{,}351}{35{,}000}, \\dfrac{20{,}444}{35{,}000}, \\dfrac{20{,}638}{35{,}000}, \\dfrac{20{,}644}{35{,}000}, \\dfrac{20{,}660}{35{,}000}, \\text{ and } \\dfrac{20{,}781}{35{,}000}", "__seed__": "0847"}}, {"seed": 848, "data": {"p1_how_many": "11", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.615, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995", "7.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}160}{3{,}500}, \\dfrac{2{,}311}{3{,}500}, \\dfrac{2{,}536}{3{,}500}, \\dfrac{2{,}663}{3{,}500}, \\dfrac{2{,}673}{3{,}500}, \\dfrac{2{,}692}{3{,}500}, \\dfrac{2{,}717}{3{,}500}, \\text{ and } \\dfrac{2{,}727}{3{,}500}", "__seed__": "0848"}}, {"seed": 849, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}545}{20{,}000}, \\dfrac{5{,}630}{20{,}000}, \\dfrac{5{,}687}{20{,}000}, \\dfrac{6{,}888}{20{,}000}, \\dfrac{6{,}974}{20{,}000}, \\dfrac{7{,}133}{20{,}000}, \\dfrac{7{,}186}{20{,}000}, \\dfrac{7{,}204}{20{,}000}, \\dfrac{7{,}902}{20{,}000}, \\text{ and } \\dfrac{7{,}920}{20{,}000}", "__seed__": "0849"}}, {"seed": 850, "data": {"p1_how_many": "10", "p1_a": "4.3", "p1_b": "4.4", "p1_numbers": "4.305, 4.31, 4.32, 4.33, 4.34, 4.35, 4.36, 4.37, 4.38, and 4.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.31", "4.319999999999999", "4.33", "4.34", "4.35", "4.359999999999999", "4.37", "4.38", "4.39"], "p1_2_xs": ["4.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{616}{4{,}200}, \\dfrac{621}{4{,}200}, \\dfrac{625}{4{,}200}, \\dfrac{627}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{675}{4{,}200}, \\text{ and } \\dfrac{689}{4{,}200}", "__seed__": "0850"}}, {"seed": 851, "data": {"p1_how_many": "12", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.3005, 5.301, 5.3015, 5.302, 5.3025, 5.303, 5.304, 5.305, 5.306, 5.307, 5.308, and 5.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.301", "5.302", "5.303", "5.303999999999999", "5.305", "5.306", "5.3069999999999995", "5.308", "5.309"], "p1_2_xs": ["5.3004999999999995", "5.3015", "5.302499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{632}{1{,}500}, \\dfrac{653}{1{,}500}, \\dfrac{709}{1{,}500}, \\dfrac{861}{1{,}500}, \\dfrac{883}{1{,}500}, \\dfrac{888}{1{,}500}, \\dfrac{917}{1{,}500}, \\dfrac{922}{1{,}500}, \\dfrac{933}{1{,}500}, \\text{ and } \\dfrac{996}{1{,}500}", "__seed__": "0851"}}, {"seed": 852, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{42{,}846}{77{,}000}, \\dfrac{42{,}872}{77{,}000}, \\dfrac{49{,}102}{77{,}000}, \\dfrac{50{,}816}{77{,}000}, \\dfrac{55{,}449}{77{,}000}, \\dfrac{60{,}418}{77{,}000}, \\dfrac{60{,}755}{77{,}000}, \\text{ and } \\dfrac{63{,}153}{77{,}000}", "__seed__": "0852"}}, {"seed": 853, "data": {"p1_how_many": "13", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}045}{4{,}200}, \\dfrac{3{,}183}{4{,}200}, \\dfrac{3{,}192}{4{,}200}, \\dfrac{3{,}229}{4{,}200}, \\dfrac{3{,}246}{4{,}200}, \\dfrac{3{,}311}{4{,}200}, \\dfrac{3{,}313}{4{,}200}, \\text{ and } \\dfrac{3{,}474}{4{,}200}", "__seed__": "0853"}}, {"seed": 854, "data": {"p1_how_many": "11", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}055}{56{,}000}, \\dfrac{35{,}095}{56{,}000}, \\dfrac{35{,}212}{56{,}000}, \\dfrac{35{,}759}{56{,}000}, \\dfrac{37{,}116}{56{,}000}, \\dfrac{37{,}274}{56{,}000}, \\dfrac{38{,}796}{56{,}000}, \\dfrac{38{,}816}{56{,}000}, \\text{ and } \\dfrac{39{,}757}{56{,}000}", "__seed__": "0854"}}, {"seed": 855, "data": {"p1_how_many": "12", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{163}{560}, \\dfrac{166}{560}, \\dfrac{169}{560}, \\dfrac{189}{560}, \\dfrac{191}{560}, \\dfrac{205}{560}, \\dfrac{207}{560}, \\text{ and } \\dfrac{209}{560}", "__seed__": "0855"}}, {"seed": 856, "data": {"p1_how_many": "14", "p1_a": "6.35", "p1_b": "6.36", "p1_numbers": "6.3505, 6.351, 6.3515, 6.352, 6.3525, 6.353, 6.3535, 6.354, 6.3545, 6.355, 6.356, 6.357, 6.358, and 6.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.351", "6.351999999999999", "6.353", "6.353999999999999", "6.3549999999999995", "6.356", "6.356999999999999", "6.358", "6.359"], "p1_2_xs": ["6.350499999999999", "6.3515", "6.352499999999999", "6.3534999999999995", "6.354499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}028}{42{,}000}, \\dfrac{6{,}104}{42{,}000}, \\dfrac{6{,}376}{42{,}000}, \\dfrac{6{,}468}{42{,}000}, \\dfrac{6{,}549}{42{,}000}, \\dfrac{6{,}583}{42{,}000}, \\dfrac{6{,}771}{42{,}000}, \\dfrac{6{,}812}{42{,}000}, \\text{ and } \\dfrac{6{,}943}{42{,}000}", "__seed__": "0856"}}, {"seed": 857, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{502}{1{,}500}, \\dfrac{520}{1{,}500}, \\dfrac{525}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{552}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{564}{1{,}500}, \\dfrac{582}{1{,}500}, \\text{ and } \\dfrac{599}{1{,}500}", "__seed__": "0857"}}, {"seed": 858, "data": {"p1_how_many": "13", "p1_a": "7.91", "p1_b": "7.92", "p1_numbers": "7.9105, 7.911, 7.9115, 7.912, 7.9125, 7.913, 7.9135, 7.914, 7.915, 7.916, 7.917, 7.918, and 7.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.9110000000000005", "7.912", "7.913", "7.914", "7.915", "7.916", "7.917", "7.918", "7.9190000000000005"], "p1_2_xs": ["7.9105", "7.9115", "7.9125", "7.9135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}516}{42{,}000}, \\dfrac{7{,}523}{42{,}000}, \\dfrac{7{,}705}{42{,}000}, \\dfrac{7{,}845}{42{,}000}, \\dfrac{8{,}182}{42{,}000}, \\dfrac{8{,}202}{42{,}000}, \\dfrac{9{,}091}{42{,}000}, \\dfrac{9{,}464}{42{,}000}, \\dfrac{10{,}488}{42{,}000}, \\dfrac{10{,}663}{42{,}000}, \\text{ and } \\dfrac{10{,}982}{42{,}000}", "__seed__": "0858"}}, {"seed": 859, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}043}{15{,}000}, \\dfrac{5{,}088}{15{,}000}, \\dfrac{5{,}090}{15{,}000}, \\dfrac{5{,}182}{15{,}000}, \\dfrac{5{,}213}{15{,}000}, \\dfrac{5{,}360}{15{,}000}, \\dfrac{5{,}366}{15{,}000}, \\dfrac{5{,}505}{15{,}000}, \\dfrac{5{,}670}{15{,}000}, \\dfrac{5{,}680}{15{,}000}, \\text{ and } \\dfrac{5{,}899}{15{,}000}", "__seed__": "0859"}}, {"seed": 860, "data": {"p1_how_many": "14", "p1_a": "2.2", "p1_b": "2.3", "p1_numbers": "2.205, 2.21, 2.215, 2.22, 2.225, 2.23, 2.235, 2.24, 2.245, 2.25, 2.26, 2.27, 2.28, and 2.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.21", "2.22", "2.23", "2.24", "2.25", "2.2600000000000002", "2.27", "2.2800000000000002", "2.29"], "p1_2_xs": ["2.205", "2.215", "2.225", "2.235", "2.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\text{ and } \\dfrac{88}{120}", "__seed__": "0860"}}, {"seed": 861, "data": {"p1_how_many": "11", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.5005, 7.501, 7.5015, 7.502, 7.503, 7.504, 7.505, 7.506, 7.507, 7.508, and 7.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.501", "7.502", "7.503", "7.504", "7.505", "7.506", "7.507", "7.508", "7.509"], "p1_2_xs": ["7.5005", "7.5015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}106}{20{,}000}, \\dfrac{4{,}184}{20{,}000}, \\dfrac{4{,}226}{20{,}000}, \\dfrac{4{,}329}{20{,}000}, \\dfrac{4{,}413}{20{,}000}, \\dfrac{4{,}428}{20{,}000}, \\dfrac{4{,}541}{20{,}000}, \\dfrac{4{,}878}{20{,}000}, \\dfrac{4{,}959}{20{,}000}, \\text{ and } \\dfrac{4{,}963}{20{,}000}", "__seed__": "0861"}}, {"seed": 862, "data": {"p1_how_many": "12", "p1_a": "1.17", "p1_b": "1.18", "p1_numbers": "1.1705, 1.171, 1.1715, 1.172, 1.1725, 1.173, 1.174, 1.175, 1.176, 1.177, 1.178, and 1.179", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.1709999999999998", "1.172", "1.1729999999999998", "1.174", "1.1749999999999998", "1.176", "1.1769999999999998", "1.178", "1.1789999999999998"], "p1_2_xs": ["1.1704999999999999", "1.1714999999999998", "1.1724999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}352}{63{,}000}, \\dfrac{15{,}448}{63{,}000}, \\dfrac{15{,}789}{63{,}000}, \\dfrac{15{,}930}{63{,}000}, \\dfrac{15{,}945}{63{,}000}, \\dfrac{15{,}966}{63{,}000}, \\dfrac{16{,}034}{63{,}000}, \\dfrac{16{,}356}{63{,}000}, \\dfrac{16{,}595}{63{,}000}, \\dfrac{16{,}883}{63{,}000}, \\text{ and } \\dfrac{17{,}280}{63{,}000}", "__seed__": "0862"}}, {"seed": 863, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}078}{20{,}000}, \\dfrac{4{,}140}{20{,}000}, \\dfrac{4{,}510}{20{,}000}, \\dfrac{4{,}519}{20{,}000}, \\dfrac{4{,}617}{20{,}000}, \\dfrac{4{,}641}{20{,}000}, \\dfrac{4{,}667}{20{,}000}, \\dfrac{4{,}673}{20{,}000}, \\dfrac{4{,}830}{20{,}000}, \\dfrac{4{,}893}{20{,}000}, \\text{ and } \\dfrac{4{,}910}{20{,}000}", "__seed__": "0863"}}, {"seed": 864, "data": {"p1_how_many": "10", "p1_a": "9.82", "p1_b": "9.83", "p1_numbers": "9.8205, 9.821, 9.822, 9.823, 9.824, 9.825, 9.826, 9.827, 9.828, and 9.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.821", "9.822000000000001", "9.823", "9.824", "9.825000000000001", "9.826", "9.827", "9.828", "9.829"], "p1_2_xs": ["9.820500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{212}{560}, \\dfrac{216}{560}, \\dfrac{218}{560}, \\dfrac{226}{560}, \\dfrac{228}{560}, \\dfrac{232}{560}, \\text{ and } \\dfrac{236}{560}", "__seed__": "0864"}}, {"seed": 865, "data": {"p1_how_many": "14", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.545, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997", "2.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, \\dfrac{243}{300}, \\dfrac{245}{300}, \\dfrac{246}{300}, \\dfrac{247}{300}, \\dfrac{248}{300}, \\text{ and } \\dfrac{249}{300}", "__seed__": "0865"}}, {"seed": 866, "data": {"p1_how_many": "14", "p1_a": "4.0", "p1_b": "4.1", "p1_numbers": "4.005, 4.01, 4.015, 4.02, 4.025, 4.03, 4.035, 4.04, 4.045, 4.05, 4.06, 4.07, 4.08, and 4.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.01", "4.02", "4.03", "4.04", "4.05", "4.06", "4.07", "4.08", "4.09"], "p1_2_xs": ["4.005", "4.015", "4.0249999999999995", "4.035", "4.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}012}{30{,}000}, \\dfrac{5{,}058}{30{,}000}, \\dfrac{5{,}066}{30{,}000}, \\dfrac{5{,}073}{30{,}000}, \\dfrac{5{,}207}{30{,}000}, \\dfrac{5{,}289}{30{,}000}, \\dfrac{5{,}291}{30{,}000}, \\dfrac{5{,}442}{30{,}000}, \\text{ and } \\dfrac{5{,}640}{30{,}000}", "__seed__": "0866"}}, {"seed": 867, "data": {"p1_how_many": "11", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}169}{35{,}000}, \\dfrac{20{,}949}{35{,}000}, \\dfrac{21{,}081}{35{,}000}, \\dfrac{21{,}714}{35{,}000}, \\dfrac{22{,}481}{35{,}000}, \\dfrac{22{,}575}{35{,}000}, \\dfrac{23{,}365}{35{,}000}, \\dfrac{25{,}548}{35{,}000}, \\dfrac{25{,}857}{35{,}000}, \\text{ and } \\dfrac{26{,}329}{35{,}000}", "__seed__": "0867"}}, {"seed": 868, "data": {"p1_how_many": "10", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}148}{35{,}000}, \\dfrac{14{,}184}{35{,}000}, \\dfrac{14{,}351}{35{,}000}, \\dfrac{14{,}389}{35{,}000}, \\dfrac{14{,}575}{35{,}000}, \\dfrac{14{,}666}{35{,}000}, \\dfrac{14{,}767}{35{,}000}, \\dfrac{14{,}819}{35{,}000}, \\text{ and } \\dfrac{14{,}921}{35{,}000}", "__seed__": "0868"}}, {"seed": 869, "data": {"p1_how_many": "12", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}520}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}543}{4{,}200}, \\dfrac{3{,}549}{4{,}200}, \\dfrac{3{,}550}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}579}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\text{ and } \\dfrac{3{,}588}{4{,}200}", "__seed__": "0869"}}, {"seed": 870, "data": {"p1_how_many": "10", "p1_a": "9.36", "p1_b": "9.37", "p1_numbers": "9.3605, 9.361, 9.362, 9.363, 9.364, 9.365, 9.366, 9.367, 9.368, and 9.369", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.360999999999999", "9.362", "9.363", "9.363999999999999", "9.365", "9.366", "9.366999999999999", "9.367999999999999", "9.369"], "p1_2_xs": ["9.3605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}653}{5{,}600}, \\dfrac{1{,}688}{5{,}600}, \\dfrac{1{,}698}{5{,}600}, \\dfrac{1{,}749}{5{,}600}, \\dfrac{1{,}921}{5{,}600}, \\dfrac{2{,}083}{5{,}600}, \\dfrac{2{,}086}{5{,}600}, \\dfrac{2{,}090}{5{,}600}, \\dfrac{2{,}091}{5{,}600}, \\text{ and } \\dfrac{2{,}098}{5{,}600}", "__seed__": "0870"}}, {"seed": 871, "data": {"p1_how_many": "10", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}409}{3{,}500}, \\dfrac{1{,}418}{3{,}500}, \\dfrac{1{,}427}{3{,}500}, \\dfrac{1{,}430}{3{,}500}, \\dfrac{1{,}432}{3{,}500}, \\dfrac{1{,}433}{3{,}500}, \\dfrac{1{,}464}{3{,}500}, \\dfrac{1{,}467}{3{,}500}, \\dfrac{1{,}469}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}481}{3{,}500}, \\text{ and } \\dfrac{1{,}482}{3{,}500}", "__seed__": "0871"}}, {"seed": 872, "data": {"p1_how_many": "14", "p1_a": "2.96", "p1_b": "2.97", "p1_numbers": "2.9605, 2.961, 2.9615, 2.962, 2.9625, 2.963, 2.9635, 2.964, 2.9645, 2.965, 2.966, 2.967, 2.968, and 2.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.961", "2.9619999999999997", "2.963", "2.964", "2.965", "2.9659999999999997", "2.967", "2.968", "2.969"], "p1_2_xs": ["2.9605", "2.9615", "2.9625", "2.9635000000000002", "2.9645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{607}{4{,}200}, \\dfrac{626}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{647}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{657}{4{,}200}, \\dfrac{675}{4{,}200}, \\dfrac{688}{4{,}200}, \\text{ and } \\dfrac{692}{4{,}200}", "__seed__": "0872"}}, {"seed": 873, "data": {"p1_how_many": "13", "p1_a": "3.25", "p1_b": "3.26", "p1_numbers": "3.2505, 3.251, 3.2515, 3.252, 3.2525, 3.253, 3.2535, 3.254, 3.255, 3.256, 3.257, 3.258, and 3.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.251", "3.252", "3.253", "3.254", "3.255", "3.256", "3.257", "3.258", "3.259"], "p1_2_xs": ["3.2505", "3.2515", "3.2525", "3.2535000000000003"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{76}{420}, \\dfrac{79}{420}, \\dfrac{80}{420}, \\dfrac{84}{420}, \\dfrac{90}{420}, \\dfrac{92}{420}, \\dfrac{101}{420}, \\dfrac{104}{420}, \\text{ and } \\dfrac{119}{420}", "__seed__": "0873"}}, {"seed": 874, "data": {"p1_how_many": "13", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{506}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{534}{1{,}500}, \\dfrac{543}{1{,}500}, \\dfrac{551}{1{,}500}, \\dfrac{554}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{586}{1{,}500}, \\dfrac{593}{1{,}500}, \\text{ and } \\dfrac{598}{1{,}500}", "__seed__": "0874"}}, {"seed": 875, "data": {"p1_how_many": "10", "p1_a": "3.96", "p1_b": "3.97", "p1_numbers": "3.9605, 3.961, 3.962, 3.963, 3.964, 3.965, 3.966, 3.967, 3.968, and 3.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.961", "3.9619999999999997", "3.963", "3.964", "3.965", "3.9659999999999997", "3.967", "3.968", "3.969"], "p1_2_xs": ["3.9605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}506}{2{,}000}, \\dfrac{1{,}517}{2{,}000}, \\dfrac{1{,}522}{2{,}000}, \\dfrac{1{,}524}{2{,}000}, \\dfrac{1{,}526}{2{,}000}, \\dfrac{1{,}527}{2{,}000}, \\dfrac{1{,}539}{2{,}000}, \\dfrac{1{,}568}{2{,}000}, \\dfrac{1{,}570}{2{,}000}, \\dfrac{1{,}575}{2{,}000}, \\dfrac{1{,}579}{2{,}000}, \\text{ and } \\dfrac{1{,}581}{2{,}000}", "__seed__": "0875"}}, {"seed": 876, "data": {"p1_how_many": "10", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{481}{560}, \\dfrac{483}{560}, \\dfrac{484}{560}, \\dfrac{485}{560}, \\dfrac{487}{560}, \\dfrac{488}{560}, \\text{ and } \\dfrac{489}{560}", "__seed__": "0876"}}, {"seed": 877, "data": {"p1_how_many": "13", "p1_a": "1.42", "p1_b": "1.43", "p1_numbers": "1.4205, 1.421, 1.4215, 1.422, 1.4225, 1.423, 1.4235, 1.424, 1.425, 1.426, 1.427, 1.428, and 1.429", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4209999999999998", "1.422", "1.4229999999999998", "1.424", "1.4249999999999998", "1.426", "1.4269999999999998", "1.428", "1.4289999999999998"], "p1_2_xs": ["1.4204999999999999", "1.4214999999999998", "1.4224999999999999", "1.4234999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{717}{3{,}500}, \\dfrac{721}{3{,}500}, \\dfrac{731}{3{,}500}, \\dfrac{759}{3{,}500}, \\dfrac{769}{3{,}500}, \\dfrac{794}{3{,}500}, \\dfrac{796}{3{,}500}, \\dfrac{802}{3{,}500}, \\dfrac{818}{3{,}500}, \\dfrac{839}{3{,}500}, \\dfrac{854}{3{,}500}, \\text{ and } \\dfrac{946}{3{,}500}", "__seed__": "0877"}}, {"seed": 878, "data": {"p1_how_many": "11", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.515, 8.52, 8.53, 8.54, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505", "8.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{22{,}458}{35{,}000}, \\dfrac{23{,}084}{35{,}000}, \\dfrac{23{,}552}{35{,}000}, \\dfrac{24{,}001}{35{,}000}, \\dfrac{24{,}288}{35{,}000}, \\dfrac{24{,}962}{35{,}000}, \\dfrac{25{,}123}{35{,}000}, \\dfrac{25{,}592}{35{,}000}, \\dfrac{25{,}664}{35{,}000}, \\dfrac{25{,}706}{35{,}000}, \\dfrac{27{,}718}{35{,}000}, \\text{ and } \\dfrac{27{,}741}{35{,}000}", "__seed__": "0878"}}, {"seed": 879, "data": {"p1_how_many": "14", "p1_a": "8.35", "p1_b": "8.36", "p1_numbers": "8.3505, 8.351, 8.3515, 8.352, 8.3525, 8.353, 8.3535, 8.354, 8.3545, 8.355, 8.356, 8.357, 8.358, and 8.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.350999999999999", "8.352", "8.353", "8.354", "8.355", "8.356", "8.357", "8.357999999999999", "8.359"], "p1_2_xs": ["8.3505", "8.3515", "8.352500000000001", "8.3535", "8.3545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}018}{20{,}000}, \\dfrac{12{,}356}{20{,}000}, \\dfrac{13{,}276}{20{,}000}, \\dfrac{13{,}355}{20{,}000}, \\dfrac{13{,}421}{20{,}000}, \\dfrac{13{,}558}{20{,}000}, \\dfrac{13{,}946}{20{,}000}, \\dfrac{14{,}150}{20{,}000}, \\dfrac{14{,}245}{20{,}000}, \\dfrac{14{,}352}{20{,}000}, \\dfrac{14{,}442}{20{,}000}, \\text{ and } \\dfrac{14{,}797}{20{,}000}", "__seed__": "0879"}}, {"seed": 880, "data": {"p1_how_many": "11", "p1_a": "7.06", "p1_b": "7.07", "p1_numbers": "7.0605, 7.061, 7.0615, 7.062, 7.063, 7.064, 7.065, 7.066, 7.067, 7.068, and 7.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.061", "7.061999999999999", "7.063", "7.063999999999999", "7.0649999999999995", "7.066", "7.066999999999999", "7.068", "7.069"], "p1_2_xs": ["7.060499999999999", "7.0615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}262}{56{,}000}, \\dfrac{21{,}461}{56{,}000}, \\dfrac{21{,}471}{56{,}000}, \\dfrac{21{,}536}{56{,}000}, \\dfrac{21{,}799}{56{,}000}, \\dfrac{21{,}926}{56{,}000}, \\dfrac{22{,}359}{56{,}000}, \\text{ and } \\dfrac{23{,}756}{56{,}000}", "__seed__": "0880"}}, {"seed": 881, "data": {"p1_how_many": "11", "p1_a": "5.34", "p1_b": "5.35", "p1_numbers": "5.3405, 5.341, 5.3415, 5.342, 5.343, 5.344, 5.345, 5.346, 5.347, 5.348, and 5.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.341", "5.342", "5.343", "5.343999999999999", "5.345", "5.346", "5.3469999999999995", "5.348", "5.349"], "p1_2_xs": ["5.3405", "5.3415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{61}{420}, \\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, 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1.671, 1.6715, 1.672, 1.6725, 1.673, 1.674, 1.675, 1.676, 1.677, 1.678, and 1.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.6709999999999998", "1.672", "1.6729999999999998", "1.674", "1.6749999999999998", "1.676", "1.6769999999999998", "1.678", "1.6789999999999998"], "p1_2_xs": ["1.6704999999999999", "1.6714999999999998", "1.6724999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{506}{3{,}000}, \\dfrac{516}{3{,}000}, \\dfrac{531}{3{,}000}, \\dfrac{556}{3{,}000}, \\dfrac{558}{3{,}000}, \\dfrac{566}{3{,}000}, \\dfrac{574}{3{,}000}, \\dfrac{578}{3{,}000}, \\dfrac{579}{3{,}000}, \\dfrac{585}{3{,}000}, \\dfrac{588}{3{,}000}, \\text{ and } \\dfrac{591}{3{,}000}", "__seed__": "0883"}}, {"seed": 884, "data": {"p1_how_many": "13", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.225, 3.23, 3.235, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215", "3.225", "3.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}423}{3{,}500}, \\dfrac{1{,}441}{3{,}500}, \\dfrac{1{,}450}{3{,}500}, \\dfrac{1{,}452}{3{,}500}, \\dfrac{1{,}459}{3{,}500}, \\dfrac{1{,}482}{3{,}500}, \\dfrac{1{,}485}{3{,}500}, \\text{ and } \\dfrac{1{,}487}{3{,}500}", "__seed__": "0884"}}, {"seed": 885, "data": {"p1_how_many": "12", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.74, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}257}{20{,}000}, \\dfrac{5{,}343}{20{,}000}, \\dfrac{6{,}058}{20{,}000}, \\dfrac{6{,}600}{20{,}000}, \\dfrac{6{,}674}{20{,}000}, \\dfrac{6{,}825}{20{,}000}, \\dfrac{6{,}852}{20{,}000}, \\text{ and } \\dfrac{7{,}492}{20{,}000}", "__seed__": "0885"}}, {"seed": 886, "data": {"p1_how_many": "13", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.035, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995", "7.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{3{,}164}{6{,}300}, \\dfrac{3{,}191}{6{,}300}, \\dfrac{3{,}222}{6{,}300}, \\dfrac{3{,}231}{6{,}300}, \\dfrac{3{,}243}{6{,}300}, \\dfrac{3{,}268}{6{,}300}, \\dfrac{3{,}271}{6{,}300}, \\dfrac{3{,}299}{6{,}300}, \\dfrac{3{,}305}{6{,}300}, \\dfrac{3{,}415}{6{,}300}, \\text{ and } \\dfrac{3{,}516}{6{,}300}", "__seed__": "0886"}}, {"seed": 887, "data": {"p1_how_many": "10", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}057}{35{,}000}, \\dfrac{7{,}643}{35{,}000}, \\dfrac{8{,}260}{35{,}000}, \\dfrac{9{,}068}{35{,}000}, \\dfrac{9{,}139}{35{,}000}, \\dfrac{9{,}277}{35{,}000}, \\dfrac{9{,}597}{35{,}000}, \\dfrac{9{,}614}{35{,}000}, \\dfrac{9{,}729}{35{,}000}, \\text{ and } \\dfrac{9{,}902}{35{,}000}", "__seed__": "0887"}}, {"seed": 888, "data": {"p1_how_many": "13", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.625, 5.63, 5.635, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999", "5.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}020}{20{,}000}, \\dfrac{4{,}139}{20{,}000}, \\dfrac{4{,}179}{20{,}000}, \\dfrac{4{,}283}{20{,}000}, \\dfrac{4{,}354}{20{,}000}, \\dfrac{4{,}517}{20{,}000}, \\dfrac{4{,}604}{20{,}000}, \\dfrac{4{,}718}{20{,}000}, \\text{ and } \\dfrac{4{,}761}{20{,}000}", "__seed__": "0888"}}, {"seed": 889, "data": {"p1_how_many": "12", "p1_a": "6.53", "p1_b": "6.54", "p1_numbers": "6.5305, 6.531, 6.5315, 6.532, 6.5325, 6.533, 6.534, 6.535, 6.536, 6.537, 6.538, and 6.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.531000000000001", "6.532", "6.533", "6.534", "6.535", "6.5360000000000005", "6.537", "6.538", "6.539000000000001"], "p1_2_xs": ["6.5305", "6.5315", "6.5325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}586}{42{,}000}, \\dfrac{7{,}651}{42{,}000}, \\dfrac{7{,}926}{42{,}000}, \\dfrac{8{,}101}{42{,}000}, \\dfrac{8{,}481}{42{,}000}, \\dfrac{9{,}147}{42{,}000}, \\dfrac{9{,}330}{42{,}000}, \\dfrac{9{,}443}{42{,}000}, \\dfrac{11{,}438}{42{,}000}, \\text{ and } \\dfrac{11{,}942}{42{,}000}", "__seed__": "0889"}}, {"seed": 890, "data": {"p1_how_many": "10", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.6005, 2.601, 2.602, 2.603, 2.604, 2.605, 2.606, 2.607, 2.608, and 2.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.601", "2.602", "2.603", "2.604", "2.605", "2.606", "2.607", "2.608", "2.609"], "p1_2_xs": ["2.6005000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}244}{56{,}000}, \\dfrac{35{,}917}{56{,}000}, \\dfrac{36{,}841}{56{,}000}, \\dfrac{37{,}914}{56{,}000}, \\dfrac{38{,}611}{56{,}000}, \\dfrac{39{,}580}{56{,}000}, \\dfrac{39{,}612}{56{,}000}, \\text{ and } \\dfrac{39{,}921}{56{,}000}", "__seed__": "0890"}}, {"seed": 891, "data": {"p1_how_many": "14", "p1_a": "4.23", "p1_b": "4.24", "p1_numbers": "4.2305, 4.231, 4.2315, 4.232, 4.2325, 4.233, 4.2335, 4.234, 4.2345, 4.235, 4.236, 4.237, 4.238, and 4.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.231000000000001", "4.232", "4.2330000000000005", "4.234", "4.235", "4.236000000000001", "4.237", "4.238", "4.239000000000001"], "p1_2_xs": ["4.2305", "4.2315000000000005", "4.2325", "4.2335", "4.2345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{624}{4{,}200}, \\dfrac{626}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{641}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{658}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{677}{4{,}200}, \\text{ and } \\dfrac{696}{4{,}200}", "__seed__": "0891"}}, {"seed": 892, "data": {"p1_how_many": "10", "p1_a": "7.54", "p1_b": "7.55", "p1_numbers": "7.5405, 7.541, 7.542, 7.543, 7.544, 7.545, 7.546, 7.547, 7.548, and 7.549", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.541", "7.542", "7.543", "7.544", "7.545", "7.546", "7.547", "7.548", "7.549"], "p1_2_xs": ["7.5405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}051}{15{,}000}, \\dfrac{5{,}124}{15{,}000}, \\dfrac{5{,}248}{15{,}000}, \\dfrac{5{,}451}{15{,}000}, \\dfrac{5{,}464}{15{,}000}, \\dfrac{5{,}467}{15{,}000}, \\dfrac{5{,}480}{15{,}000}, \\dfrac{5{,}564}{15{,}000}, \\dfrac{5{,}636}{15{,}000}, \\text{ and } \\dfrac{5{,}742}{15{,}000}", "__seed__": "0892"}}, {"seed": 893, "data": {"p1_how_many": "14", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.345, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335", "5.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}406}{3{,}500}, \\dfrac{1{,}409}{3{,}500}, \\dfrac{1{,}414}{3{,}500}, \\dfrac{1{,}416}{3{,}500}, \\dfrac{1{,}432}{3{,}500}, \\dfrac{1{,}434}{3{,}500}, \\dfrac{1{,}459}{3{,}500}, \\dfrac{1{,}464}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}472}{3{,}500}, \\text{ and } \\dfrac{1{,}477}{3{,}500}", "__seed__": "0893"}}, {"seed": 894, "data": {"p1_how_many": "11", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}160}{5{,}600}, \\dfrac{2{,}177}{5{,}600}, \\dfrac{2{,}188}{5{,}600}, \\dfrac{2{,}191}{5{,}600}, \\dfrac{2{,}220}{5{,}600}, \\dfrac{2{,}226}{5{,}600}, \\dfrac{2{,}233}{5{,}600}, \\dfrac{2{,}245}{5{,}600}, \\dfrac{2{,}326}{5{,}600}, \\dfrac{2{,}342}{5{,}600}, \\text{ and } \\dfrac{2{,}394}{5{,}600}", "__seed__": "0894"}}, {"seed": 895, "data": {"p1_how_many": "10", "p1_a": "1.75", "p1_b": "1.76", "p1_numbers": "1.7505, 1.751, 1.752, 1.753, 1.754, 1.755, 1.756, 1.757, 1.758, and 1.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.751", "1.752", "1.753", "1.754", "1.755", "1.756", "1.757", "1.758", "1.759"], "p1_2_xs": ["1.7505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}280}{63{,}000}, \\dfrac{9{,}508}{63{,}000}, \\dfrac{9{,}822}{63{,}000}, \\dfrac{10{,}529}{63{,}000}, \\dfrac{10{,}596}{63{,}000}, \\dfrac{10{,}904}{63{,}000}, \\dfrac{12{,}510}{63{,}000}, \\dfrac{13{,}213}{63{,}000}, \\dfrac{13{,}698}{63{,}000}, \\text{ and } \\dfrac{13{,}742}{63{,}000}", "__seed__": "0895"}}, {"seed": 896, "data": {"p1_how_many": "10", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}008}{12{,}000}, \\dfrac{3{,}227}{12{,}000}, \\dfrac{3{,}299}{12{,}000}, \\dfrac{3{,}417}{12{,}000}, \\dfrac{3{,}436}{12{,}000}, \\dfrac{3{,}445}{12{,}000}, \\dfrac{3{,}572}{12{,}000}, \\dfrac{3{,}586}{12{,}000}, \\dfrac{3{,}627}{12{,}000}, \\dfrac{3{,}901}{12{,}000}, \\text{ and } \\dfrac{3{,}946}{12{,}000}", "__seed__": "0896"}}, {"seed": 897, "data": {"p1_how_many": "10", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.62, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0897"}}, {"seed": 898, "data": {"p1_how_many": "12", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.125, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115", "1.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}036}{20{,}000}, \\dfrac{5{,}373}{20{,}000}, \\dfrac{5{,}586}{20{,}000}, \\dfrac{5{,}751}{20{,}000}, \\dfrac{5{,}833}{20{,}000}, \\dfrac{6{,}149}{20{,}000}, \\dfrac{6{,}313}{20{,}000}, \\dfrac{6{,}813}{20{,}000}, \\dfrac{7{,}668}{20{,}000}, \\text{ and } \\dfrac{7{,}751}{20{,}000}", "__seed__": "0898"}}, {"seed": 899, "data": {"p1_how_many": "10", "p1_a": "5.97", "p1_b": "5.98", "p1_numbers": "5.9705, 5.971, 5.972, 5.973, 5.974, 5.975, 5.976, 5.977, 5.978, and 5.979", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.971", "5.9719999999999995", "5.973", "5.973999999999999", "5.975", "5.976", "5.976999999999999", "5.978", "5.979"], "p1_2_xs": ["5.9704999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{128}{200}, \\dfrac{132}{200}, \\dfrac{133}{200}, \\dfrac{136}{200}, \\dfrac{140}{200}, \\dfrac{145}{200}, \\dfrac{147}{200}, \\text{ and } \\dfrac{148}{200}", "__seed__": "0899"}}, {"seed": 900, "data": {"p1_how_many": "11", "p1_a": "8.43", "p1_b": "8.44", "p1_numbers": "8.4305, 8.431, 8.4315, 8.432, 8.433, 8.434, 8.435, 8.436, 8.437, 8.438, and 8.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.431", "8.432", "8.433", "8.434", "8.435", "8.436", "8.437", "8.437999999999999", "8.439"], "p1_2_xs": ["8.4305", "8.4315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}016}{63{,}000}, \\dfrac{27{,}080}{63{,}000}, \\dfrac{27{,}227}{63{,}000}, \\dfrac{27{,}423}{63{,}000}, \\dfrac{27{,}449}{63{,}000}, \\dfrac{27{,}741}{63{,}000}, \\dfrac{27{,}754}{63{,}000}, \\dfrac{27{,}846}{63{,}000}, \\dfrac{27{,}873}{63{,}000}, \\dfrac{27{,}949}{63{,}000}, \\text{ and } \\dfrac{27{,}990}{63{,}000}", "__seed__": "0900"}}, {"seed": 901, "data": {"p1_how_many": "12", "p1_a": "4.33", "p1_b": "4.34", "p1_numbers": "4.3305, 4.331, 4.3315, 4.332, 4.3325, 4.333, 4.334, 4.335, 4.336, 4.337, 4.338, and 4.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.331", "4.332", "4.333", "4.334", "4.335", "4.336", "4.337", "4.338", "4.339"], "p1_2_xs": ["4.3305", "4.3315", "4.3325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{507}{3{,}000}, \\dfrac{528}{3{,}000}, \\dfrac{560}{3{,}000}, \\dfrac{575}{3{,}000}, \\dfrac{581}{3{,}000}, \\dfrac{582}{3{,}000}, \\dfrac{588}{3{,}000}, \\text{ and } \\dfrac{594}{3{,}000}", "__seed__": "0901"}}, {"seed": 902, "data": {"p1_how_many": "13", "p1_a": "2.34", "p1_b": "2.35", "p1_numbers": "2.3405, 2.341, 2.3415, 2.342, 2.3425, 2.343, 2.3435, 2.344, 2.345, 2.346, 2.347, 2.348, and 2.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3409999999999997", "2.3419999999999996", "2.343", "2.344", "2.3449999999999998", "2.3459999999999996", "2.347", "2.348", "2.3489999999999998"], "p1_2_xs": ["2.3405", "2.3415", "2.3425", "2.3435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{505}{1{,}500}, \\dfrac{516}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{570}{1{,}500}, \\dfrac{577}{1{,}500}, \\dfrac{580}{1{,}500}, \\dfrac{585}{1{,}500}, \\dfrac{586}{1{,}500}, \\text{ and } \\dfrac{595}{1{,}500}", "__seed__": "0902"}}, {"seed": 903, "data": {"p1_how_many": "10", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.52, 8.53, 8.54, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}063}{42{,}000}, \\dfrac{6{,}407}{42{,}000}, \\dfrac{6{,}439}{42{,}000}, \\dfrac{6{,}452}{42{,}000}, \\dfrac{6{,}462}{42{,}000}, \\dfrac{6{,}502}{42{,}000}, \\dfrac{6{,}536}{42{,}000}, \\text{ and } \\dfrac{6{,}957}{42{,}000}", "__seed__": "0903"}}, {"seed": 904, "data": {"p1_how_many": "14", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.545, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535", "9.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{613}{4{,}200}, \\dfrac{621}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{631}{4{,}200}, \\dfrac{653}{4{,}200}, \\dfrac{691}{4{,}200}, \\text{ and } \\dfrac{694}{4{,}200}", "__seed__": "0904"}}, {"seed": 905, "data": {"p1_how_many": "11", "p1_a": "5.14", "p1_b": "5.15", "p1_numbers": "5.1405, 5.141, 5.1415, 5.142, 5.143, 5.144, 5.145, 5.146, 5.147, 5.148, and 5.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.141", "5.1419999999999995", "5.143", "5.143999999999999", "5.145", "5.146", "5.146999999999999", "5.148", "5.149"], "p1_2_xs": ["5.140499999999999", "5.1415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}029}{4{,}200}, \\dfrac{3{,}061}{4{,}200}, \\dfrac{3{,}138}{4{,}200}, \\dfrac{3{,}297}{4{,}200}, \\dfrac{3{,}311}{4{,}200}, \\dfrac{3{,}429}{4{,}200}, \\dfrac{3{,}432}{4{,}200}, \\text{ and } \\dfrac{3{,}448}{4{,}200}", "__seed__": "0905"}}, {"seed": 906, "data": {"p1_how_many": "14", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.135, 3.14, 3.145, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125", "3.135", "3.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}017}{15{,}000}, \\dfrac{5{,}064}{15{,}000}, \\dfrac{5{,}169}{15{,}000}, \\dfrac{5{,}386}{15{,}000}, \\dfrac{5{,}440}{15{,}000}, \\dfrac{5{,}551}{15{,}000}, \\dfrac{5{,}735}{15{,}000}, \\dfrac{5{,}865}{15{,}000}, \\dfrac{5{,}915}{15{,}000}, \\text{ and } \\dfrac{5{,}935}{15{,}000}", "__seed__": "0906"}}, {"seed": 907, "data": {"p1_how_many": "13", "p1_a": "2.22", "p1_b": "2.23", "p1_numbers": "2.2205, 2.221, 2.2215, 2.222, 2.2225, 2.223, 2.2235, 2.224, 2.225, 2.226, 2.227, 2.228, and 2.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.221", "2.222", "2.2230000000000003", "2.224", "2.225", "2.226", "2.2270000000000003", "2.228", "2.229"], "p1_2_xs": ["2.2205000000000004", "2.2215000000000003", "2.2225", "2.2235000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}230}{15{,}000}, \\dfrac{5{,}275}{15{,}000}, \\dfrac{5{,}291}{15{,}000}, \\dfrac{5{,}607}{15{,}000}, \\dfrac{5{,}793}{15{,}000}, \\dfrac{5{,}802}{15{,}000}, \\dfrac{5{,}823}{15{,}000}, \\dfrac{5{,}883}{15{,}000}, \\dfrac{5{,}932}{15{,}000}, \\dfrac{5{,}979}{15{,}000}, \\text{ and } \\dfrac{5{,}988}{15{,}000}", "__seed__": "0907"}}, {"seed": 908, "data": {"p1_how_many": "10", "p1_a": "8.44", "p1_b": "8.45", "p1_numbers": "8.4405, 8.441, 8.442, 8.443, 8.444, 8.445, 8.446, 8.447, 8.448, and 8.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.440999999999999", "8.442", "8.443", "8.443999999999999", "8.445", "8.446", "8.447", "8.447999999999999", "8.449"], "p1_2_xs": ["8.4405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{628}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{634}{4{,}200}, \\dfrac{647}{4{,}200}, \\dfrac{670}{4{,}200}, \\dfrac{679}{4{,}200}, \\text{ and } \\dfrac{687}{4{,}200}", "__seed__": "0908"}}, {"seed": 909, "data": {"p1_how_many": "14", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.225, 3.23, 3.235, 3.24, 3.245, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215", "3.225", "3.235", "3.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}003}{20{,}000}, \\dfrac{15{,}030}{20{,}000}, \\dfrac{15{,}051}{20{,}000}, \\dfrac{15{,}314}{20{,}000}, \\dfrac{15{,}441}{20{,}000}, \\dfrac{15{,}518}{20{,}000}, \\dfrac{15{,}573}{20{,}000}, \\dfrac{15{,}614}{20{,}000}, \\dfrac{15{,}725}{20{,}000}, \\dfrac{15{,}902}{20{,}000}, \\text{ and } \\dfrac{15{,}904}{20{,}000}", "__seed__": "0909"}}, {"seed": 910, "data": {"p1_how_many": "11", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\dfrac{48}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0910"}}, {"seed": 911, "data": {"p1_how_many": "13", "p1_a": "9.45", "p1_b": "9.46", "p1_numbers": "9.4505, 9.451, 9.4515, 9.452, 9.4525, 9.453, 9.4535, 9.454, 9.455, 9.456, 9.457, 9.458, and 9.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.450999999999999", "9.452", "9.453", "9.453999999999999", "9.455", "9.456", "9.456999999999999", "9.457999999999998", "9.459"], "p1_2_xs": ["9.4505", "9.4515", "9.4525", "9.4535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}044}{15{,}000}, \\dfrac{5{,}080}{15{,}000}, \\dfrac{5{,}240}{15{,}000}, \\dfrac{5{,}263}{15{,}000}, \\dfrac{5{,}369}{15{,}000}, \\dfrac{5{,}438}{15{,}000}, \\dfrac{5{,}574}{15{,}000}, \\dfrac{5{,}831}{15{,}000}, \\dfrac{5{,}881}{15{,}000}, \\dfrac{5{,}925}{15{,}000}, \\dfrac{5{,}976}{15{,}000}, \\text{ and } \\dfrac{5{,}986}{15{,}000}", "__seed__": "0911"}}, {"seed": 912, "data": {"p1_how_many": "13", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}250}{7{,}700}, \\dfrac{4{,}363}{7{,}700}, \\dfrac{4{,}431}{7{,}700}, \\dfrac{5{,}003}{7{,}700}, \\dfrac{5{,}089}{7{,}700}, \\dfrac{5{,}120}{7{,}700}, \\dfrac{5{,}217}{7{,}700}, \\text{ and } \\dfrac{5{,}430}{7{,}700}", "__seed__": "0912"}}, {"seed": 913, "data": {"p1_how_many": "11", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.015, 9.02, 9.03, 9.04, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005", "9.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{301}{1{,}200}, \\dfrac{332}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{360}{1{,}200}, \\dfrac{394}{1{,}200}, \\dfrac{395}{1{,}200}, \\dfrac{397}{1{,}200}, \\text{ and } \\dfrac{399}{1{,}200}", "__seed__": "0913"}}, {"seed": 914, "data": {"p1_how_many": "12", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.625, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998", "2.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}197}{56{,}000}, \\dfrac{21{,}242}{56{,}000}, \\dfrac{21{,}524}{56{,}000}, \\dfrac{21{,}932}{56{,}000}, \\dfrac{22{,}200}{56{,}000}, \\dfrac{22{,}908}{56{,}000}, \\dfrac{23{,}113}{56{,}000}, \\dfrac{23{,}154}{56{,}000}, \\dfrac{23{,}703}{56{,}000}, \\text{ and } \\dfrac{23{,}745}{56{,}000}", "__seed__": "0914"}}, {"seed": 915, "data": {"p1_how_many": "11", "p1_a": "8.64", "p1_b": "8.65", "p1_numbers": "8.6405, 8.641, 8.6415, 8.642, 8.643, 8.644, 8.645, 8.646, 8.647, 8.648, and 8.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.641", "8.642000000000001", "8.643", "8.644", "8.645000000000001", "8.646", "8.647", "8.648", "8.649000000000001"], "p1_2_xs": ["8.640500000000001", "8.6415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{152}{350}, \\dfrac{157}{350}, \\dfrac{170}{350}, \\dfrac{171}{350}, \\dfrac{176}{350}, \\dfrac{181}{350}, \\dfrac{184}{350}, \\text{ and } \\dfrac{193}{350}", "__seed__": "0915"}}, {"seed": 916, "data": {"p1_how_many": "13", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.635, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625", "3.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}509}{5{,}600}, \\dfrac{3{,}521}{5{,}600}, \\dfrac{3{,}544}{5{,}600}, \\dfrac{3{,}554}{5{,}600}, \\dfrac{3{,}602}{5{,}600}, \\dfrac{3{,}613}{5{,}600}, \\dfrac{3{,}687}{5{,}600}, \\dfrac{3{,}703}{5{,}600}, \\dfrac{3{,}788}{5{,}600}, \\dfrac{3{,}881}{5{,}600}, \\dfrac{3{,}906}{5{,}600}, \\text{ and } \\dfrac{3{,}967}{5{,}600}", "__seed__": "0916"}}, {"seed": 917, "data": {"p1_how_many": "12", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.1005, 2.101, 2.1015, 2.102, 2.1025, 2.103, 2.104, 2.105, 2.106, 2.107, 2.108, and 2.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.101", "2.102", "2.103", "2.104", "2.105", "2.106", "2.107", "2.108", "2.109"], "p1_2_xs": ["2.1005000000000003", "2.1015", "2.1025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{415}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{427}{2{,}000}, \\dfrac{445}{2{,}000}, \\dfrac{450}{2{,}000}, \\dfrac{489}{2{,}000}, \\text{ and } \\dfrac{499}{2{,}000}", "__seed__": "0917"}}, {"seed": 918, "data": {"p1_how_many": "10", "p1_a": "5.74", "p1_b": "5.75", "p1_numbers": "5.7405, 5.741, 5.742, 5.743, 5.744, 5.745, 5.746, 5.747, 5.748, and 5.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7410000000000005", "5.742", "5.743", "5.744", "5.745", "5.746", "5.747", "5.748", "5.7490000000000006"], "p1_2_xs": ["5.7405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}048}{63{,}000}, \\dfrac{14{,}137}{63{,}000}, \\dfrac{14{,}257}{63{,}000}, \\dfrac{14{,}488}{63{,}000}, \\dfrac{14{,}680}{63{,}000}, \\dfrac{14{,}995}{63{,}000}, \\dfrac{15{,}854}{63{,}000}, \\dfrac{16{,}274}{63{,}000}, \\dfrac{16{,}724}{63{,}000}, \\dfrac{16{,}849}{63{,}000}, \\dfrac{17{,}468}{63{,}000}, \\text{ and } \\dfrac{17{,}901}{63{,}000}", "__seed__": "0918"}}, {"seed": 919, "data": {"p1_how_many": "11", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{281}{630}, \\dfrac{287}{630}, \\dfrac{288}{630}, \\dfrac{290}{630}, \\dfrac{326}{630}, \\dfrac{338}{630}, \\text{ and } \\dfrac{346}{630}", "__seed__": "0919"}}, {"seed": 920, "data": {"p1_how_many": "11", "p1_a": "3.01", "p1_b": "3.02", "p1_numbers": "3.0105, 3.011, 3.0115, 3.012, 3.013, 3.014, 3.015, 3.016, 3.017, 3.018, and 3.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.0109999999999997", "3.0119999999999996", "3.013", "3.014", "3.0149999999999997", "3.0159999999999996", "3.017", "3.018", "3.0189999999999997"], "p1_2_xs": ["3.0105", "3.0115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}897}{20{,}000}, \\dfrac{5{,}978}{20{,}000}, \\dfrac{6{,}636}{20{,}000}, \\dfrac{6{,}655}{20{,}000}, \\dfrac{6{,}912}{20{,}000}, \\dfrac{7{,}152}{20{,}000}, \\dfrac{7{,}410}{20{,}000}, \\dfrac{7{,}528}{20{,}000}, \\dfrac{7{,}947}{20{,}000}, \\text{ and } \\dfrac{7{,}997}{20{,}000}", "__seed__": "0920"}}, {"seed": 921, "data": {"p1_how_many": "11", "p1_a": "1.97", "p1_b": "1.98", "p1_numbers": "1.9705, 1.971, 1.9715, 1.972, 1.973, 1.974, 1.975, 1.976, 1.977, 1.978, and 1.979", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9709999999999999", "1.972", "1.9729999999999999", "1.974", "1.9749999999999999", "1.976", "1.9769999999999999", "1.978", "1.9789999999999999"], "p1_2_xs": ["1.9705", "1.9714999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}101}{5{,}600}, \\dfrac{2{,}102}{5{,}600}, \\dfrac{2{,}121}{5{,}600}, \\dfrac{2{,}232}{5{,}600}, \\dfrac{2{,}235}{5{,}600}, \\dfrac{2{,}247}{5{,}600}, \\dfrac{2{,}277}{5{,}600}, \\dfrac{2{,}286}{5{,}600}, \\dfrac{2{,}303}{5{,}600}, \\dfrac{2{,}325}{5{,}600}, \\text{ and } \\dfrac{2{,}345}{5{,}600}", "__seed__": "0921"}}, {"seed": 922, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", "2.4349999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{720}{4{,}200}, \\dfrac{744}{4{,}200}, \\dfrac{779}{4{,}200}, \\dfrac{791}{4{,}200}, \\dfrac{856}{4{,}200}, \\dfrac{875}{4{,}200}, \\dfrac{940}{4{,}200}, \\dfrac{994}{4{,}200}, \\dfrac{1{,}013}{4{,}200}, \\dfrac{1{,}022}{4{,}200}, \\text{ and } \\dfrac{1{,}041}{4{,}200}", "__seed__": "0922"}}, {"seed": 923, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{505}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{544}{1{,}500}, \\dfrac{559}{1{,}500}, 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"11", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{2{,}009}{3{,}500}, \\dfrac{2{,}018}{3{,}500}, \\dfrac{2{,}028}{3{,}500}, \\dfrac{2{,}042}{3{,}500}, \\dfrac{2{,}046}{3{,}500}, \\dfrac{2{,}047}{3{,}500}, \\dfrac{2{,}052}{3{,}500}, \\dfrac{2{,}078}{3{,}500}, \\dfrac{2{,}079}{3{,}500}, \\text{ and } \\dfrac{2{,}095}{3{,}500}", "__seed__": "0925"}}, {"seed": 926, "data": {"p1_how_many": "13", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.325, 9.33, 9.335, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001", "9.325000000000001", "9.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}419}{6{,}300}, \\dfrac{1{,}466}{6{,}300}, \\dfrac{1{,}533}{6{,}300}, \\dfrac{1{,}541}{6{,}300}, \\dfrac{1{,}591}{6{,}300}, \\dfrac{1{,}661}{6{,}300}, \\dfrac{1{,}766}{6{,}300}, \\text{ and } \\dfrac{1{,}781}{6{,}300}", "__seed__": "0926"}}, {"seed": 927, "data": {"p1_how_many": "11", "p1_a": "5.5", "p1_b": "5.6", "p1_numbers": "5.505, 5.51, 5.515, 5.52, 5.53, 5.54, 5.55, 5.56, 5.57, 5.58, and 5.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.51", "5.52", "5.53", "5.54", "5.55", "5.56", "5.57", "5.58", "5.59"], "p1_2_xs": ["5.505", "5.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{96}{630}, \\dfrac{100}{630}, \\dfrac{105}{630}, \\dfrac{110}{630}, \\dfrac{120}{630}, \\dfrac{122}{630}, \\dfrac{125}{630}, \\text{ and } \\dfrac{128}{630}", "__seed__": "0927"}}, {"seed": 928, "data": {"p1_how_many": "11", "p1_a": "7.64", "p1_b": "7.65", "p1_numbers": "7.6405, 7.641, 7.6415, 7.642, 7.643, 7.644, 7.645, 7.646, 7.647, 7.648, and 7.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.641", "7.6419999999999995", "7.643", "7.643999999999999", "7.645", "7.646", "7.646999999999999", "7.648", "7.649"], "p1_2_xs": ["7.640499999999999", "7.6415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{761}{4{,}200}, \\dfrac{815}{4{,}200}, \\dfrac{866}{4{,}200}, \\dfrac{888}{4{,}200}, \\dfrac{932}{4{,}200}, \\dfrac{966}{4{,}200}, \\dfrac{981}{4{,}200}, \\dfrac{1{,}128}{4{,}200}, \\dfrac{1{,}153}{4{,}200}, \\text{ and } \\dfrac{1{,}181}{4{,}200}", "__seed__": "0928"}}, {"seed": 929, "data": {"p1_how_many": "12", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{823}{1{,}200}, \\dfrac{837}{1{,}200}, \\dfrac{843}{1{,}200}, \\dfrac{853}{1{,}200}, \\dfrac{864}{1{,}200}, \\dfrac{872}{1{,}200}, \\dfrac{881}{1{,}200}, \\dfrac{887}{1{,}200}, \\text{ and } \\dfrac{894}{1{,}200}", "__seed__": "0929"}}, {"seed": 930, "data": {"p1_how_many": "11", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.705, 5.71, 5.715, 5.72, 5.73, 5.74, 5.75, 5.76, 5.77, 5.78, and 5.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.71", "5.72", "5.73", "5.74", "5.75", "5.76", "5.7700000000000005", "5.78", "5.79"], "p1_2_xs": ["5.705", "5.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}006}{3{,}500}, \\dfrac{1{,}055}{3{,}500}, \\dfrac{1{,}063}{3{,}500}, \\dfrac{1{,}099}{3{,}500}, \\dfrac{1{,}131}{3{,}500}, \\dfrac{1{,}143}{3{,}500}, \\dfrac{1{,}170}{3{,}500}, \\dfrac{1{,}178}{3{,}500}, \\dfrac{1{,}258}{3{,}500}, \\dfrac{1{,}284}{3{,}500}, \\dfrac{1{,}371}{3{,}500}, \\text{ and } \\dfrac{1{,}395}{3{,}500}", "__seed__": "0930"}}, {"seed": 931, "data": {"p1_how_many": "10", "p1_a": "7.2", "p1_b": "7.3", "p1_numbers": "7.205, 7.21, 7.22, 7.23, 7.24, 7.25, 7.26, 7.27, 7.28, and 7.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.21", "7.22", "7.23", "7.24", "7.25", "7.26", "7.2700000000000005", "7.28", "7.29"], "p1_2_xs": ["7.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}238}{12{,}000}, \\dfrac{8{,}273}{12{,}000}, \\dfrac{8{,}309}{12{,}000}, \\dfrac{8{,}357}{12{,}000}, \\dfrac{8{,}600}{12{,}000}, \\dfrac{8{,}747}{12{,}000}, \\dfrac{8{,}756}{12{,}000}, \\text{ and } \\dfrac{8{,}930}{12{,}000}", "__seed__": "0931"}}, {"seed": 932, "data": {"p1_how_many": "13", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.425, 8.43, 8.435, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001", "8.425", "8.435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}114}{20{,}000}, \\dfrac{5{,}433}{20{,}000}, \\dfrac{5{,}562}{20{,}000}, \\dfrac{5{,}713}{20{,}000}, \\dfrac{5{,}869}{20{,}000}, \\dfrac{6{,}046}{20{,}000}, \\dfrac{6{,}117}{20{,}000}, \\dfrac{6{,}265}{20{,}000}, \\dfrac{6{,}686}{20{,}000}, \\dfrac{7{,}156}{20{,}000}, \\dfrac{7{,}271}{20{,}000}, \\text{ and } \\dfrac{7{,}496}{20{,}000}", "__seed__": "0932"}}, {"seed": 933, "data": {"p1_how_many": "13", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.615, 7.62, 7.625, 7.63, 7.635, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995", "7.614999999999999", "7.624999999999999", "7.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{48}{200}", "__seed__": "0933"}}, {"seed": 934, "data": {"p1_how_many": "13", "p1_a": "2.04", "p1_b": "2.05", "p1_numbers": "2.0405, 2.041, 2.0415, 2.042, 2.0425, 2.043, 2.0435, 2.044, 2.045, 2.046, 2.047, 2.048, and 2.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.041", "2.042", "2.043", "2.044", "2.045", "2.046", "2.047", "2.048", "2.049"], "p1_2_xs": ["2.0405", "2.0415", "2.0425", "2.0435000000000003"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{627}{1{,}500}, \\dfrac{631}{1{,}500}, \\dfrac{713}{1{,}500}, \\dfrac{756}{1{,}500}, \\dfrac{802}{1{,}500}, \\dfrac{819}{1{,}500}, \\dfrac{856}{1{,}500}, \\dfrac{945}{1{,}500}, \\dfrac{964}{1{,}500}, \\text{ and } \\dfrac{986}{1{,}500}", "__seed__": "0934"}}, {"seed": 935, "data": {"p1_how_many": "13", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}002}{63{,}000}, \\dfrac{27{,}105}{63{,}000}, \\dfrac{27{,}114}{63{,}000}, \\dfrac{27{,}184}{63{,}000}, \\dfrac{27{,}250}{63{,}000}, \\dfrac{27{,}475}{63{,}000}, \\dfrac{27{,}589}{63{,}000}, \\dfrac{27{,}835}{63{,}000}, \\text{ and } \\dfrac{27{,}945}{63{,}000}", "__seed__": "0935"}}, {"seed": 936, "data": {"p1_how_many": "14", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.635, 8.64, 8.645, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625", "8.635", "8.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{31{,}357}{42{,}000}, \\dfrac{32{,}180}{42{,}000}, \\dfrac{32{,}599}{42{,}000}, \\dfrac{32{,}733}{42{,}000}, \\dfrac{33{,}448}{42{,}000}, \\dfrac{33{,}589}{42{,}000}, \\dfrac{33{,}712}{42{,}000}, \\dfrac{34{,}150}{42{,}000}, \\text{ and } \\dfrac{34{,}516}{42{,}000}", "__seed__": "0936"}}, {"seed": 937, "data": {"p1_how_many": "13", "p1_a": "1.67", "p1_b": "1.68", "p1_numbers": "1.6705, 1.671, 1.6715, 1.672, 1.6725, 1.673, 1.6735, 1.674, 1.675, 1.676, 1.677, 1.678, and 1.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.6709999999999998", "1.672", "1.6729999999999998", "1.674", "1.6749999999999998", "1.676", "1.6769999999999998", "1.678", "1.6789999999999998"], "p1_2_xs": ["1.6704999999999999", "1.6714999999999998", "1.6724999999999999", "1.6734999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}203}{2{,}000}, \\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}248}{2{,}000}, \\dfrac{1{,}278}{2{,}000}, \\dfrac{1{,}311}{2{,}000}, \\dfrac{1{,}360}{2{,}000}, \\dfrac{1{,}370}{2{,}000}, \\dfrac{1{,}464}{2{,}000}, \\text{ and } \\dfrac{1{,}488}{2{,}000}", "__seed__": "0937"}}, {"seed": 938, "data": {"p1_how_many": "12", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.2005, 6.201, 6.2015, 6.202, 6.2025, 6.203, 6.204, 6.205, 6.206, 6.207, 6.208, and 6.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.2010000000000005", "6.202", "6.203", "6.204", "6.205", "6.206", "6.207", "6.208", "6.2090000000000005"], "p1_2_xs": ["6.2005", "6.2015", "6.2025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}364}{7{,}700}, \\dfrac{4{,}476}{7{,}700}, \\dfrac{4{,}846}{7{,}700}, \\dfrac{4{,}863}{7{,}700}, \\dfrac{4{,}918}{7{,}700}, \\dfrac{5{,}078}{7{,}700}, \\dfrac{5{,}207}{7{,}700}, \\dfrac{5{,}372}{7{,}700}, \\dfrac{5{,}725}{7{,}700}, \\dfrac{5{,}780}{7{,}700}, \\text{ and } \\dfrac{6{,}556}{7{,}700}", "__seed__": "0938"}}, {"seed": 939, "data": {"p1_how_many": "13", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{44{,}562}{77{,}000}, \\dfrac{46{,}118}{77{,}000}, \\dfrac{48{,}566}{77{,}000}, \\dfrac{54{,}929}{77{,}000}, \\dfrac{55{,}240}{77{,}000}, \\dfrac{55{,}424}{77{,}000}, \\dfrac{56{,}339}{77{,}000}, \\dfrac{57{,}547}{77{,}000}, \\dfrac{58{,}264}{77{,}000}, \\text{ and } \\dfrac{58{,}553}{77{,}000}", "__seed__": "0939"}}, {"seed": 940, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{96}{630}, \\dfrac{101}{630}, \\dfrac{105}{630}, \\dfrac{111}{630}, \\dfrac{119}{630}, \\dfrac{130}{630}, \\dfrac{131}{630}, \\dfrac{136}{630}, \\text{ and } \\dfrac{138}{630}", "__seed__": "0940"}}, {"seed": 941, "data": {"p1_how_many": "14", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.735, 6.74, 6.745, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725", "6.735", "6.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}515}{4{,}200}, \\dfrac{3{,}537}{4{,}200}, \\dfrac{3{,}544}{4{,}200}, \\dfrac{3{,}547}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}570}{4{,}200}, \\dfrac{3{,}588}{4{,}200}, \\text{ and } \\dfrac{3{,}599}{4{,}200}", "__seed__": "0941"}}, {"seed": 942, "data": {"p1_how_many": "11", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}046}{15{,}000}, \\dfrac{6{,}708}{15{,}000}, \\dfrac{6{,}747}{15{,}000}, \\dfrac{6{,}936}{15{,}000}, \\dfrac{7{,}633}{15{,}000}, \\dfrac{7{,}719}{15{,}000}, \\dfrac{7{,}957}{15{,}000}, \\dfrac{8{,}449}{15{,}000}, \\dfrac{8{,}621}{15{,}000}, \\dfrac{9{,}577}{15{,}000}, \\text{ and } \\dfrac{9{,}592}{15{,}000}", "__seed__": "0942"}}, {"seed": 943, "data": {"p1_how_many": "10", "p1_a": "6.26", "p1_b": "6.27", "p1_numbers": "6.2605, 6.261, 6.262, 6.263, 6.264, 6.265, 6.266, 6.267, 6.268, and 6.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.261", "6.262", "6.263", "6.263999999999999", "6.265", "6.266", "6.2669999999999995", "6.268", "6.269"], "p1_2_xs": ["6.2604999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}157}{42{,}000}, \\dfrac{6{,}329}{42{,}000}, \\dfrac{6{,}361}{42{,}000}, \\dfrac{6{,}545}{42{,}000}, \\dfrac{6{,}581}{42{,}000}, \\dfrac{6{,}813}{42{,}000}, \\text{ and } \\dfrac{6{,}815}{42{,}000}", "__seed__": "0943"}}, {"seed": 944, "data": {"p1_how_many": "10", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}097}{12{,}000}, \\dfrac{8{,}162}{12{,}000}, \\dfrac{8{,}179}{12{,}000}, \\dfrac{8{,}204}{12{,}000}, \\dfrac{8{,}234}{12{,}000}, \\dfrac{8{,}385}{12{,}000}, \\dfrac{8{,}427}{12{,}000}, \\dfrac{8{,}680}{12{,}000}, \\dfrac{8{,}815}{12{,}000}, \\dfrac{8{,}855}{12{,}000}, \\text{ and } \\dfrac{8{,}948}{12{,}000}", "__seed__": "0944"}}, {"seed": 945, "data": {"p1_how_many": "12", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}019}{15{,}000}, \\dfrac{5{,}034}{15{,}000}, \\dfrac{5{,}072}{15{,}000}, \\dfrac{5{,}144}{15{,}000}, \\dfrac{5{,}375}{15{,}000}, \\dfrac{5{,}440}{15{,}000}, \\dfrac{5{,}463}{15{,}000}, \\dfrac{5{,}566}{15{,}000}, \\dfrac{5{,}664}{15{,}000}, \\dfrac{5{,}819}{15{,}000}, \\text{ and } \\dfrac{5{,}874}{15{,}000}", "__seed__": "0945"}}, {"seed": 946, "data": {"p1_how_many": "14", "p1_a": "4.23", "p1_b": "4.24", "p1_numbers": "4.2305, 4.231, 4.2315, 4.232, 4.2325, 4.233, 4.2335, 4.234, 4.2345, 4.235, 4.236, 4.237, 4.238, and 4.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.231000000000001", "4.232", "4.2330000000000005", "4.234", "4.235", "4.236000000000001", "4.237", "4.238", "4.239000000000001"], "p1_2_xs": ["4.2305", "4.2315000000000005", "4.2325", "4.2335", "4.2345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{71}{350}, \\dfrac{73}{350}, \\dfrac{74}{350}, \\dfrac{79}{350}, \\dfrac{81}{350}, \\dfrac{84}{350}, \\text{ and } \\dfrac{90}{350}", "__seed__": "0946"}}, {"seed": 947, "data": {"p1_how_many": "14", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.725, 4.73, 4.735, 4.74, 4.745, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715", "4.725", "4.735", "4.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}078}{56{,}000}, \\dfrac{48{,}299}{56{,}000}, \\dfrac{48{,}322}{56{,}000}, \\dfrac{48{,}379}{56{,}000}, \\dfrac{48{,}453}{56{,}000}, \\dfrac{48{,}522}{56{,}000}, \\dfrac{48{,}552}{56{,}000}, \\dfrac{48{,}637}{56{,}000}, \\dfrac{48{,}727}{56{,}000}, \\dfrac{48{,}729}{56{,}000}, \\dfrac{48{,}764}{56{,}000}, \\text{ and } \\dfrac{48{,}792}{56{,}000}", "__seed__": "0947"}}, {"seed": 948, "data": {"p1_how_many": "13", "p1_a": "6.23", "p1_b": "6.24", "p1_numbers": "6.2305, 6.231, 6.2315, 6.232, 6.2325, 6.233, 6.2335, 6.234, 6.235, 6.236, 6.237, 6.238, and 6.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.231000000000001", "6.232", "6.2330000000000005", "6.234", "6.235", "6.236000000000001", "6.237", "6.238", "6.239000000000001"], "p1_2_xs": ["6.2305", "6.2315000000000005", "6.2325", "6.2335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}514}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}538}{4{,}200}, \\dfrac{3{,}552}{4{,}200}, \\dfrac{3{,}584}{4{,}200}, \\text{ and } \\dfrac{3{,}594}{4{,}200}", "__seed__": "0948"}}, {"seed": 949, "data": {"p1_how_many": "11", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}514}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}542}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}566}{4{,}200}, \\dfrac{3{,}573}{4{,}200}, \\dfrac{3{,}579}{4{,}200}, \\dfrac{3{,}584}{4{,}200}, \\dfrac{3{,}589}{4{,}200}, \\dfrac{3{,}595}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0949"}}, {"seed": 950, "data": {"p1_how_many": "10", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}010}{20{,}000}, \\dfrac{4{,}015}{20{,}000}, \\dfrac{4{,}085}{20{,}000}, \\dfrac{4{,}118}{20{,}000}, \\dfrac{4{,}176}{20{,}000}, \\dfrac{4{,}482}{20{,}000}, \\dfrac{4{,}612}{20{,}000}, \\dfrac{4{,}621}{20{,}000}, \\dfrac{4{,}851}{20{,}000}, \\text{ and } \\dfrac{4{,}853}{20{,}000}", "__seed__": "0950"}}, {"seed": 951, "data": {"p1_how_many": "11", "p1_a": "1.16", "p1_b": "1.17", "p1_numbers": "1.1605, 1.161, 1.1615, 1.162, 1.163, 1.164, 1.165, 1.166, 1.167, 1.168, and 1.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.1609999999999998", "1.162", "1.1629999999999998", "1.164", "1.1649999999999998", "1.166", "1.1669999999999998", "1.168", "1.1689999999999998"], "p1_2_xs": ["1.1604999999999999", "1.1614999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{82}{420}, \\dfrac{89}{420}, \\dfrac{97}{420}, \\dfrac{104}{420}, \\dfrac{105}{420}, \\dfrac{109}{420}, \\dfrac{112}{420}, \\text{ and } \\dfrac{116}{420}", "__seed__": "0951"}}, {"seed": 952, "data": {"p1_how_many": "14", "p1_a": "4.82", "p1_b": "4.83", "p1_numbers": "4.8205, 4.821, 4.8215, 4.822, 4.8225, 4.823, 4.8235, 4.824, 4.8245, 4.825, 4.826, 4.827, 4.828, and 4.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.821000000000001", "4.822", "4.823", "4.824", "4.825", "4.8260000000000005", "4.827", "4.828", "4.829000000000001"], "p1_2_xs": ["4.8205", "4.8215", "4.8225", "4.8235", "4.8245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{819}{1{,}200}, \\dfrac{833}{1{,}200}, \\dfrac{854}{1{,}200}, \\dfrac{863}{1{,}200}, \\dfrac{878}{1{,}200}, \\dfrac{888}{1{,}200}, \\text{ and } \\dfrac{893}{1{,}200}", "__seed__": "0952"}}, {"seed": 953, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": 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"7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0954"}}, {"seed": 955, "data": {"p1_how_many": "11", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.2005, 3.201, 3.2015, 3.202, 3.203, 3.204, 3.205, 3.206, 3.207, 3.208, and 3.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.201", "3.202", "3.2030000000000003", "3.204", "3.205", "3.206", "3.2070000000000003", "3.208", "3.209"], "p1_2_xs": ["3.2005000000000003", "3.2015000000000002"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}385}{20{,}000}, \\dfrac{12{,}859}{20{,}000}, \\dfrac{12{,}882}{20{,}000}, \\dfrac{12{,}889}{20{,}000}, \\dfrac{13{,}292}{20{,}000}, \\dfrac{13{,}624}{20{,}000}, \\dfrac{14{,}349}{20{,}000}, \\dfrac{14{,}428}{20{,}000}, \\text{ and } \\dfrac{14{,}559}{20{,}000}", "__seed__": "0955"}}, {"seed": 956, "data": {"p1_how_many": "11", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.7005, 6.701, 6.7015, 6.702, 6.703, 6.704, 6.705, 6.706, 6.707, 6.708, and 6.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.7010000000000005", "6.702", "6.703", "6.704", "6.705", "6.706", "6.707", "6.708", "6.7090000000000005"], "p1_2_xs": ["6.7005", "6.7015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}134}{15{,}000}, \\dfrac{6{,}769}{15{,}000}, \\dfrac{7{,}129}{15{,}000}, \\dfrac{7{,}774}{15{,}000}, \\dfrac{9{,}096}{15{,}000}, \\dfrac{9{,}149}{15{,}000}, \\dfrac{9{,}306}{15{,}000}, \\dfrac{9{,}330}{15{,}000}, \\dfrac{9{,}335}{15{,}000}, \\dfrac{9{,}812}{15{,}000}, \\dfrac{9{,}900}{15{,}000}, \\text{ and } \\dfrac{9{,}992}{15{,}000}", "__seed__": "0956"}}, {"seed": 957, "data": {"p1_how_many": "13", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.335, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999", "7.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{644}{1{,}500}, \\dfrac{678}{1{,}500}, \\dfrac{696}{1{,}500}, \\dfrac{714}{1{,}500}, \\dfrac{741}{1{,}500}, \\dfrac{770}{1{,}500}, \\dfrac{784}{1{,}500}, \\dfrac{871}{1{,}500}, \\text{ and } \\dfrac{904}{1{,}500}", "__seed__": "0957"}}, {"seed": 958, "data": {"p1_how_many": "11", "p1_a": "7.05", "p1_b": "7.06", "p1_numbers": "7.0505, 7.051, 7.0515, 7.052, 7.053, 7.054, 7.055, 7.056, 7.057, 7.058, and 7.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.051", "7.052", "7.053", "7.053999999999999", "7.055", "7.056", "7.0569999999999995", "7.058", "7.059"], "p1_2_xs": ["7.0504999999999995", "7.0515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}418}{3{,}000}, \\dfrac{2{,}426}{3{,}000}, \\dfrac{2{,}453}{3{,}000}, \\dfrac{2{,}468}{3{,}000}, \\dfrac{2{,}474}{3{,}000}, \\dfrac{2{,}476}{3{,}000}, \\text{ and } \\dfrac{2{,}497}{3{,}000}", "__seed__": "0958"}}, {"seed": 959, "data": {"p1_how_many": "10", "p1_a": "1.46", "p1_b": "1.47", "p1_numbers": "1.4605, 1.461, 1.462, 1.463, 1.464, 1.465, 1.466, 1.467, 1.468, and 1.469", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4609999999999999", "1.462", "1.4629999999999999", "1.464", "1.4649999999999999", "1.466", "1.4669999999999999", "1.468", "1.4689999999999999"], "p1_2_xs": ["1.4605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{628}{1{,}500}, \\dfrac{643}{1{,}500}, \\dfrac{646}{1{,}500}, \\dfrac{658}{1{,}500}, \\dfrac{735}{1{,}500}, \\dfrac{810}{1{,}500}, \\dfrac{825}{1{,}500}, \\dfrac{850}{1{,}500}, \\dfrac{894}{1{,}500}, \\dfrac{897}{1{,}500}, \\text{ and } \\dfrac{907}{1{,}500}", "__seed__": "0959"}}, {"seed": 960, "data": {"p1_how_many": 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8.415, 8.416, 8.417, 8.418, and 8.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.411", "8.412", "8.413", "8.414", "8.415000000000001", "8.416", "8.417", "8.418", "8.419"], "p1_2_xs": ["8.4105", "8.4115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{610}{4{,}200}, \\dfrac{611}{4{,}200}, \\dfrac{613}{4{,}200}, \\dfrac{618}{4{,}200}, \\dfrac{635}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{669}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{682}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0961"}}, {"seed": 962, "data": {"p1_how_many": "11", "p1_a": "5.33", "p1_b": "5.34", "p1_numbers": "5.3305, 5.331, 5.3315, 5.332, 5.333, 5.334, 5.335, 5.336, 5.337, 5.338, and 5.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.331", "5.332", "5.333", "5.334", "5.335", "5.336", "5.337", "5.338", "5.339"], "p1_2_xs": ["5.3305", "5.3315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}712}{6{,}300}, \\dfrac{2{,}713}{6{,}300}, \\dfrac{2{,}726}{6{,}300}, \\dfrac{2{,}728}{6{,}300}, \\dfrac{2{,}729}{6{,}300}, \\dfrac{2{,}757}{6{,}300}, \\dfrac{2{,}763}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}765}{6{,}300}, \\dfrac{2{,}770}{6{,}300}, \\dfrac{2{,}775}{6{,}300}, \\text{ and } \\dfrac{2{,}777}{6{,}300}", "__seed__": "0962"}}, {"seed": 963, "data": {"p1_how_many": "11", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.015, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}158}{15{,}000}, \\dfrac{6{,}423}{15{,}000}, \\dfrac{6{,}979}{15{,}000}, \\dfrac{7{,}263}{15{,}000}, \\dfrac{8{,}003}{15{,}000}, \\dfrac{8{,}033}{15{,}000}, \\dfrac{8{,}219}{15{,}000}, \\dfrac{8{,}540}{15{,}000}, \\dfrac{8{,}982}{15{,}000}, \\text{ and } \\dfrac{9{,}535}{15{,}000}", "__seed__": "0963"}}, {"seed": 964, "data": {"p1_how_many": "10", "p1_a": "5.8", "p1_b": "5.9", "p1_numbers": "5.8005, 5.801, 5.802, 5.803, 5.804, 5.805, 5.806, 5.807, 5.808, and 5.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.801", "5.802", "5.803", "5.803999999999999", "5.805", "5.806", "5.8069999999999995", "5.808", "5.809"], "p1_2_xs": ["5.8004999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}060}{35{,}000}, \\dfrac{14{,}146}{35{,}000}, \\dfrac{14{,}311}{35{,}000}, \\dfrac{14{,}327}{35{,}000}, \\dfrac{14{,}558}{35{,}000}, \\dfrac{14{,}642}{35{,}000}, \\dfrac{14{,}701}{35{,}000}, \\dfrac{14{,}920}{35{,}000}, \\text{ and } \\dfrac{14{,}936}{35{,}000}", "__seed__": "0964"}}, {"seed": 965, "data": {"p1_how_many": "14", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.4005, 2.401, 2.4015, 2.402, 2.4025, 2.403, 2.4035, 2.404, 2.4045, 2.405, 2.406, 2.407, 2.408, and 2.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.401", "2.4019999999999997", "2.403", "2.404", "2.405", "2.4059999999999997", "2.407", "2.408", "2.409"], "p1_2_xs": ["2.4005", "2.4015", "2.4025", "2.4035", "2.4045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}427}{6{,}300}, \\dfrac{1{,}437}{6{,}300}, \\dfrac{1{,}445}{6{,}300}, \\dfrac{1{,}575}{6{,}300}, \\dfrac{1{,}582}{6{,}300}, \\dfrac{1{,}652}{6{,}300}, \\dfrac{1{,}738}{6{,}300}, \\dfrac{1{,}743}{6{,}300}, \\text{ and } \\dfrac{1{,}784}{6{,}300}", "__seed__": "0965"}}, {"seed": 966, "data": {"p1_how_many": "11", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}066}{4{,}200}, \\dfrac{3{,}106}{4{,}200}, \\dfrac{3{,}173}{4{,}200}, \\dfrac{3{,}201}{4{,}200}, \\dfrac{3{,}277}{4{,}200}, \\dfrac{3{,}366}{4{,}200}, \\text{ and } \\dfrac{3{,}495}{4{,}200}", "__seed__": "0966"}}, {"seed": 967, "data": {"p1_how_many": "13", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}151}{20{,}000}, \\dfrac{12{,}235}{20{,}000}, \\dfrac{12{,}326}{20{,}000}, \\dfrac{12{,}592}{20{,}000}, \\dfrac{12{,}753}{20{,}000}, \\dfrac{12{,}813}{20{,}000}, \\text{ and } \\dfrac{14{,}192}{20{,}000}", "__seed__": "0967"}}, {"seed": 968, 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"p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999", "5.635", "5.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}100}{30{,}000}, \\dfrac{5{,}200}{30{,}000}, \\dfrac{5{,}210}{30{,}000}, \\dfrac{5{,}250}{30{,}000}, \\dfrac{5{,}445}{30{,}000}, \\dfrac{5{,}463}{30{,}000}, \\dfrac{5{,}680}{30{,}000}, \\dfrac{5{,}685}{30{,}000}, \\dfrac{5{,}835}{30{,}000}, \\dfrac{5{,}849}{30{,}000}, \\dfrac{5{,}901}{30{,}000}, \\text{ and } \\dfrac{5{,}991}{30{,}000}", "__seed__": "0978"}}, {"seed": 979, "data": {"p1_how_many": "14", "p1_a": "4.54", "p1_b": "4.55", "p1_numbers": "4.5405, 4.541, 4.5415, 4.542, 4.5425, 4.543, 4.5435, 4.544, 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"num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}405}{3{,}000}, \\dfrac{2{,}409}{3{,}000}, \\dfrac{2{,}436}{3{,}000}, \\dfrac{2{,}438}{3{,}000}, \\dfrac{2{,}451}{3{,}000}, \\dfrac{2{,}461}{3{,}000}, \\text{ and } \\dfrac{2{,}488}{3{,}000}", "__seed__": "0980"}}, {"seed": 981, "data": {"p1_how_many": "11", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": 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"p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435", "9.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}052}{4{,}200}, \\dfrac{3{,}063}{4{,}200}, \\dfrac{3{,}081}{4{,}200}, \\dfrac{3{,}158}{4{,}200}, \\dfrac{3{,}195}{4{,}200}, \\dfrac{3{,}238}{4{,}200}, \\dfrac{3{,}239}{4{,}200}, \\text{ and } \\dfrac{3{,}267}{4{,}200}", "__seed__": "0985"}}, {"seed": 986, "data": {"p1_how_many": "12", "p1_a": "7.12", "p1_b": "7.13", "p1_numbers": "7.1205, 7.121, 7.1215, 7.122, 7.1225, 7.123, 7.124, 7.125, 7.126, 7.127, 7.128, and 7.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.121", "7.122", "7.123", "7.124", "7.125", "7.126", "7.127", "7.128", "7.1290000000000004"], "p1_2_xs": ["7.1205", "7.1215", "7.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}450}{20{,}000}, \\dfrac{5{,}548}{20{,}000}, \\dfrac{5{,}991}{20{,}000}, \\dfrac{6{,}176}{20{,}000}, \\dfrac{6{,}335}{20{,}000}, \\dfrac{6{,}454}{20{,}000}, \\dfrac{6{,}996}{20{,}000}, \\dfrac{7{,}324}{20{,}000}, \\dfrac{7{,}716}{20{,}000}, \\text{ and } \\dfrac{7{,}848}{20{,}000}", "__seed__": "0986"}}, {"seed": 987, "data": {"p1_how_many": "13", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}318}{15{,}000}, \\dfrac{6{,}918}{15{,}000}, \\dfrac{7{,}708}{15{,}000}, \\dfrac{7{,}886}{15{,}000}, \\dfrac{8{,}229}{15{,}000}, \\dfrac{8{,}604}{15{,}000}, \\text{ and } \\dfrac{8{,}775}{15{,}000}", "__seed__": "0987"}}, {"seed": 988, "data": {"p1_how_many": "12", "p1_a": "2.53", "p1_b": "2.54", "p1_numbers": "2.5305, 2.531, 2.5315, 2.532, 2.5325, 2.533, 2.534, 2.535, 2.536, 2.537, 2.538, and 2.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5309999999999997", "2.5319999999999996", "2.533", "2.534", "2.5349999999999997", "2.5359999999999996", "2.537", "2.538", "2.5389999999999997"], "p1_2_xs": ["2.5305", "2.5315", "2.5324999999999998"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{33{,}130}{56{,}000}, \\dfrac{33{,}254}{56{,}000}, \\dfrac{33{,}798}{56{,}000}, \\dfrac{34{,}065}{56{,}000}, \\dfrac{34{,}094}{56{,}000}, \\dfrac{34{,}145}{56{,}000}, \\dfrac{34{,}180}{56{,}000}, \\dfrac{34{,}301}{56{,}000}, \\text{ and } \\dfrac{34{,}540}{56{,}000}", "__seed__": "0988"}}, {"seed": 989, "data": {"p1_how_many": "10", "p1_a": "9.86", "p1_b": "9.87", "p1_numbers": "9.8605, 9.861, 9.862, 9.863, 9.864, 9.865, 9.866, 9.867, 9.868, and 9.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.860999999999999", "9.862", "9.863", "9.863999999999999", "9.865", "9.866", "9.866999999999999", "9.867999999999999", "9.869"], "p1_2_xs": ["9.8605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}715}{6{,}300}, \\dfrac{2{,}716}{6{,}300}, \\dfrac{2{,}720}{6{,}300}, \\dfrac{2{,}740}{6{,}300}, \\dfrac{2{,}746}{6{,}300}, \\dfrac{2{,}760}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}773}{6{,}300}, \\dfrac{2{,}775}{6{,}300}, \\text{ and } \\dfrac{2{,}796}{6{,}300}", "__seed__": "0989"}}, {"seed": 990, "data": {"p1_how_many": "10", "p1_a": "3.22", "p1_b": "3.23", "p1_numbers": "3.2205, 3.221, 3.222, 3.223, 3.224, 3.225, 3.226, 3.227, 3.228, and 3.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.221", "3.222", "3.2230000000000003", "3.224", "3.225", "3.226", "3.2270000000000003", "3.228", "3.229"], "p1_2_xs": ["3.2205000000000004"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{2{,}018}{3{,}500}, \\dfrac{2{,}023}{3{,}500}, \\dfrac{2{,}043}{3{,}500}, \\dfrac{2{,}055}{3{,}500}, \\dfrac{2{,}058}{3{,}500}, \\dfrac{2{,}068}{3{,}500}, \\text{ and } \\dfrac{2{,}069}{3{,}500}", "__seed__": "0990"}}, {"seed": 991, "data": {"p1_how_many": "13", "p1_a": "5.02", "p1_b": "5.03", "p1_numbers": "5.0205, 5.021, 5.0215, 5.022, 5.0225, 5.023, 5.0235, 5.024, 5.025, 5.026, 5.027, 5.028, and 5.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.021", "5.021999999999999", "5.023", "5.023999999999999", "5.0249999999999995", "5.026", "5.026999999999999", "5.028", "5.029"], "p1_2_xs": ["5.020499999999999", "5.0215", "5.022499999999999", "5.023499999999999"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}015}{20{,}000}, \\dfrac{4{,}158}{20{,}000}, \\dfrac{4{,}383}{20{,}000}, \\dfrac{4{,}405}{20{,}000}, \\dfrac{4{,}473}{20{,}000}, \\dfrac{4{,}630}{20{,}000}, \\text{ and } \\dfrac{4{,}792}{20{,}000}", "__seed__": "0991"}}, {"seed": 992, "data": {"p1_how_many": "11", "p1_a": "7.95", "p1_b": "7.96", "p1_numbers": "7.9505, 7.951, 7.9515, 7.952, 7.953, 7.954, 7.955, 7.956, 7.957, 7.958, and 7.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.9510000000000005", "7.952", "7.953", "7.954", "7.955", "7.956", "7.957", "7.958", "7.9590000000000005"], "p1_2_xs": ["7.9505", "7.9515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}025}{35{,}000}, \\dfrac{14{,}047}{35{,}000}, \\dfrac{14{,}279}{35{,}000}, \\dfrac{14{,}710}{35{,}000}, \\dfrac{14{,}829}{35{,}000}, \\dfrac{14{,}892}{35{,}000}, \\dfrac{14{,}898}{35{,}000}, \\dfrac{14{,}958}{35{,}000}, \\dfrac{14{,}973}{35{,}000}, \\text{ and } \\dfrac{14{,}995}{35{,}000}", "__seed__": "0992"}}, {"seed": 993, "data": {"p1_how_many": "12", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{48}{200}", "__seed__": "0993"}}, {"seed": 994, "data": {"p1_how_many": "12", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.225, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215", "3.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{102}{350}, \\dfrac{110}{350}, \\dfrac{111}{350}, \\dfrac{112}{350}, \\dfrac{117}{350}, \\dfrac{119}{350}, \\text{ and } \\dfrac{136}{350}", "__seed__": "0994"}}, {"seed": 995, "data": {"p1_how_many": "10", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.42, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}088}{35{,}000}, \\dfrac{14{,}367}{35{,}000}, \\dfrac{14{,}430}{35{,}000}, \\dfrac{14{,}492}{35{,}000}, \\dfrac{14{,}516}{35{,}000}, \\dfrac{14{,}565}{35{,}000}, \\dfrac{14{,}665}{35{,}000}, \\dfrac{14{,}680}{35{,}000}, \\dfrac{14{,}734}{35{,}000}, \\dfrac{14{,}740}{35{,}000}, \\dfrac{14{,}880}{35{,}000}, \\text{ and } \\dfrac{14{,}949}{35{,}000}", "__seed__": "0995"}}, {"seed": 996, "data": {"p1_how_many": "13", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.635, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625", "3.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}399}{20{,}000}, \\dfrac{5{,}438}{20{,}000}, \\dfrac{5{,}506}{20{,}000}, \\dfrac{6{,}485}{20{,}000}, \\dfrac{6{,}746}{20{,}000}, \\dfrac{7{,}068}{20{,}000}, \\text{ and } \\dfrac{7{,}243}{20{,}000}", "__seed__": "0996"}}, {"seed": 997, "data": {"p1_how_many": "11", "p1_a": "5.24", "p1_b": "5.25", "p1_numbers": "5.2405, 5.241, 5.2415, 5.242, 5.243, 5.244, 5.245, 5.246, 5.247, 5.248, and 5.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.2410000000000005", "5.242", "5.243", "5.244", "5.245", "5.246", "5.247", "5.248", "5.2490000000000006"], "p1_2_xs": ["5.2405", "5.2415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{503}{1{,}500}, \\dfrac{519}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{547}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{587}{1{,}500}, \\dfrac{591}{1{,}500}, \\dfrac{592}{1{,}500}, \\text{ and } \\dfrac{595}{1{,}500}", "__seed__": "0997"}}, {"seed": 998, "data": {"p1_how_many": "13", "p1_a": "8.64", "p1_b": "8.65", "p1_numbers": "8.6405, 8.641, 8.6415, 8.642, 8.6425, 8.643, 8.6435, 8.644, 8.645, 8.646, 8.647, 8.648, and 8.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.641", "8.642000000000001", "8.643", "8.644", "8.645000000000001", "8.646", "8.647", "8.648", "8.649000000000001"], "p1_2_xs": ["8.640500000000001", "8.6415", "8.642500000000002", "8.643500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}507}{2{,}000}, \\dfrac{1{,}508}{2{,}000}, \\dfrac{1{,}510}{2{,}000}, \\dfrac{1{,}515}{2{,}000}, \\dfrac{1{,}518}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}539}{2{,}000}, \\dfrac{1{,}547}{2{,}000}, \\dfrac{1{,}555}{2{,}000}, \\dfrac{1{,}564}{2{,}000}, \\dfrac{1{,}567}{2{,}000}, \\text{ and } \\dfrac{1{,}584}{2{,}000}", "__seed__": "0998"}}, {"seed": 999, "data": {"p1_how_many": "12", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}796}{56{,}000}, \\dfrac{22{,}029}{56{,}000}, \\dfrac{22{,}775}{56{,}000}, \\dfrac{22{,}810}{56{,}000}, \\dfrac{22{,}873}{56{,}000}, \\dfrac{23{,}084}{56{,}000}, \\dfrac{23{,}239}{56{,}000}, \\dfrac{23{,}295}{56{,}000}, \\dfrac{23{,}796}{56{,}000}, \\text{ and } \\dfrac{23{,}969}{56{,}000}", "__seed__": "0999"}}], "generated_on": "2024-07-27T01:27:06.744329+00:00"} \ No newline at end of file diff --git a/docs/assets/bank.json b/docs/assets/bank.json index 6362dbf..cf732cd 100644 --- a/docs/assets/bank.json +++ b/docs/assets/bank.json @@ -1 +1 @@ -{"title": "MAT 106 - Number Systems and Operations - CheckIt Bank", "slug": "mat-106-bank", "url": "https://checkit.clontz.org", "generated_on": "2024-07-24T13:31:14.792228+00:00", "outcomes": [{"title": "Ancient Numeration Systems", "slug": "W1", "description": "\n I can convert the ancient Roman/Babylonian/Egyptian numeration systems to modern Hindu-Arabic base ten, and vice versa.\n ", "template": "\n\n \n \n

Convert {{to_a_modern}} to {{to_a_system}}.

\n
\n \n

{{to_a_ancient}}

\n
\n
\n \n \n

Convert the following {{to_m_system}} numeral to modern Hindu-Arabic base ten.

\n

{{to_m_ancient}}

\n
\n \n

{{to_m_modern}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"to_a_modern": "2,754", "to_a_system": "Roman", "to_a_ancient": "MMDCCLIV", "to_m_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udcf5\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_system": "ancient Babylonian", "to_m_modern": "122,433", "egy_test": false, "__seed__": "0000"}}, {"seed": 1, "data": {"to_a_modern": "112,495", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\u2003\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_ancient": 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"\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_system": "ancient Babylonian", "to_m_modern": "85,905", "egy_test": false, "__seed__": "0997"}}, {"seed": 998, "data": {"to_a_modern": "142,361", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79", "to_m_ancient": "MMMDCLXXXIX", "to_m_system": "Roman", "to_m_modern": "3,689", "egy_test": false, "__seed__": "0998"}}, {"seed": 999, "data": {"to_a_modern": "3,243,842", "to_a_system": "ancient Egyptian", "to_a_ancient": "\ud80c\udc68\ud80c\udc68\ud80c\udc68\ud80c\udd90\ud80c\udd90\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udffa\ud80c\udffa", "to_m_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_system": "ancient Babylonian", "to_m_modern": "97,457", "egy_test": true, "__seed__": "0999"}}]}, {"title": "Base-b Addition and Subtraction Algorithms", "slug": "W2", "description": "\n I can compute addition and subtraction of multi-digit base-b whole numbers using non-standard addition and subtraction algorithms.\n ", "template": "\n\n \n

Compute each of the following using the stated algorithm. You must show all calculations in the desired base, and not by converting between bases.

\n
\n \n \n

{{base_ten_prob}} ({{base_ten_alg}})

\n
\n \n

{{base_ten_ans}}

\n
\n
\n \n \n

{{base_b_prob}} ({{base_b_alg}})

\n
\n \n

{{base_b_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"base_ten_prob": "8986 + 2758", "base_ten_alg": "Lattice", "base_ten_ans": "11744", "base_b_prob": "1324_\\text{nine} - 1086_\\text{nine}", "base_b_alg": "Subtract from the Base", "base_b_ans": "227_\\text{nine}", "__seed__": "0000"}}, {"seed": 1, "data": {"base_ten_prob": "4168 - 3648", "base_ten_alg": "Equal Additions", "base_ten_ans": "520", "base_b_prob": "1410_\\text{eight} + 1456_\\text{eight}", "base_b_alg": "Partial Sums", "base_b_ans": "3066_\\text{eight}", "__seed__": "0001"}}, {"seed": 2, "data": {"base_ten_prob": "6846 - 6578", "base_ten_alg": "Subtract from the Base", "base_ten_ans": "268", "base_b_prob": "2507_\\text{eight} + 6666_\\text{eight}", "base_b_alg": "Partial Sums", "base_b_ans": "11375_\\text{eight}", "__seed__": "0002"}}, {"seed": 3, "data": {"base_ten_prob": "7586 - 5306", "base_ten_alg": "Trades First", "base_ten_ans": "2280", "base_b_prob": "2000_\\text{six} + 1533_\\text{six}", "base_b_alg": "Partial Sums", "base_b_ans": "3533_\\text{six}", "__seed__": "0003"}}, {"seed": 4, "data": {"base_ten_prob": "7587 + 1889", "base_ten_alg": "Lattice", "base_ten_ans": "9476", "base_b_prob": "5530_\\text{seven} - 1464_\\text{seven}", "base_b_alg": "Trades First", "base_b_ans": "4033_\\text{seven}", "__seed__": "0004"}}, {"seed": 5, "data": {"base_ten_prob": "9882 + 2708", "base_ten_alg": "Partial Sums", "base_ten_ans": "12590", "base_b_prob": "1415_\\text{nine} - 556_\\text{nine}", "base_b_alg": "Equal Additions", "base_b_ans": "748_\\text{nine}", "__seed__": "0005"}}, {"seed": 6, "data": {"base_ten_prob": "8665 + 6557", "base_ten_alg": "Partial Sums", "base_ten_ans": "15222", "base_b_prob": "1304_\\text{six} - 544_\\text{six}", "base_b_alg": "Subtract from the Base", "base_b_ans": "320_\\text{six}", "__seed__": "0006"}}, {"seed": 7, "data": {"base_ten_prob": "5686 + 9939", "base_ten_alg": "Lattice", "base_ten_ans": "15625", "base_b_prob": "2004_\\text{five} - 344_\\text{five}", "base_b_alg": "Subtract from the Base", "base_b_ans": "1110_\\text{five}", "__seed__": "0007"}}, {"seed": 8, "data": {"base_ten_prob": "3999 + 9574", "base_ten_alg": "Column Addition", "base_ten_ans": "13573", "base_b_prob": "1313_\\text{four} - 232_\\text{four}", "base_b_alg": "Equal Additions", "base_b_ans": "1021_\\text{four}", "__seed__": "0008"}}, {"seed": 9, "data": {"base_ten_prob": "8775 + 7595", "base_ten_alg": "Column Addition", "base_ten_ans": "16370", "base_b_prob": "1301_\\text{four} - 323_\\text{four}", "base_b_alg": "Trades First", "base_b_ans": "312_\\text{four}", "__seed__": "0009"}}, {"seed": 10, "data": {"base_ten_prob": "3405 + 9686", "base_ten_alg": "Lattice", "base_ten_ans": "13091", "base_b_prob": "1113_\\text{seven} - 1064_\\text{seven}", "base_b_alg": "Equal Additions", "base_b_ans": "16_\\text{seven}", "__seed__": "0010"}}, {"seed": 11, "data": {"base_ten_prob": "8860 + 9086", "base_ten_alg": "Lattice", "base_ten_ans": "17946", "base_b_prob": "2130_\\text{five} - 220_\\text{five}", "base_b_alg": "Subtract from the Base", "base_b_ans": "1410_\\text{five}", "__seed__": "0011"}}, {"seed": 12, "data": {"base_ten_prob": "6890 + 9792", "base_ten_alg": "Partial Sums", "base_ten_ans": "16682", "base_b_prob": "5013_\\text{seven} - 5013_\\text{seven}", "base_b_alg": "Equal Additions", "base_b_ans": "0_\\text{seven}", "__seed__": "0012"}}, {"seed": 13, "data": {"base_ten_prob": "7650 + 1837", "base_ten_alg": "Lattice", "base_ten_ans": "9487", "base_b_prob": "3002_\\text{four} - 3002_\\text{four}", "base_b_alg": "Subtract from the Base", "base_b_ans": "0_\\text{four}", "__seed__": "0013"}}, {"seed": 14, "data": {"base_ten_prob": "7978 - 6566", "base_ten_alg": "Equal Additions", "base_ten_ans": "1412", "base_b_prob": "2484_\\text{nine} + 1666_\\text{nine}", "base_b_alg": "Partial Sums", "base_b_ans": "4261_\\text{nine}", "__seed__": "0014"}}, {"seed": 15, "data": {"base_ten_prob": "6789 + 8769", "base_ten_alg": "Lattice", "base_ten_ans": "15558", "base_b_prob": "3212_\\text{six} - 2545_\\text{six}", "base_b_alg": "Subtract from the Base", "base_b_ans": "223_\\text{six}", "__seed__": "0015"}}, {"seed": 16, "data": {"base_ten_prob": "8786 - 5896", "base_ten_alg": "Trades First", "base_ten_ans": "2890", "base_b_prob": "6333_\\text{seven} + 6656_\\text{seven}", "base_b_alg": "Column Addition", "base_b_ans": "16322_\\text{seven}", "__seed__": "0016"}}, {"seed": 17, "data": {"base_ten_prob": "9864 + 8969", "base_ten_alg": "Lattice", "base_ten_ans": "18833", "base_b_prob": "2302_\\text{eight} - 754_\\text{eight}", "base_b_alg": "Equal Additions", "base_b_ans": "1326_\\text{eight}", "__seed__": "0017"}}, {"seed": 18, "data": {"base_ten_prob": "6678 + 6654", "base_ten_alg": "Column Addition", "base_ten_ans": "13332", "base_b_prob": "4185_\\text{nine} - 4058_\\text{nine}", "base_b_alg": "Subtract from the Base", "base_b_ans": "126_\\text{nine}", "__seed__": "0018"}}, {"seed": 19, "data": {"base_ten_prob": "9868 - 5889", "base_ten_alg": "Subtract from the Base", "base_ten_ans": "3979", "base_b_prob": "7841_\\text{nine} + 7665_\\text{nine}", "base_b_alg": "Partial Sums", "base_b_ans": "16616_\\text{nine}", "__seed__": "0019"}}, {"seed": 20, "data": {"base_ten_prob": "1617 - 593", "base_ten_alg": "Subtract from the Base", "base_ten_ans": "1024", "base_b_prob": "2101_\\text{six} + 5154_\\text{six}", "base_b_alg": "Column Addition", "base_b_ans": "11255_\\text{six}", "__seed__": "0020"}}, {"seed": 21, "data": {"base_ten_prob": "8659 + 6088", "base_ten_alg": "Lattice", "base_ten_ans": "14747", "base_b_prob": "1101_\\text{four} - 232_\\text{four}", "base_b_alg": "Trades First", "base_b_ans": "203_\\text{four}", "__seed__": "0021"}}, {"seed": 22, "data": {"base_ten_prob": "5757 + 9719", "base_ten_alg": "Partial Sums", "base_ten_ans": "15476", "base_b_prob": "2332_\\text{nine} - 2158_\\text{nine}", "base_b_alg": "Equal Additions", "base_b_ans": "163_\\text{nine}", "__seed__": "0022"}}, {"seed": 23, "data": {"base_ten_prob": "8892 - 8293", "base_ten_alg": "Trades First", "base_ten_ans": "599", "base_b_prob": "6020_\\text{eight} + 7766_\\text{eight}", "base_b_alg": "Partial Sums", "base_b_ans": "16006_\\text{eight}", "__seed__": "0023"}}, {"seed": 24, "data": {"base_ten_prob": "8698 - 6599", "base_ten_alg": "Equal Additions", "base_ten_ans": "2099", "base_b_prob": "3102_\\text{four} + 3022_\\text{four}", "base_b_alg": "Partial Sums", "base_b_ans": "12130_\\text{four}", "__seed__": "0024"}}, {"seed": 25, "data": {"base_ten_prob": "6866 + 6975", "base_ten_alg": "Partial Sums", "base_ten_ans": "13841", "base_b_prob": "4063_\\text{eight} - 1664_\\text{eight}", "base_b_alg": "Trades First", "base_b_ans": "2177_\\text{eight}", "__seed__": "0025"}}, {"seed": 26, "data": {"base_ten_prob": "5786 - 3988", "base_ten_alg": "Subtract from the Base", "base_ten_ans": "1798", "base_b_prob": "2120_\\text{five} + 3414_\\text{five}", "base_b_alg": "Column Addition", "base_b_ans": "11034_\\text{five}", "__seed__": "0026"}}, {"seed": 27, "data": {"base_ten_prob": "6687 + 2778", "base_ten_alg": "Column Addition", "base_ten_ans": "9465", "base_b_prob": "2221_\\text{five} - 1344_\\text{five}", "base_b_alg": "Equal Additions", "base_b_ans": "322_\\text{five}", "__seed__": "0027"}}, {"seed": 28, "data": {"base_ten_prob": "1086 + 9679", "base_ten_alg": "Column Addition", "base_ten_ans": "10765", "base_b_prob": "1002_\\text{four} - 1001_\\text{four}", "base_b_alg": "Equal Additions", "base_b_ans": "1_\\text{four}", "__seed__": "0028"}}, {"seed": 29, "data": {"base_ten_prob": "7766 + 1997", "base_ten_alg": "Partial Sums", "base_ten_ans": "9763", "base_b_prob": "3121_\\text{four} - 2322_\\text{four}", "base_b_alg": "Trades First", "base_b_ans": "133_\\text{four}", "__seed__": "0029"}}, {"seed": 30, "data": {"base_ten_prob": "8971 + 2585", "base_ten_alg": "Lattice", "base_ten_ans": "11556", "base_b_prob": "6310_\\text{seven} - 2606_\\text{seven}", "base_b_alg": "Subtract from the Base", "base_b_ans": "3401_\\text{seven}", "__seed__": "0030"}}, {"seed": 31, "data": {"base_ten_prob": "5991 - 5498", "base_ten_alg": "Trades First", "base_ten_ans": "493", "base_b_prob": "3617_\\text{nine} + 1182_\\text{nine}", "base_b_alg": "Partial Sums", "base_b_ans": "4810_\\text{nine}", "__seed__": "0031"}}, {"seed": 32, "data": {"base_ten_prob": "5654 + 5896", "base_ten_alg": "Partial Sums", "base_ten_ans": "11550", "base_b_prob": "1210_\\text{five} - 1203_\\text{five}", "base_b_alg": "Equal Additions", "base_b_ans": "2_\\text{five}", "__seed__": "0032"}}, {"seed": 33, "data": {"base_ten_prob": "7916 + 9693", "base_ten_alg": "Partial Sums", "base_ten_ans": "17609", "base_b_prob": "3204_\\text{six} - 2554_\\text{six}", "base_b_alg": "Subtract from the Base", "base_b_ans": "210_\\text{six}", "__seed__": "0033"}}, {"seed": 34, "data": {"base_ten_prob": "8686 + 5875", "base_ten_alg": "Lattice", "base_ten_ans": "14561", "base_b_prob": "1001_\\text{four} - 1001_\\text{four}", "base_b_alg": "Trades First", "base_b_ans": "0_\\text{four}", "__seed__": "0034"}}, {"seed": 35, "data": {"base_ten_prob": "5658 + 7516", "base_ten_alg": "Column Addition", "base_ten_ans": "13174", "base_b_prob": "5210_\\text{eight} - 1703_\\text{eight}", "base_b_alg": "Subtract from the Base", "base_b_ans": "3305_\\text{eight}", "__seed__": "0035"}}, {"seed": 36, "data": {"base_ten_prob": "1887 + 8862", "base_ten_alg": "Column Addition", "base_ten_ans": "10749", "base_b_prob": "3731_\\text{eight} - 2640_\\text{eight}", "base_b_alg": "Equal Additions", "base_b_ans": "1071_\\text{eight}", "__seed__": "0036"}}, {"seed": 37, "data": {"base_ten_prob": "5892 + 5995", "base_ten_alg": "Partial Sums", "base_ten_ans": "11887", "base_b_prob": "4300_\\text{nine} - 2501_\\text{nine}", "base_b_alg": "Trades First", "base_b_ans": "1688_\\text{nine}", "__seed__": "0037"}}, {"seed": 38, "data": {"base_ten_prob": "7859 + 2685", "base_ten_alg": "Column Addition", "base_ten_ans": "10544", "base_b_prob": "6521_\\text{seven} - 3266_\\text{seven}", "base_b_alg": "Trades First", "base_b_ans": "3222_\\text{seven}", "__seed__": "0038"}}, {"seed": 39, "data": {"base_ten_prob": "5514 + 9669", "base_ten_alg": "Partial Sums", "base_ten_ans": "15183", "base_b_prob": "3608_\\text{nine} - 1038_\\text{nine}", "base_b_alg": "Subtract from the Base", "base_b_ans": "2560_\\text{nine}", "__seed__": "0039"}}, {"seed": 40, "data": {"base_ten_prob": "4157 + 2785", "base_ten_alg": "Column Addition", "base_ten_ans": "6942", "base_b_prob": "2320_\\text{seven} - 1425_\\text{seven}", "base_b_alg": "Equal Additions", "base_b_ans": "562_\\text{seven}", "__seed__": "0040"}}, {"seed": 41, "data": {"base_ten_prob": "8785 + 6706", "base_ten_alg": "Lattice", "base_ten_ans": "15491", "base_b_prob": "4331_\\text{seven} - 4330_\\text{seven}", "base_b_alg": "Subtract from the Base", "base_b_ans": "1_\\text{seven}", "__seed__": "0041"}}, {"seed": 42, "data": {"base_ten_prob": "8897 - 1568", "base_ten_alg": "Trades First", "base_ten_ans": "7329", "base_b_prob": "1326_\\text{seven} + 1655_\\text{seven}", "base_b_alg": "Lattice", "base_b_ans": "3314_\\text{seven}", "__seed__": "0042"}}, {"seed": 43, "data": {"base_ten_prob": "3686 - 939", "base_ten_alg": "Trades First", "base_ten_ans": "2747", "base_b_prob": "2220_\\text{six} + 4542_\\text{six}", "base_b_alg": "Partial Sums", "base_b_ans": "11202_\\text{six}", "__seed__": "0043"}}, {"seed": 44, "data": {"base_ten_prob": "9952 - 596", "base_ten_alg": "Equal Additions", "base_ten_ans": "9356", "base_b_prob": "2012_\\text{five} + 3324_\\text{five}", "base_b_alg": "Lattice", "base_b_ans": "10341_\\text{five}", "__seed__": "0044"}}, {"seed": 45, "data": {"base_ten_prob": "6732 - 2971", "base_ten_alg": "Trades First", "base_ten_ans": "3761", "base_b_prob": "1300_\\text{seven} + 4460_\\text{seven}", "base_b_alg": "Partial Sums", "base_b_ans": "6060_\\text{seven}", "__seed__": "0045"}}, {"seed": 46, "data": {"base_ten_prob": "5867 - 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2065_\\text{seven}", "base_b_alg": "Subtract from the Base", "base_b_ans": "23_\\text{seven}", "__seed__": "0987"}}, {"seed": 988, "data": {"base_ten_prob": "6695 - 6650", "base_ten_alg": "Equal Additions", "base_ten_ans": "45", "base_b_prob": "1220_\\text{six} + 5534_\\text{six}", "base_b_alg": "Partial Sums", "base_b_ans": "11154_\\text{six}", "__seed__": "0988"}}, {"seed": 989, "data": {"base_ten_prob": "6766 - 6760", "base_ten_alg": "Equal Additions", "base_ten_ans": "6", "base_b_prob": "1151_\\text{eight} + 7557_\\text{eight}", "base_b_alg": "Column Addition", "base_b_ans": "10730_\\text{eight}", "__seed__": "0989"}}, {"seed": 990, "data": {"base_ten_prob": "4588 - 2356", "base_ten_alg": "Equal Additions", "base_ten_ans": "2232", "base_b_prob": "2010_\\text{four} + 2323_\\text{four}", "base_b_alg": "Lattice", "base_b_ans": "10333_\\text{four}", "__seed__": "0990"}}, {"seed": 991, "data": {"base_ten_prob": "9797 - 1566", "base_ten_alg": "Equal Additions", "base_ten_ans": "8231", "base_b_prob": "4025_\\text{six} + 5343_\\text{six}", "base_b_alg": "Lattice", "base_b_ans": "13412_\\text{six}", "__seed__": "0991"}}, {"seed": 992, "data": {"base_ten_prob": "8996 - 8345", "base_ten_alg": "Trades First", "base_ten_ans": "651", "base_b_prob": "1122_\\text{seven} + 4514_\\text{seven}", "base_b_alg": "Lattice", "base_b_ans": "5636_\\text{seven}", "__seed__": "0992"}}, {"seed": 993, "data": {"base_ten_prob": "6591 - 5758", "base_ten_alg": "Trades First", "base_ten_ans": "833", "base_b_prob": "3317_\\text{nine} + 6753_\\text{nine}", "base_b_alg": "Column Addition", "base_b_ans": "11171_\\text{nine}", "__seed__": "0993"}}, {"seed": 994, "data": {"base_ten_prob": "9776 + 6492", "base_ten_alg": "Column Addition", "base_ten_ans": "16268", "base_b_prob": "2210_\\text{seven} - 406_\\text{seven}", "base_b_alg": "Equal Additions", "base_b_ans": "1501_\\text{seven}", "__seed__": "0994"}}, {"seed": 995, "data": {"base_ten_prob": "4597 - 2725", "base_ten_alg": "Trades First", "base_ten_ans": "1872", "base_b_prob": "3121_\\text{eight} + 4646_\\text{eight}", "base_b_alg": "Lattice", "base_b_ans": "7767_\\text{eight}", "__seed__": "0995"}}, {"seed": 996, "data": {"base_ten_prob": "8679 + 5885", "base_ten_alg": "Partial Sums", "base_ten_ans": "14564", "base_b_prob": "1313_\\text{seven} - 1205_\\text{seven}", "base_b_alg": "Equal Additions", "base_b_ans": "105_\\text{seven}", "__seed__": "0996"}}, {"seed": 997, "data": {"base_ten_prob": "5629 - 4655", "base_ten_alg": "Subtract from the Base", "base_ten_ans": "974", "base_b_prob": "7303_\\text{nine} + 6877_\\text{nine}", "base_b_alg": "Column Addition", "base_b_ans": "15281_\\text{nine}", "__seed__": "0997"}}, {"seed": 998, "data": {"base_ten_prob": "6676 + 3976", "base_ten_alg": "Lattice", "base_ten_ans": "10652", "base_b_prob": "2502_\\text{six} - 1434_\\text{six}", "base_b_alg": "Trades First", "base_b_ans": "1024_\\text{six}", "__seed__": "0998"}}, {"seed": 999, "data": {"base_ten_prob": "9558 - 5786", "base_ten_alg": "Trades First", "base_ten_ans": "3772", "base_b_prob": "1347_\\text{eight} + 7075_\\text{eight}", "base_b_alg": "Column Addition", "base_b_ans": "10444_\\text{eight}", "__seed__": "0999"}}]}, {"title": "Properties of Addition and Multiplication", "slug": "W3", "description": "\n I can identify uses of the associative, commutative, identity, zero product, and distributive properties of addition and multiplication.\n ", "template": "\n\n \n

For each of the following equations, state the property that is being exemplified.

\n
\n \n \n

{{p1_prob}}

\n
\n \n

{{p1_ans}}

\n
\n
\n \n \n

{{p2_prob}}

\n
\n \n

{{p2_ans}}

\n
\n
\n \n \n

{{p3_prob}}

\n
\n \n

{{p3_ans}}

\n
\n
\n \n \n

{{p4_prob}}

\n
\n \n

{{p4_ans}}

\n
\n
\n \n \n

{{p5_prob}}

\n
\n \n

{{p5_ans}}

\n
\n
\n \n \n

{{p6_prob}}

\n
\n \n

{{p6_ans}}

\n
\n
\n \n \n

{{p7_prob}}

\n
\n \n

{{p7_ans}}

\n
\n
\n \n \n

{{p8_prob}}

\n
\n \n

{{p8_ans}}

\n
\n
\n \n \n

{{p9_prob}}

\n
\n \n

{{p9_ans}}

\n
\n
\n \n \n

{{p10_prob}}

\n
\n \n

{{p10_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"p1_prob": "g \\times 0 = 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "d \\times 0 = 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "n \\times (a \\times w) = (a \\times w) \\times n", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vB", "p4_prob": "p + f \\times j - f \\times m = p + f(j - m)", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "(v \\times a) \\times w = v \\times (a \\times w)", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": " (n - 0 + b) - p = (n - b) - p", "p6_ans": "Identity Property of Addition", "p6_ver": "vB", "p7_prob": "(19 \\times 6) \\times 7 = 19 \\times (6 \\times 7)", "p7_ans": "Associative Property of Multiplication", "p7_ver": "v0", "p8_prob": "(q + y) \\times p = (y + q) \\times p", "p8_ans": "Commutative Property of Addition", "p8_ver": "vA", "p9_prob": "7 \\times 0 + 6 = 0 \\times 7 + 6", "p9_ans": "Commutative Property of Multiplication", "p9_ver": "vC", "p10_prob": "19 \\times 0 \\times 15 = 19 \\times 0", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0000"}}, {"seed": 1, "data": {"p1_prob": "(19 \\times 11) \\times 3 - 2 = 19 \\times (11 \\times 3) - 2", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "7 \\times (21 - 5) = (21 - 5) \\times 7", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vB", "p3_prob": "(6 \\times 3) \\times 13 = 6 \\times (3 \\times 13)", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": "17 + 21 + 8 = 17 + 8 + 21", "p4_ans": "Commutative Property of Addition", "p4_ver": "vC", "p5_prob": "m \\times y + m \\times q + d = m(y + q) + d", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "12 \\times 1 + 18 = 12 + 18", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "k + w \\times u - x \\times u = k + (w - x) \\times u", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "g - (u - j) = g - (u - j + 0) ", "p8_ans": "Identity Property of Addition", "p8_ver": "vB", "p9_prob": "d + (g + q) = (d + g) + q", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "3 - 0 \\times 10 = 3 - 0", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0001"}}, {"seed": 2, "data": {"p1_prob": "5 + 9 = 0 + 5 + 9", "p1_ans": "Identity Property of Addition", "p1_ver": "vA", "p2_prob": "(13 + 18) + 8 = (18 + 13) + 8", "p2_ans": "Commutative Property of Addition", "p2_ver": "vA", "p3_prob": "(g + q) + j + f = g + (q + j) + f", "p3_ans": "Associative Property of Addition", "p3_ver": "v0", "p4_prob": "s \\times (p - a - b) = (p - a - b) \\times s", "p4_ans": "Commutative Property of Multiplication", "p4_ver": "vB", "p5_prob": "0 \\times n - s = 0 - s", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "u \\times c - s \\times c = (u - s) \\times c", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "t(y - w) + m = t \\times y - t \\times w + m", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "36 + 30 = 2(18 + 15)", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "t + s + w = s + t + w", "p9_ans": "Commutative Property of Addition", "p9_ver": "vC", "p10_prob": "s + (p + a) + b = (s + p) + a + b", "p10_ans": "Associative Property of Addition", "p10_ver": "v0", "__seed__": "0002"}}, {"seed": 3, "data": {"p1_prob": "20 + (5 + 8) + 3 = (20 + 5) + 8 + 3", "p1_ans": "Associative Property of Addition", "p1_ver": "v0", "p2_prob": "19 \\times 0 = 19 \\times 0 \\times 10", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "g - d \\times 0 = g - 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "p + (t + k + 0) = p + (t + k) ", "p4_ans": "Identity Property of Addition", "p4_ver": "vB", "p5_prob": "z(s + r) = z \\times s + z \\times r", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "(x + f) \\times d = d \\times (x + f)", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vB", "p7_prob": "v = v \\times 1", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vA", "p8_prob": "u + 0 = u + 0 \\times q", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "(x + p) - y = (p + x) - y", "p9_ans": "Commutative Property of Addition", "p9_ver": "vA", "p10_prob": "v \\times k - v \\times j = v(k - j)", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0003"}}, {"seed": 4, "data": {"p1_prob": "36 - 216 = (3 - 18) \\times 12", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "(z + k) + s = z + (k + s)", "p2_ans": "Associative Property of Addition", "p2_ver": "v0", "p3_prob": "y \\times b \\times m = b \\times y \\times m", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vC", "p4_prob": "16 \\times (0 \\times 19) = (16 \\times 0) \\times 19", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "91 + 39 = 13(7 + 3)", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "y + (g + c) = (g + c) + y", "p6_ans": "Commutative Property of Addition", "p6_ver": "vB", "p7_prob": "0 = 0 \\times 17", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "c - (q \\times y) = c - (y \\times q)", "p8_ans": "Commutative Property of Multiplication", "p8_ver": "vA", "p9_prob": "19 \\times (20 \\times 8) \\times 12 = 19 \\times 20 \\times (8 \\times 12)", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "r = 0 + r", "p10_ans": "Identity Property of Addition", "p10_ver": "vA", "__seed__": "0004"}}, {"seed": 5, "data": {"p1_prob": "13 + (9 + 19) = (9 + 19) + 13", "p1_ans": "Commutative Property of Addition", "p1_ver": "vB", "p2_prob": "(21 + 2) - 13 = (2 + 21) - 13", "p2_ans": "Commutative Property of Addition", "p2_ver": "vA", "p3_prob": "0 + u = 0 \\times w + u", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "(16 + 21) + 2 + 19 = 16 + (21 + 2) + 19", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "n + v = 0 + n + v", "p5_ans": "Identity Property of Addition", "p5_ver": "vA", "p6_prob": "0 \\times 7 + 4 = 7 \\times 0 + 4", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vC", "p7_prob": "13 - 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(19 - 22 + 0) = 18 - (19 - 22) ", "p3_ans": "Identity Property of Addition", "p3_ver": "vB", "p4_prob": "21 + (17 + 0) + 1 = 21 + 17 + (0 + 1)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "7(18 - 17) = 126 - 119", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "22 \\times (14 + 19) = 22 \\times (19 + 14)", "p6_ans": "Commutative Property of Addition", "p6_ver": "vA", "p7_prob": "0 = 0 \\times m", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "0 \\times j = 0", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "k \\times c - h \\times c = (k - h) \\times c", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "0 \\times z = j \\times 0 \\times z", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0994"}}, {"seed": 995, "data": {"p1_prob": "0 \\times 5 \\times 2 = 0 \\times 2", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "(g \\times u) \\times w \\times v = g \\times (u \\times w) \\times v", "p2_ans": "Associative Property of Multiplication", "p2_ver": "v0", "p3_prob": "0 \\times g = h \\times 0 \\times g", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "s - (q + x) = s - (x + q)", "p4_ans": "Commutative Property of Addition", "p4_ver": "vA", "p5_prob": "t + (q + j) = (q + j) + t", "p5_ans": "Commutative Property of Addition", "p5_ver": "vB", "p6_prob": " (b + x) + p = (b + 1 \\times x) + p", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vB", "p7_prob": "5 + 105 + 133 = 5 + (15 + 19) \\times 7", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "21 - 0 = 21 - 0 \\times 16", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "8 - 4 \\times (13 \\times 1) = 8 - (4 \\times 13) \\times 1", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "h \\times (x \\times s) = (h \\times x) \\times s", "p10_ans": "Associative Property of Multiplication", "p10_ver": "v0", "__seed__": "0995"}}, {"seed": 996, "data": {"p1_prob": "(22 \\times 11) \\times 19 = 19 \\times (22 \\times 11)", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vB", "p2_prob": "h + 0 - c = h - c", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "0 - 19 = 13 \\times 0 - 19", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "w + v + (g + b) = w + (v + g) + b", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "j + 0 = j + 0 \\times p", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "t + b \\times v - n \\times v = t + (b - n) \\times v", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "(y + a) - n = (a + y) - n", "p7_ans": "Commutative Property of Addition", "p7_ver": "vA", "p8_prob": "21 \\times 13 \\times (5 \\times 19) = 21 \\times (13 \\times 5) \\times 19", "p8_ans": "Associative Property of Multiplication", "p8_ver": "v0", "p9_prob": "1 \\times (15 \\times 7) + 21 = (1 \\times 15) \\times 7 + 21", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "z + b + k = z + k + b", "p10_ans": "Commutative Property of Addition", "p10_ver": "vC", "__seed__": "0996"}}, {"seed": 997, "data": {"p1_prob": "r + h \\times 0 = r + 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "a + t = 0 + a + t", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "(a + p) \\times b = b \\times (a + p)", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vB", "p4_prob": "24 + 28 + 2 = 4(6 + 7) + 2", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "14 + 126 - 60 = 14 + 6(21 - 10)", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "0 = 14 \\times 0", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "v - m \\times w = v - w \\times m", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vC", "p8_prob": "9 \\times 0 - 22 = 0 - 22", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "20 + (14 + 9) + 12 = (20 + 14) + 9 + 12", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "(p + m) + j + z = p + (m + j) + z", "p10_ans": "Associative Property of Addition", "p10_ver": "v0", "__seed__": "0997"}}, {"seed": 998, "data": {"p1_prob": "12 + 48 + 24 = 12 + (8 + 4) \\times 6", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": " (0 + 20 + 3) + 9 = (20 + 3) + 9", "p2_ans": "Identity Property of Addition", "p2_ver": "vB", "p3_prob": "22 + (12 \\times 14) \\times 16 = 22 + 12 \\times (14 \\times 16)", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": "(8 \\times 0) \\times 14 = 8 \\times (0 \\times 14)", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "(10 - 11) \\times 8 + 5 = 80 - 88 + 5", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "18 + 12 \\times 0 = 18 + 0", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "0 \\times m = 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "d - z = d - 1 \\times z", "p8_ans": "Identity Property of Multiplication", "p8_ver": "vA", "p9_prob": "(y + z + w) \\times u = u \\times (y + z + w)", "p9_ans": "Commutative Property of Multiplication", "p9_ver": "vB", "p10_prob": "z + u + y = u + z + y", "p10_ans": "Commutative Property of Addition", "p10_ver": "vC", "__seed__": "0998"}}, {"seed": 999, "data": {"p1_prob": "17 + (18 + 12) \\times 16 = 17 + 288 + 192", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "q + (c + s) = q + (s + c)", "p2_ans": "Commutative Property of Addition", "p2_ver": "vA", "p3_prob": "n + t \\times f - x \\times f = n + (t - x) \\times f", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "b \\times s - n \\times s + w = (b - n) \\times s + w", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "a - (1 \\times h) = a - (h) ", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vB", "p6_prob": "1 \\times 3 = 3", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "(11 \\times 14) \\times 0 = 11 \\times (14 \\times 0)", "p7_ans": "Associative Property of Multiplication", "p7_ver": "v0", "p8_prob": "10 \\times 0 = 0", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "p \\times 0 = 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "h \\times 0 + x = 0 + x", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0999"}}]}, {"title": "Base-b Multiplication Algorithms", "slug": "W5", "description": "\n I can compute multiplication of multi-digit base-b whole numbers using non-standard multiplication algorithms.\n ", "template": "\n\n \n

Compute each of the following using the stated algorithm. You must show all calculations in the desired base, and not by converting between bases.

\n
\n \n \n

{{base_ten_prob}} ({{base_ten_alg}})

\n
\n \n

{{base_ten_ans}}

\n
\n
\n \n \n

{{base_b_prob}} ({{base_b_alg}})

\n
\n \n

{{base_b_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"base_ten_prob": "4556 \\times 342", "base_ten_alg": "Lattice", "base_ten_ans": "1558152", "base_b_prob": "333_\\text{four} \\times 33_\\text{four}", "base_b_alg": "Partial Sums", "base_b_ans": "32301_\\text{four}", "base_b_base": "4", "__seed__": "0000"}}, {"seed": 1, "data": {"base_ten_prob": "8728 \\times 79", "base_ten_alg": "Partial Sums", "base_ten_ans": "689512", "base_b_prob": "387_\\text{nine} \\times 35_\\text{nine}", "base_b_alg": "Lattice", "base_b_ans": "15118_\\text{nine}", "base_b_base": "9", "__seed__": "0001"}}, {"seed": 2, "data": {"base_ten_prob": "6233 \\times 884", "base_ten_alg": "Partial Sums", "base_ten_ans": "5509972", "base_b_prob": "534_\\text{seven} \\times 55_\\text{seven}", "base_b_alg": "Lattice", "base_b_ans": "43326_\\text{seven}", "base_b_base": "7", "__seed__": "0002"}}, {"seed": 3, "data": {"base_ten_prob": "7858 \\times 89", "base_ten_alg": "Partial Sums", "base_ten_ans": "699362", "base_b_prob": 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{"base_ten_prob": "865 \\times 52", "base_ten_alg": "Lattice", "base_ten_ans": "44980", "base_b_prob": "64_\\text{nine} \\times 33_\\text{nine}", "base_b_alg": "Partial Sums", "base_b_ans": "2343_\\text{nine}", "base_b_base": "9", "__seed__": "0007"}}, {"seed": 8, "data": {"base_ten_prob": "3886 \\times 557", "base_ten_alg": "Partial Sums", "base_ten_ans": "2164502", "base_b_prob": "8767_\\text{nine} \\times 76_\\text{nine}", "base_b_alg": "Lattice", "base_b_ans": "748386_\\text{nine}", "base_b_base": "9", "__seed__": "0008"}}, {"seed": 9, "data": {"base_ten_prob": "954 \\times 52", "base_ten_alg": "Partial Sums", "base_ten_ans": "49608", "base_b_prob": "425_\\text{six} \\times 34_\\text{six}", "base_b_alg": "Lattice", "base_b_ans": "24222_\\text{six}", "base_b_base": "6", "__seed__": "0009"}}, {"seed": 10, "data": {"base_ten_prob": "9489 \\times 788", "base_ten_alg": "Lattice", "base_ten_ans": "7477332", "base_b_prob": "78_\\text{nine} \\times 47_\\text{nine}", "base_b_alg": "Partial 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25, "data": {"base_ten_prob": "5649 \\times 26", "base_ten_alg": "Lattice", "base_ten_ans": "146874", "base_b_prob": "66_\\text{seven} \\times 26_\\text{seven}", "base_b_alg": "Partial Sums", "base_b_ans": "2541_\\text{seven}", "base_b_base": "7", "__seed__": "0025"}}, {"seed": 26, "data": {"base_ten_prob": "7286 \\times 436", "base_ten_alg": "Partial Sums", "base_ten_ans": "3176696", "base_b_prob": "444_\\text{five} \\times 34_\\text{five}", "base_b_alg": "Lattice", "base_b_ans": "33411_\\text{five}", "base_b_base": "5", "__seed__": "0026"}}, {"seed": 27, "data": {"base_ten_prob": "876 \\times 99", "base_ten_alg": "Lattice", "base_ten_ans": "86724", "base_b_prob": "35_\\text{six} \\times 53_\\text{six}", "base_b_alg": "Partial Sums", "base_b_ans": "3303_\\text{six}", "base_b_base": "6", "__seed__": "0027"}}, {"seed": 28, "data": {"base_ten_prob": "7972 \\times 59", "base_ten_alg": "Lattice", "base_ten_ans": "470348", "base_b_prob": "3553_\\text{eight} \\times 632_\\text{eight}", 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{"base_ten_prob": "992 \\times 62", "base_ten_alg": "Partial Sums", "base_ten_ans": "61504", "base_b_prob": "4467_\\text{eight} \\times 22_\\text{eight}", "base_b_alg": "Lattice", "base_b_ans": "122736_\\text{eight}", "base_b_base": "8", "__seed__": "0976"}}, {"seed": 977, "data": {"base_ten_prob": "9275 \\times 233", "base_ten_alg": "Lattice", "base_ten_ans": "2161075", "base_b_prob": "6423_\\text{seven} \\times 56_\\text{seven}", "base_b_alg": "Partial Sums", "base_b_ans": "535314_\\text{seven}", "base_b_base": "7", "__seed__": "0977"}}, {"seed": 978, "data": {"base_ten_prob": "38 \\times 23", "base_ten_alg": "Partial Sums", "base_ten_ans": "874", "base_b_prob": "436_\\text{seven} \\times 33_\\text{seven}", "base_b_alg": "Lattice", "base_b_ans": "21414_\\text{seven}", "base_b_base": "7", "__seed__": "0978"}}, {"seed": 979, "data": {"base_ten_prob": "455 \\times 42", "base_ten_alg": "Partial Sums", "base_ten_ans": "19110", "base_b_prob": "7736_\\text{nine} \\times 57_\\text{nine}", 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"base_b_base": "8", "__seed__": "0993"}}, {"seed": 994, "data": {"base_ten_prob": "64 \\times 23", "base_ten_alg": "Partial Sums", "base_ten_ans": "1472", "base_b_prob": "2323_\\text{four} \\times 332_\\text{four}", "base_b_alg": "Lattice", "base_b_ans": "2311022_\\text{four}", "base_b_base": "4", "__seed__": "0994"}}, {"seed": 995, "data": {"base_ten_prob": "393 \\times 22", "base_ten_alg": "Lattice", "base_ten_ans": "8646", "base_b_prob": "224_\\text{five} \\times 22_\\text{five}", "base_b_alg": "Partial Sums", "base_b_ans": "11033_\\text{five}", "base_b_base": "5", "__seed__": "0995"}}, {"seed": 996, "data": {"base_ten_prob": "842 \\times 92", "base_ten_alg": "Lattice", "base_ten_ans": "77464", "base_b_prob": "32_\\text{seven} \\times 43_\\text{seven}", "base_b_alg": "Partial Sums", "base_b_ans": "2036_\\text{seven}", "base_b_base": "7", "__seed__": "0996"}}, {"seed": 997, "data": {"base_ten_prob": "4638 \\times 369", "base_ten_alg": "Partial Sums", "base_ten_ans": "1711422", "base_b_prob": "523_\\text{six} \\times 54_\\text{six}", "base_b_alg": "Lattice", "base_b_ans": "50410_\\text{six}", "base_b_base": "6", "__seed__": "0997"}}, {"seed": 998, "data": {"base_ten_prob": "2324 \\times 422", "base_ten_alg": "Lattice", "base_ten_ans": "980728", "base_b_prob": "22_\\text{five} \\times 32_\\text{five}", "base_b_alg": "Partial Sums", "base_b_ans": "1304_\\text{five}", "base_b_base": "5", "__seed__": "0998"}}, {"seed": 999, "data": {"base_ten_prob": "2997 \\times 836", "base_ten_alg": "Partial Sums", "base_ten_ans": "2505492", "base_b_prob": "8346_\\text{nine} \\times 34_\\text{nine}", "base_b_alg": "Lattice", "base_b_ans": "318106_\\text{nine}", "base_b_base": "9", "__seed__": "0999"}}]}, {"title": "Long Division Algorithms", "slug": "W6", "description": "\n I can compute the quotient of two whole or decimal numbers using standard and non-standard algorithms.\n ", "template": "\n\n \n

{{directions}}

\n
\n \n \n

{{div_prob}}

\n
\n \n

{{answer}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"algorithm": "Standard", "answer": "1.407", "directions": "Compute the following quotient. Give your final answer as a decimal. 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There should not be a remainder.", "div_prob": "373,659.9 \\div 63.3", "__seed__": "0753"}}, {"seed": 754, "data": {"algorithm": "Standard", "answer": "8,228 remainder 3", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "3,587,411 \\div 436", "__seed__": "0754"}}, {"seed": 755, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "77,586 remainder 8", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "4,887,926 \\div 63", "__seed__": "0755"}}, {"seed": 756, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "64,225 remainder 5", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "4,046,180 \\div 63", "__seed__": "0756"}}, {"seed": 757, "data": {"algorithm": "Standard", "answer": "16,055", "directions": "Compute the following quotient. 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There should not be a remainder.", "div_prob": "321.056 \\div 790", "__seed__": "0907"}}, {"seed": 908, "data": {"algorithm": "Standard", "answer": "7,644 remainder 433", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "4,326,937 \\div 566", "__seed__": "0908"}}, {"seed": 909, "data": {"algorithm": "Standard", "answer": "92,280 remainder 13", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "7,936,093 \\div 86", "__seed__": "0909"}}, {"seed": 910, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "5,433 remainder 54", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "4,427,949 \\div 815", "__seed__": "0910"}}, {"seed": 911, "data": {"algorithm": "Standard", "answer": "121.8", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "401.94 \\div 3.3", "__seed__": "0911"}}, {"seed": 912, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "24,146 remainder 1", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "1,448,761 \\div 60", "__seed__": "0912"}}, {"seed": 913, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "20,150 remainder 23", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "1,853,823 \\div 92", "__seed__": "0913"}}, {"seed": 914, "data": {"algorithm": "Standard", "answer": "1,807 remainder 622", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "1,178,786 \\div 652", "__seed__": "0914"}}, {"seed": 915, "data": {"algorithm": "Standard", "answer": "2.659", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "7,897.23 \\div 2,970", "__seed__": "0915"}}, {"seed": 916, "data": {"algorithm": "Standard", "answer": "9,613 remainder 354", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "9,536,450 \\div 992", "__seed__": "0916"}}, {"seed": 917, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "5,641 remainder 129", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "2,245,247 \\div 398", "__seed__": "0917"}}, {"seed": 918, "data": {"algorithm": "Standard", "answer": "8,712 remainder 61", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "766,717 \\div 88", "__seed__": "0918"}}, {"seed": 919, "data": {"algorithm": "Standard", "answer": "7,555.7", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "355,117.9 \\div 47", "__seed__": "0919"}}, {"seed": 920, "data": {"algorithm": "Standard", "answer": "51,882 remainder 25", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "2,386,597 \\div 46", "__seed__": "0920"}}, {"seed": 921, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "59,359 remainder 50", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "3,739,667 \\div 63", "__seed__": "0921"}}, {"seed": 922, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "68,411 remainder 10", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "6,772,699 \\div 99", "__seed__": "0922"}}, {"seed": 923, "data": {"algorithm": "Standard", "answer": "5.6261", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "787.654 \\div 140", "__seed__": "0923"}}, {"seed": 924, "data": {"algorithm": "Standard", "answer": "0.83321", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "31.66198 \\div 38", "__seed__": "0924"}}, {"seed": 925, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "55,086 remainder 28", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "2,038,210 \\div 37", "__seed__": "0925"}}, {"seed": 926, "data": {"algorithm": "Standard", "answer": "39,946 remainder 26", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "1,757,650 \\div 44", "__seed__": "0926"}}, {"seed": 927, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "1,956 remainder 0", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "119,316 \\div 61", "__seed__": "0927"}}, {"seed": 928, "data": {"algorithm": "Standard", "answer": "21.067", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "969.082 \\div 46", "__seed__": "0928"}}, {"seed": 929, "data": {"algorithm": "Standard", "answer": "6,992 remainder 91", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "1,342,555 \\div 192", "__seed__": "0929"}}, {"seed": 930, "data": {"algorithm": "Standard", "answer": "56.378", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "411.5594 \\div 7.3", "__seed__": "0930"}}, {"seed": 931, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "4,839 remainder 6", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "251,634 \\div 52", "__seed__": "0931"}}, {"seed": 932, "data": {"algorithm": "Standard", "answer": "90,656 remainder 34", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "5,439,394 \\div 60", "__seed__": "0932"}}, {"seed": 933, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "9,806 remainder 873", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "9,542,111 \\div 973", "__seed__": "0933"}}, {"seed": 934, "data": {"algorithm": "Standard", "answer": "12,155 remainder 18", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "668,543 \\div 55", "__seed__": "0934"}}, {"seed": 935, "data": {"algorithm": "Standard", "answer": "85,137", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "136,219.2 \\div 1.6", "__seed__": "0935"}}, {"seed": 936, "data": {"algorithm": "Standard", "answer": "9,945.4", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "845,359 \\div 85", "__seed__": "0936"}}, {"seed": 937, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "5,860 remainder 764", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "4,512,964 \\div 770", "__seed__": "0937"}}, {"seed": 938, "data": {"algorithm": "Standard", "answer": "2,021 remainder 26", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "139,475 \\div 69", "__seed__": "0938"}}, {"seed": 939, "data": {"algorithm": "Standard", "answer": "2,899", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "376.87 \\div 0.13", "__seed__": "0939"}}, {"seed": 940, "data": {"algorithm": "Standard", "answer": "539.92", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "917.864 \\div 1.7", "__seed__": "0940"}}, {"seed": 941, "data": {"algorithm": "Standard", "answer": "89.21", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "52.6339 \\div 0.59", "__seed__": "0941"}}, {"seed": 942, "data": {"algorithm": "Standard", "answer": "0.2898", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,249.038 \\div 4,310", "__seed__": "0942"}}, {"seed": 943, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "46,323 remainder 20", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "2,177,201 \\div 47", "__seed__": "0943"}}, {"seed": 944, "data": {"algorithm": "Standard", "answer": "9.0006", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,980.132 \\div 220", "__seed__": "0944"}}, {"seed": 945, "data": {"algorithm": "Standard", "answer": "9,583", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,149,960 \\div 120", "__seed__": "0945"}}, {"seed": 946, "data": {"algorithm": "Standard", "answer": "19,245", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,366,395 \\div 71", "__seed__": "0946"}}, {"seed": 947, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "8,775 remainder 16", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "693,241 \\div 79", "__seed__": "0947"}}, {"seed": 948, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "2,107 remainder 208", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "1,245,445 \\div 591", "__seed__": "0948"}}, {"seed": 949, "data": {"algorithm": "Standard", "answer": "2.0093", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "884.092 \\div 440", "__seed__": "0949"}}, {"seed": 950, "data": {"algorithm": "Standard", "answer": "98,613 remainder 12", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "5,423,727 \\div 55", "__seed__": "0950"}}, {"seed": 951, "data": {"algorithm": "Standard", "answer": "537.4", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "112,854 \\div 210", "__seed__": "0951"}}, {"seed": 952, "data": {"algorithm": "Standard", "answer": "42,965 remainder 34", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "2,749,794 \\div 64", "__seed__": "0952"}}, {"seed": 953, "data": {"algorithm": "Standard", "answer": "1.3974", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1.32753 \\div 0.95", "__seed__": "0953"}}, {"seed": 954, "data": {"algorithm": "Standard", "answer": "0.1521", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "31.941 \\div 210", "__seed__": "0954"}}, {"seed": 955, "data": {"algorithm": "Standard", "answer": "7,835 remainder 586", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "7,200,951 \\div 919", "__seed__": "0955"}}, {"seed": 956, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "3,730 remainder 2", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "343,162 \\div 92", "__seed__": "0956"}}, {"seed": 957, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "3,129 remainder 8", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "225,296 \\div 72", "__seed__": "0957"}}, {"seed": 958, "data": {"algorithm": "Standard", "answer": "230", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,879.1 \\div 8.17", "__seed__": "0958"}}, {"seed": 959, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "1,646 remainder 33", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "75,749 \\div 46", "__seed__": "0959"}}, {"seed": 960, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "8,748 remainder 307", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "4,173,103 \\div 477", "__seed__": "0960"}}, {"seed": 961, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "8,504 remainder 13", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "8,010,781 \\div 942", "__seed__": "0961"}}, {"seed": 962, "data": {"algorithm": "Standard", "answer": "94,403 remainder 25", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "4,248,160 \\div 45", "__seed__": "0962"}}, {"seed": 963, "data": {"algorithm": "Standard", "answer": "0.9186", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1.65348 \\div 1.8", "__seed__": "0963"}}, {"seed": 964, "data": {"algorithm": "Standard", "answer": "54.101", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "20,558.38 \\div 380", "__seed__": "0964"}}, {"seed": 965, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "5,893 remainder 20", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "182,703 \\div 31", "__seed__": "0965"}}, {"seed": 966, "data": {"algorithm": "Standard", "answer": "9,255 remainder 76", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "860,791 \\div 93", "__seed__": "0966"}}, {"seed": 967, "data": {"algorithm": "Standard", "answer": "5,466 remainder 20", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "202,262 \\div 37", "__seed__": "0967"}}, {"seed": 968, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "87,608 remainder 61", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "6,745,877 \\div 77", "__seed__": "0968"}}, {"seed": 969, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "6,248 remainder 271", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "4,523,823 \\div 724", "__seed__": "0969"}}, {"seed": 970, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "9,593 remainder 43", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "815,448 \\div 85", "__seed__": "0970"}}, {"seed": 971, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "55,214 remainder 8", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "5,024,482 \\div 91", "__seed__": "0971"}}, {"seed": 972, "data": {"algorithm": "Standard", "answer": "21.85", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,201.75 \\div 55", "__seed__": "0972"}}, {"seed": 973, "data": {"algorithm": "Standard", "answer": "585.7", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "37,484.8 \\div 64", "__seed__": "0973"}}, {"seed": 974, "data": {"algorithm": "Standard", "answer": "64,669", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "34,921,260 \\div 540", "__seed__": "0974"}}, {"seed": 975, "data": {"algorithm": "Standard", "answer": "5.617", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "19.54716 \\div 3.48", "__seed__": "0975"}}, {"seed": 976, "data": {"algorithm": "Standard", "answer": "767.4", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "26,091.6 \\div 34", "__seed__": "0976"}}, {"seed": 977, "data": {"algorithm": "Standard", "answer": "7,539", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "624,229.2 \\div 82.8", "__seed__": "0977"}}, {"seed": 978, "data": {"algorithm": "Standard", "answer": "0.12637", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "0.859316 \\div 6.8", "__seed__": "0978"}}, {"seed": 979, "data": {"algorithm": "Standard", "answer": "81.386", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "36,623.7 \\div 450", "__seed__": "0979"}}, {"seed": 980, "data": {"algorithm": "Standard", "answer": "0.24408", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "18.306 \\div 75", "__seed__": "0980"}}, {"seed": 981, "data": {"algorithm": "Standard", "answer": "8,890 remainder 0", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "160,020 \\div 18", "__seed__": "0981"}}, {"seed": 982, "data": {"algorithm": "Standard", "answer": "747.82", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "358.9536 \\div 0.48", "__seed__": "0982"}}, {"seed": 983, "data": {"algorithm": "Standard", "answer": "1,585 remainder 10", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "30,125 \\div 19", "__seed__": "0983"}}, {"seed": 984, "data": {"algorithm": "Standard", "answer": "4,537 remainder 107", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "3,797,576 \\div 837", "__seed__": "0984"}}, {"seed": 985, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "2,139 remainder 246", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "1,251,561 \\div 585", "__seed__": "0985"}}, {"seed": 986, "data": {"algorithm": "Standard", "answer": "2,563.5", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,333.02 \\div 0.52", "__seed__": "0986"}}, {"seed": 987, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "22,255 remainder 10", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "489,620 \\div 22", "__seed__": "0987"}}, {"seed": 988, "data": {"algorithm": "Standard", "answer": "55.176", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "209.6688 \\div 3.8", "__seed__": "0988"}}, {"seed": 989, "data": {"algorithm": "Standard", "answer": "3.6993", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "192.3636 \\div 52", "__seed__": "0989"}}, {"seed": 990, "data": {"algorithm": "Standard", "answer": "273.68", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,094.72 \\div 4", "__seed__": "0990"}}, {"seed": 991, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "37,280 remainder 47", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "2,945,167 \\div 79", "__seed__": "0991"}}, {"seed": 992, "data": {"algorithm": "Standard", "answer": "5.574", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "33,722.7 \\div 6,050", "__seed__": "0992"}}, {"seed": 993, "data": {"algorithm": "Standard", "answer": "32,826 remainder 38", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "3,184,160 \\div 97", "__seed__": "0993"}}, {"seed": 994, "data": {"algorithm": "Standard", "answer": "0.1274", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "8.918 \\div 70", "__seed__": "0994"}}, {"seed": 995, "data": {"algorithm": "Standard", "answer": "0.2564", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "789.712 \\div 3,080", "__seed__": "0995"}}, {"seed": 996, "data": {"algorithm": "Standard", "answer": "92,442 remainder 21", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "4,159,911 \\div 45", "__seed__": "0996"}}, {"seed": 997, "data": {"algorithm": "Standard", "answer": "1,458", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "5,103 \\div 3.5", "__seed__": "0997"}}, {"seed": 998, "data": {"algorithm": "Standard", "answer": "12.769", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,659.97 \\div 130", "__seed__": "0998"}}, {"seed": 999, "data": {"algorithm": "Standard", "answer": "0.1769", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "0.72529 \\div 4.1", "__seed__": "0999"}}]}, {"title": "Divisibility Statements", "slug": "N1", "description": "\n I can identify divisibility statements as true or false.\n ", "template": "\n\n \n

Determine if each of the statements below is true or false.

\n
\n \n \n

{{p1_prob}}

\n
\n \n

{{p1_ans}}

\n
\n
\n \n \n

{{p2_prob}}

\n
\n \n

{{p2_ans}}

\n
\n
\n \n \n

{{p3_prob}}

\n
\n \n

{{p3_ans}}

\n
\n
\n \n \n

{{p4_prob}}

\n
\n \n

{{p4_ans}}

\n
\n
\n \n \n

{{p5_prob}}

\n
\n \n

{{p5_ans}}

\n
\n
\n \n \n

{{p6_prob}}

\n
\n \n

{{p6_ans}}

\n
\n
\n \n \n

{{p7_prob}}

\n
\n \n

{{p7_ans}}

\n
\n
\n \n \n

{{p8_prob}}

\n
\n \n

{{p8_ans}}

\n
\n
\n \n \n

{{p9_prob}}

\n
\n \n

{{p9_ans}}

\n
\n
\n \n \n

{{p10_prob}}

\n
\n \n

{{p10_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"p1_prob": "4 \\times (21 \\times 1) + 8 = (4 \\times 21) \\times 1 + 8", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "(9 \\times 11) \\times 12 = 9 \\times (11 \\times 12)", "p2_ans": "Associative Property of Multiplication", "p2_ver": "v0", "p3_prob": "6 \\times 0 = 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "22(6 - 5) = 132 - 110", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "s \\times 0 = s \\times 0 \\times m", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "(12 + 2) + 5 = 12 + (2 + 5)", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "(10 - 22 - 0) + (9 - 7) = (9 - 7) + (10 - 22 - 0)", "p7_ans": "Commutative Property of Addition", "p7_ver": "vB", "p8_prob": "(0 + 11) - 9 = (11 + 0) - 9", "p8_ans": "Commutative Property of Addition", "p8_ver": "vA", "p9_prob": "(f - h) \\times v + z = f \\times v - h \\times v + z", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "16 = 16 \\times 1", "p10_ans": "Identity Property of Multiplication", "p10_ver": "vA", "__seed__": "0000"}}, {"seed": 1, "data": {"p1_prob": "19 + 33 - 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162 + 21 = (22 - 18) \\times 9 + 21", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": " (n + 0 + b) + d = (n + b) + d", "p8_ans": "Identity Property of Addition", "p8_ver": "vB", "p9_prob": "15 \\times (2 + 20) = 15 \\times (20 + 2)", "p9_ans": "Commutative Property of Addition", "p9_ver": "vA", "p10_prob": "0 \\times j \\times s = 0 \\times s", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0986"}}, {"seed": 987, "data": {"p1_prob": "(r \\times d) \\times m = r \\times (d \\times m)", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "x - (a \\times d) = x - (d \\times a)", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vA", "p3_prob": "b + f = f + b", "p3_ans": "Commutative Property of Addition", "p3_ver": "vC", "p4_prob": "(w + v) \\times (f + k) = (f + k) \\times (w + v)", "p4_ans": "Commutative Property of Multiplication", "p4_ver": "vB", "p5_prob": "(10 + 21) + 22 = 10 + (21 + 22)", "p5_ans": "Associative Property of Addition", "p5_ver": "v0", "p6_prob": "p \\times k - p \\times j + c = p(k - j) + c", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": " (s \\times j \\times 1) \\times w = (s \\times j) \\times w", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vB", "p8_prob": "0 = u \\times 0", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "0 \\times 21 - 15 = 0 - 15", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "0 \\times x = g \\times 0 \\times x", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0987"}}, {"seed": 988, "data": {"p1_prob": "(4 \\times 5) \\times 16 - 8 = 4 \\times (5 \\times 16) - 8", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "s - (q - u \\times 1) = s - (q - u) ", "p2_ans": "Identity Property of Multiplication", "p2_ver": "vB", "p3_prob": "j + 0 = j + 0 \\times f", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "7 \\times (1 \\times 10 \\times 18) = 7 \\times (10 \\times 18) ", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vB", "p5_prob": "h + y + c = y + h + c", "p5_ans": "Commutative Property of Addition", "p5_ver": "vC", "p6_prob": "s - z = s - z \\times 1", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "0 = 0 \\times y", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "x(c + p) = x \\times c + x \\times p", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "0 \\times v + r = 0 + r", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "132 + 72 + 18 = 12(11 + 6) + 18", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0988"}}, {"seed": 989, "data": {"p1_prob": "91 - 156 + 14 = (7 - 12) \\times 13 + 14", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "(n + j) \\times v = n \\times v + j \\times v", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "11 = 0 + 11", "p3_ans": "Identity Property of Addition", "p3_ver": "vA", "p4_prob": "252 - 357 = 21(12 - 17)", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "m - 0 = m - 0 \\times b", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": " (0 + w + z) + p = (w + z) + p", "p6_ans": "Identity Property of Addition", "p6_ver": "vB", "p7_prob": "x + (n \\times c) = (n \\times c) + x", "p7_ans": "Commutative Property of Addition", "p7_ver": "vB", "p8_prob": "0 + 21 + 6 = 21 + 0 + 6", "p8_ans": "Commutative Property of Addition", "p8_ver": "vC", "p9_prob": "5 + (13 + 1) + 16 = (5 + 13) + 1 + 16", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "11 + (10 \\times 18) + 0 = 11 + (18 \\times 10) + 0", "p10_ans": "Commutative Property of Multiplication", "p10_ver": "vA", "__seed__": "0989"}}, {"seed": 990, "data": {"p1_prob": "v \\times f = f \\times v", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vC", "p2_prob": "1 \\times (22 \\times 4) \\times 0 = 1 \\times (4 \\times 22) \\times 0", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vA", "p3_prob": "2 + 7 + (19 + 18) = 2 + (7 + 19) + 18", "p3_ans": "Associative Property of Addition", "p3_ver": "v0", "p4_prob": "0 = 0 \\times g", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": "12 + 0 + (15 + 17) = 12 + (0 + 15) + 17", "p5_ans": "Associative Property of Addition", "p5_ver": "v0", "p6_prob": "16 - (15 - 21) = 16 - (15 + 0 - 21) ", "p6_ans": "Identity Property of Addition", "p6_ver": "vB", "p7_prob": "u \\times d \\times 1 = u \\times d", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vA", "p8_prob": "5 + 15(18 - 9) = 5 + 270 - 135", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "0 - 22 = 0 \\times 18 - 22", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "0 - a = 0 \\times f - a", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0990"}}, {"seed": 991, "data": {"p1_prob": "q \\times h \\times (n \\times k) = q \\times (h \\times n) \\times k", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "0 \\times 5 \\times 14 = 0 \\times 14", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "105 + 270 + 11 = 15(7 + 18) + 11", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "0 \\times q \\times r = 0 \\times r", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": "12 \\times (4 + 9) \\times 21 = 12 \\times (9 + 4) \\times 21", "p5_ans": "Commutative Property of Addition", "p5_ver": "vA", "p6_prob": "(15 + 20) + 21 + 3 = 15 + (20 + 21) + 3", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "14 - 19 \\times 1 = 14 - 19", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vA", "p8_prob": "3 + 9 + 15 = 3 + 15 + 9", "p8_ans": "Commutative Property of Addition", "p8_ver": "vC", "p9_prob": "7 + 374 + 68 = 7 + (22 + 4) \\times 17", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "0 \\times 14 - 20 = 0 - 20", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0991"}}, {"seed": 992, "data": {"p1_prob": "10 + 0 \\times 12 = 10 + 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "x + (g \\times f) + m = x + (f \\times g) + m", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vA", "p3_prob": "64 + 76 + 17 = (16 + 19) \\times 4 + 17", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "(m + f) + x = m + (f + x)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "5 \\times (7) = 5 \\times (1 \\times 7) ", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vB", "p6_prob": "v + w = v \\times 1 + w", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "22 + 216 + 360 = 22 + (12 + 20) \\times 18", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "18 - 0 + 2 = 18 - 2", "p8_ans": "Identity Property of Addition", "p8_ver": "vA", "p9_prob": "0 + 6 = 0 \\times 3 + 6", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "(q - z) \\times m = q \\times m - z \\times m", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0992"}}, {"seed": 993, "data": {"p1_prob": "j + (w - y) \\times t = j + w \\times t - y \\times t", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "2 + 11 + 0 = 2 + 11", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "0 = f \\times 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "14 + (21 + 2) + 16 = 14 + 21 + (2 + 16)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "c + x \\times h + t \\times h = c + (x + t) \\times h", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "g + n + (b + t) = g + (n + b) + t", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "7 - 0 \\times 14 = 7 - 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "r + a = a + r", "p8_ans": "Commutative Property of Addition", "p8_ver": "vC", "p9_prob": "c + 0 \\times u = c + 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "3(9 + 11) = 27 + 33", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0993"}}, {"seed": 994, "data": {"p1_prob": "g - h = g + 0 - h", "p1_ans": "Identity Property of Addition", "p1_ver": "vA", "p2_prob": "(15 - 18) \\times 12 + 20 = 180 - 216 + 20", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "1 \\times (11 \\times 20) - 14 = (1 \\times 11) \\times 20 - 14", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": "0 \\times 22 = 0 \\times 10 \\times 22", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": " (0 + j) - b = (j) - b", "p5_ans": "Identity Property of Addition", "p5_ver": "vB", "p6_prob": "u \\times (f + d + v) = (f + d + v) \\times u", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vB", "p7_prob": "d - u \\times 0 = d - 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "z \\times w - t \\times w = (z - t) \\times w", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "g + w \\times 0 = g + 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "2(20 + 5) = 40 + 10", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0994"}}, {"seed": 995, "data": {"p1_prob": "7(3 - 13) + 17 = 21 - 91 + 17", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "0 \\times 13 = 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "22 + 0 = 22 + 21 \\times 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "d = 1 \\times d", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vA", "p5_prob": " (6 \\times 1 - 19) - 21 = (6 - 19) - 21", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vB", "p6_prob": "v \\times s = s \\times v", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vC", "p7_prob": "(y + u) + b + s = y + (u + b) + s", "p7_ans": "Associative Property of Addition", "p7_ver": "v0", "p8_prob": "2 + 7(18 - 13) = 2 + 126 - 91", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "13 - 4 = 13 - 4 + 0", "p9_ans": "Identity Property of Addition", "p9_ver": "vA", "p10_prob": "f + g \\times a - z \\times a = f + (g - z) \\times a", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0995"}}, {"seed": 996, "data": {"p1_prob": "u \\times d \\times (p \\times y) = u \\times (d \\times p) \\times y", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "m(z - f) + j = m \\times z - m \\times f + j", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "(11 \\times 5) \\times 3 = 3 \\times (11 \\times 5)", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vB", "p4_prob": "w + k(a - f) = w + k \\times a - k \\times f", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "y \\times (m \\times z) = (y \\times m) \\times z", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "w \\times k - w \\times y = w(k - y)", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "0 \\times 18 = 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "c + (w + q) = c + (w + q \\times 1) ", "p8_ans": "Identity Property of Multiplication", "p8_ver": "vB", "p9_prob": "(5 \\times 8) \\times 18 = 5 \\times (8 \\times 18)", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "1 \\times 5 - 8 = 5 - 8", "p10_ans": "Identity Property of Multiplication", "p10_ver": "vA", "__seed__": "0996"}}, {"seed": 997, "data": {"p1_prob": "5 + (9 - 15) \\times 14 = 5 + 126 - 210", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "4 + 10 = 1 \\times 4 + 10", "p2_ans": "Identity Property of Multiplication", "p2_ver": "vA", "p3_prob": "(12 \\times 7) \\times 15 = (7 \\times 12) \\times 15", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vA", "p4_prob": "(p - z) \\times g + d = p \\times g - z \\times g + d", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "(0 \\times 19) \\times 12 - 20 = 0 \\times (19 \\times 12) - 20", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "(c + n) + r + g = c + (n + r) + g", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "0 - 5 = 0 \\times 14 - 5", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "x = x \\times 1", "p8_ans": "Identity Property of Multiplication", "p8_ver": "vA", "p9_prob": " (7 - 9) - 21 = (7 + 0 - 9) - 21", "p9_ans": "Identity Property of Addition", "p9_ver": "vB", "p10_prob": "u \\times 0 = 0", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0997"}}, {"seed": 998, "data": {"p1_prob": "210 - 120 + 20 = (14 - 8) \\times 15 + 20", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "21 - (14 \\times 13) \\times 7 = 21 - 14 \\times (13 \\times 7)", "p2_ans": "Associative Property of Multiplication", "p2_ver": "v0", "p3_prob": " (4 + 14) + 13 = (0 + 4 + 14) + 13", "p3_ans": "Identity Property of Addition", "p3_ver": "vB", "p4_prob": "11 + 221 + 39 = 11 + (17 + 3) \\times 13", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "(2 \\times 0) \\times 4 = 2 \\times (0 \\times 4)", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "0 + 8 = 0 \\times 21 + 8", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "(k - n) + p = p + (k - n)", "p7_ans": "Commutative Property of Addition", "p7_ver": "vB", "p8_prob": "m + (w + d) + n = (m + w) + d + n", "p8_ans": "Associative Property of Addition", "p8_ver": "v0", "p9_prob": "21(4 - 5) = 84 - 105", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "0 \\times x \\times z = 0 \\times z", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0998"}}, {"seed": 999, "data": {"p1_prob": "g = g + 0", "p1_ans": "Identity Property of Addition", "p1_ver": "vA", "p2_prob": "c + (n + a) + b = c + n + (a + b)", "p2_ans": "Associative Property of Addition", "p2_ver": "v0", "p3_prob": "1 + (19 + 8) + 11 = 1 + (8 + 19) + 11", "p3_ans": "Commutative Property of Addition", "p3_ver": "vA", "p4_prob": "6 - (19) = 6 - (19 \\times 1) ", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vB", "p5_prob": "s - 0 = s - t \\times 0", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "(10 - 6) \\times 21 = 210 - 126", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "x \\times z + s = z \\times x + s", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vC", "p8_prob": "c(j - v) = c \\times j - c \\times v", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "(u \\times m \\times y) + w = w + (u \\times m \\times y)", "p9_ans": "Commutative Property of Addition", "p9_ver": "vB", "p10_prob": "5 + 170 + 119 = 5 + 17(10 + 7)", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0999"}}]}, {"title": "Testing for Prime or Not Prime", "slug": "N2", "description": "\n I can determine if a number is prime or composite via the prime testing method.\n ", "template": "\n\n \n

Determine if the number below is prime or composite. If it is prime, you must show all work from our prime testing method. If it is composite, you must defend your answer with the appropriate work and/or explanation.

\n
\n \n \n

{{the_number}}

\n
\n \n

{{answer}}

\n

{{quotients_and_remainders}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0000"}}, {"seed": 1, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0001"}}, {"seed": 2, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0002"}}, {"seed": 3, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0003"}}, {"seed": 4, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0004"}}, {"seed": 5, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0005"}}, {"seed": 6, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0006"}}, {"seed": 7, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0007"}}, {"seed": 8, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0008"}}, {"seed": 9, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0009"}}, {"seed": 10, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0010"}}, {"seed": 11, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0011"}}, {"seed": 12, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0012"}}, {"seed": 13, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0013"}}, {"seed": 14, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0014"}}, {"seed": 15, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0015"}}, {"seed": 16, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0016"}}, {"seed": 17, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0017"}}, {"seed": 18, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0018"}}, {"seed": 19, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0019"}}, {"seed": 20, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0020"}}, {"seed": 21, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0021"}}, {"seed": 22, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0022"}}, {"seed": 23, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0023"}}, {"seed": 24, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0024"}}, {"seed": 25, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0025"}}, {"seed": 26, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0026"}}, {"seed": 27, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0027"}}, {"seed": 28, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0028"}}, {"seed": 29, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0029"}}, {"seed": 30, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0030"}}, {"seed": 31, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0031"}}, {"seed": 32, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0032"}}, {"seed": 33, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0033"}}, {"seed": 34, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0034"}}, {"seed": 35, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0035"}}, {"seed": 36, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0036"}}, {"seed": 37, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0037"}}, {"seed": 38, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0038"}}, {"seed": 39, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0039"}}, {"seed": 40, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0040"}}, {"seed": 41, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0041"}}, {"seed": 42, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0042"}}, {"seed": 43, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0043"}}, {"seed": 44, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0044"}}, {"seed": 45, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0045"}}, {"seed": 46, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0046"}}, {"seed": 47, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0047"}}, {"seed": 48, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0048"}}, {"seed": 49, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0049"}}, {"seed": 50, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0050"}}, {"seed": 51, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0051"}}, {"seed": 52, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0052"}}, {"seed": 53, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0053"}}, {"seed": 54, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0054"}}, {"seed": 55, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0055"}}, {"seed": 56, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0056"}}, {"seed": 57, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0057"}}, {"seed": 58, "data": {"the_number": "319", "answer": "The number 319 is composite. We already know that 319 has two divisors: 1 and 319. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 18 = 29, so 11 is a factor of 319. Thus 319 has at least three divisors (1, 11, and 319), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "319 \\div 2 = 159 \\text{ remainder } 1 \\\\ 319 \\div 3 = 106 \\text{ remainder } 1 \\\\ 319 \\div 5 = 63 \\text{ remainder } 4 \\\\ 319 \\div 7 = 45 \\text{ remainder } 4 \\\\ 319 \\div 11 = 29 \\\\ 319 \\div 13 = 24 \\text{ remainder } 7 \\\\ 319 \\div 17 = 18 \\text{ remainder } 13 \\\\ ", "prime_problem": false, "__seed__": "0058"}}, {"seed": 59, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0059"}}, {"seed": 60, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0060"}}, {"seed": 61, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0061"}}, {"seed": 62, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0062"}}, {"seed": 63, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0063"}}, {"seed": 64, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0064"}}, {"seed": 65, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0065"}}, {"seed": 66, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0066"}}, {"seed": 67, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0067"}}, {"seed": 68, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0068"}}, {"seed": 69, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0069"}}, {"seed": 70, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0070"}}, {"seed": 71, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0071"}}, {"seed": 72, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0072"}}, {"seed": 73, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0073"}}, {"seed": 74, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0074"}}, {"seed": 75, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0075"}}, {"seed": 76, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0076"}}, {"seed": 77, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0077"}}, {"seed": 78, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0078"}}, {"seed": 79, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0079"}}, {"seed": 80, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0080"}}, {"seed": 81, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0081"}}, {"seed": 82, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0082"}}, {"seed": 83, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0083"}}, {"seed": 84, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0084"}}, {"seed": 85, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0085"}}, {"seed": 86, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0086"}}, {"seed": 87, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0087"}}, {"seed": 88, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0088"}}, {"seed": 89, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0089"}}, {"seed": 90, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0090"}}, {"seed": 91, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0091"}}, {"seed": 92, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0092"}}, {"seed": 93, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0093"}}, {"seed": 94, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0094"}}, {"seed": 95, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0095"}}, {"seed": 96, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0096"}}, {"seed": 97, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0097"}}, {"seed": 98, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0098"}}, {"seed": 99, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0099"}}, {"seed": 100, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0100"}}, {"seed": 101, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0101"}}, {"seed": 102, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0102"}}, {"seed": 103, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0103"}}, {"seed": 104, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0104"}}, {"seed": 105, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0105"}}, {"seed": 106, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0106"}}, {"seed": 107, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0107"}}, {"seed": 108, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0108"}}, {"seed": 109, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0109"}}, {"seed": 110, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0110"}}, {"seed": 111, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0111"}}, {"seed": 112, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0112"}}, {"seed": 113, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0113"}}, {"seed": 114, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0114"}}, {"seed": 115, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0115"}}, {"seed": 116, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0116"}}, {"seed": 117, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0117"}}, {"seed": 118, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0118"}}, {"seed": 119, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0119"}}, {"seed": 120, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0120"}}, {"seed": 121, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0121"}}, {"seed": 122, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0122"}}, {"seed": 123, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0123"}}, {"seed": 124, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0124"}}, {"seed": 125, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0125"}}, {"seed": 126, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0126"}}, {"seed": 127, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0127"}}, {"seed": 128, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0128"}}, {"seed": 129, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0129"}}, {"seed": 130, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0130"}}, {"seed": 131, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0131"}}, {"seed": 132, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0132"}}, {"seed": 133, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0133"}}, {"seed": 134, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0134"}}, {"seed": 135, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0135"}}, {"seed": 136, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0136"}}, {"seed": 137, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0137"}}, {"seed": 138, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0138"}}, {"seed": 139, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0139"}}, {"seed": 140, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0140"}}, {"seed": 141, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0141"}}, {"seed": 142, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0142"}}, {"seed": 143, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0143"}}, {"seed": 144, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0144"}}, {"seed": 145, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0145"}}, {"seed": 146, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0146"}}, {"seed": 147, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0147"}}, {"seed": 148, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0148"}}, {"seed": 149, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0149"}}, {"seed": 150, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0150"}}, {"seed": 151, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0151"}}, {"seed": 152, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0152"}}, {"seed": 153, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0153"}}, {"seed": 154, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0154"}}, {"seed": 155, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0155"}}, {"seed": 156, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0156"}}, {"seed": 157, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0157"}}, {"seed": 158, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0158"}}, {"seed": 159, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0159"}}, {"seed": 160, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0160"}}, {"seed": 161, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0161"}}, {"seed": 162, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0162"}}, {"seed": 163, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0163"}}, {"seed": 164, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0164"}}, {"seed": 165, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0165"}}, {"seed": 166, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0166"}}, {"seed": 167, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0167"}}, {"seed": 168, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0168"}}, {"seed": 169, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0169"}}, {"seed": 170, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0170"}}, {"seed": 171, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0171"}}, {"seed": 172, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0172"}}, {"seed": 173, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0173"}}, {"seed": 174, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0174"}}, {"seed": 175, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0175"}}, {"seed": 176, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0176"}}, {"seed": 177, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0177"}}, {"seed": 178, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0178"}}, {"seed": 179, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0179"}}, {"seed": 180, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0180"}}, {"seed": 181, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0181"}}, {"seed": 182, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0182"}}, {"seed": 183, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0183"}}, {"seed": 184, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0184"}}, {"seed": 185, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0185"}}, {"seed": 186, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0186"}}, {"seed": 187, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0187"}}, {"seed": 188, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0188"}}, {"seed": 189, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0189"}}, {"seed": 190, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0190"}}, {"seed": 191, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0191"}}, {"seed": 192, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0192"}}, {"seed": 193, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0193"}}, {"seed": 194, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0194"}}, {"seed": 195, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0195"}}, {"seed": 196, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0196"}}, {"seed": 197, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0197"}}, {"seed": 198, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0198"}}, {"seed": 199, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0199"}}, {"seed": 200, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0200"}}, {"seed": 201, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0201"}}, {"seed": 202, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0202"}}, {"seed": 203, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0203"}}, {"seed": 204, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0204"}}, {"seed": 205, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0205"}}, {"seed": 206, "data": {"the_number": "319", "answer": "The number 319 is composite. We already know that 319 has two divisors: 1 and 319. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 18 = 29, so 11 is a factor of 319. Thus 319 has at least three divisors (1, 11, and 319), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "319 \\div 2 = 159 \\text{ remainder } 1 \\\\ 319 \\div 3 = 106 \\text{ remainder } 1 \\\\ 319 \\div 5 = 63 \\text{ remainder } 4 \\\\ 319 \\div 7 = 45 \\text{ remainder } 4 \\\\ 319 \\div 11 = 29 \\\\ 319 \\div 13 = 24 \\text{ remainder } 7 \\\\ 319 \\div 17 = 18 \\text{ remainder } 13 \\\\ ", "prime_problem": false, "__seed__": "0206"}}, {"seed": 207, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0207"}}, {"seed": 208, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0208"}}, {"seed": 209, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0209"}}, {"seed": 210, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0210"}}, {"seed": 211, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0211"}}, {"seed": 212, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0212"}}, {"seed": 213, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0213"}}, {"seed": 214, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0214"}}, {"seed": 215, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0215"}}, {"seed": 216, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0216"}}, {"seed": 217, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0217"}}, {"seed": 218, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0218"}}, {"seed": 219, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0219"}}, {"seed": 220, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0220"}}, {"seed": 221, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0221"}}, {"seed": 222, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0222"}}, {"seed": 223, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0223"}}, {"seed": 224, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0224"}}, {"seed": 225, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0225"}}, {"seed": 226, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0226"}}, {"seed": 227, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0227"}}, {"seed": 228, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0228"}}, {"seed": 229, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0229"}}, {"seed": 230, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0230"}}, {"seed": 231, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0231"}}, {"seed": 232, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0232"}}, {"seed": 233, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0233"}}, {"seed": 234, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0234"}}, {"seed": 235, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0235"}}, {"seed": 236, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0236"}}, {"seed": 237, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0237"}}, {"seed": 238, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0238"}}, {"seed": 239, "data": {"the_number": "319", "answer": "The number 319 is composite. We already know that 319 has two divisors: 1 and 319. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 18 = 29, so 11 is a factor of 319. Thus 319 has at least three divisors (1, 11, and 319), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "319 \\div 2 = 159 \\text{ remainder } 1 \\\\ 319 \\div 3 = 106 \\text{ remainder } 1 \\\\ 319 \\div 5 = 63 \\text{ remainder } 4 \\\\ 319 \\div 7 = 45 \\text{ remainder } 4 \\\\ 319 \\div 11 = 29 \\\\ 319 \\div 13 = 24 \\text{ remainder } 7 \\\\ 319 \\div 17 = 18 \\text{ remainder } 13 \\\\ ", "prime_problem": false, "__seed__": "0239"}}, {"seed": 240, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0240"}}, {"seed": 241, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0241"}}, {"seed": 242, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0242"}}, {"seed": 243, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0243"}}, {"seed": 244, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0244"}}, {"seed": 245, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0245"}}, {"seed": 246, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0246"}}, {"seed": 247, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0247"}}, {"seed": 248, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0248"}}, {"seed": 249, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0249"}}, {"seed": 250, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0250"}}, {"seed": 251, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0251"}}, {"seed": 252, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0252"}}, {"seed": 253, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0253"}}, {"seed": 254, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0254"}}, {"seed": 255, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0255"}}, {"seed": 256, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0256"}}, {"seed": 257, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0257"}}, {"seed": 258, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0258"}}, {"seed": 259, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0259"}}, {"seed": 260, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0260"}}, {"seed": 261, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0261"}}, {"seed": 262, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0262"}}, {"seed": 263, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0263"}}, {"seed": 264, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0264"}}, {"seed": 265, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0265"}}, {"seed": 266, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0266"}}, {"seed": 267, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0267"}}, {"seed": 268, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0268"}}, {"seed": 269, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0269"}}, {"seed": 270, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0270"}}, {"seed": 271, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0271"}}, {"seed": 272, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0272"}}, {"seed": 273, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0273"}}, {"seed": 274, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0274"}}, {"seed": 275, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0275"}}, {"seed": 276, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0276"}}, {"seed": 277, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0277"}}, {"seed": 278, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0278"}}, {"seed": 279, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0279"}}, {"seed": 280, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0280"}}, {"seed": 281, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0281"}}, {"seed": 282, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0282"}}, {"seed": 283, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0283"}}, {"seed": 284, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0284"}}, {"seed": 285, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0285"}}, {"seed": 286, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0286"}}, {"seed": 287, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0287"}}, {"seed": 288, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0288"}}, {"seed": 289, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0289"}}, {"seed": 290, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0290"}}, {"seed": 291, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0291"}}, {"seed": 292, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0292"}}, {"seed": 293, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0293"}}, {"seed": 294, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0294"}}, {"seed": 295, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0295"}}, {"seed": 296, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0296"}}, {"seed": 297, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0297"}}, {"seed": 298, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0298"}}, {"seed": 299, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0299"}}, {"seed": 300, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0300"}}, {"seed": 301, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0301"}}, {"seed": 302, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0302"}}, {"seed": 303, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0303"}}, {"seed": 304, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0304"}}, {"seed": 305, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0305"}}, {"seed": 306, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0306"}}, {"seed": 307, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0307"}}, {"seed": 308, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0308"}}, {"seed": 309, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0309"}}, {"seed": 310, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0310"}}, {"seed": 311, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0311"}}, {"seed": 312, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0312"}}, {"seed": 313, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0313"}}, {"seed": 314, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0314"}}, {"seed": 315, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0315"}}, {"seed": 316, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0316"}}, {"seed": 317, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0317"}}, {"seed": 318, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0318"}}, {"seed": 319, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0319"}}, {"seed": 320, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0320"}}, {"seed": 321, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0321"}}, {"seed": 322, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0322"}}, {"seed": 323, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0323"}}, {"seed": 324, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0324"}}, {"seed": 325, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0325"}}, {"seed": 326, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0326"}}, {"seed": 327, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0327"}}, {"seed": 328, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0328"}}, {"seed": 329, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0329"}}, {"seed": 330, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0330"}}, {"seed": 331, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0331"}}, {"seed": 332, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0332"}}, {"seed": 333, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0333"}}, {"seed": 334, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0334"}}, {"seed": 335, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0335"}}, {"seed": 336, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0336"}}, {"seed": 337, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0337"}}, {"seed": 338, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0338"}}, {"seed": 339, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0339"}}, {"seed": 340, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0340"}}, {"seed": 341, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0341"}}, {"seed": 342, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0342"}}, {"seed": 343, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0343"}}, {"seed": 344, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0344"}}, {"seed": 345, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0345"}}, {"seed": 346, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0346"}}, {"seed": 347, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0347"}}, {"seed": 348, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0348"}}, {"seed": 349, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0349"}}, {"seed": 350, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0350"}}, {"seed": 351, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0351"}}, {"seed": 352, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0352"}}, {"seed": 353, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0353"}}, {"seed": 354, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0354"}}, {"seed": 355, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0355"}}, {"seed": 356, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0356"}}, {"seed": 357, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0357"}}, {"seed": 358, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0358"}}, {"seed": 359, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0359"}}, {"seed": 360, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0360"}}, {"seed": 361, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0361"}}, {"seed": 362, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0362"}}, {"seed": 363, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0363"}}, {"seed": 364, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0364"}}, {"seed": 365, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0365"}}, {"seed": 366, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0366"}}, {"seed": 367, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0367"}}, {"seed": 368, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0368"}}, {"seed": 369, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0369"}}, {"seed": 370, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0370"}}, {"seed": 371, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0371"}}, {"seed": 372, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0372"}}, {"seed": 373, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0373"}}, {"seed": 374, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0374"}}, {"seed": 375, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0375"}}, {"seed": 376, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0376"}}, {"seed": 377, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0377"}}, {"seed": 378, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0378"}}, {"seed": 379, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0379"}}, {"seed": 380, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0380"}}, {"seed": 381, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0381"}}, {"seed": 382, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0382"}}, {"seed": 383, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0383"}}, {"seed": 384, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0384"}}, {"seed": 385, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0385"}}, {"seed": 386, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0386"}}, {"seed": 387, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0387"}}, {"seed": 388, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0388"}}, {"seed": 389, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0389"}}, {"seed": 390, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0390"}}, {"seed": 391, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0391"}}, {"seed": 392, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0392"}}, {"seed": 393, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0393"}}, {"seed": 394, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0394"}}, {"seed": 395, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0395"}}, {"seed": 396, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0396"}}, {"seed": 397, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0397"}}, {"seed": 398, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0398"}}, {"seed": 399, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0399"}}, {"seed": 400, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0400"}}, {"seed": 401, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0401"}}, {"seed": 402, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0402"}}, {"seed": 403, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0403"}}, {"seed": 404, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0404"}}, {"seed": 405, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0405"}}, {"seed": 406, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0406"}}, {"seed": 407, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0407"}}, {"seed": 408, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0408"}}, {"seed": 409, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0409"}}, {"seed": 410, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0410"}}, {"seed": 411, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0411"}}, {"seed": 412, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0412"}}, {"seed": 413, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0413"}}, {"seed": 414, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0414"}}, {"seed": 415, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0415"}}, {"seed": 416, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0416"}}, {"seed": 417, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0417"}}, {"seed": 418, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0418"}}, {"seed": 419, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0419"}}, {"seed": 420, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0420"}}, {"seed": 421, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0421"}}, {"seed": 422, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0422"}}, {"seed": 423, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0423"}}, {"seed": 424, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0424"}}, {"seed": 425, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0425"}}, {"seed": 426, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0426"}}, {"seed": 427, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0427"}}, {"seed": 428, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0428"}}, {"seed": 429, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0429"}}, {"seed": 430, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0430"}}, {"seed": 431, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0431"}}, {"seed": 432, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0432"}}, {"seed": 433, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0433"}}, {"seed": 434, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0434"}}, {"seed": 435, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0435"}}, {"seed": 436, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0436"}}, {"seed": 437, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0437"}}, {"seed": 438, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0438"}}, {"seed": 439, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0439"}}, {"seed": 440, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0440"}}, {"seed": 441, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0441"}}, {"seed": 442, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0442"}}, {"seed": 443, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0443"}}, {"seed": 444, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0444"}}, {"seed": 445, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0445"}}, {"seed": 446, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0446"}}, {"seed": 447, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0447"}}, {"seed": 448, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0448"}}, {"seed": 449, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0449"}}, {"seed": 450, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0450"}}, {"seed": 451, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0451"}}, {"seed": 452, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0452"}}, {"seed": 453, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0453"}}, {"seed": 454, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0454"}}, {"seed": 455, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0455"}}, {"seed": 456, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0456"}}, {"seed": 457, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0457"}}, {"seed": 458, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0458"}}, {"seed": 459, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0459"}}, {"seed": 460, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0460"}}, {"seed": 461, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0461"}}, {"seed": 462, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0462"}}, {"seed": 463, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0463"}}, {"seed": 464, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0464"}}, {"seed": 465, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0465"}}, {"seed": 466, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0466"}}, {"seed": 467, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0467"}}, {"seed": 468, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0468"}}, {"seed": 469, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0469"}}, {"seed": 470, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0470"}}, {"seed": 471, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0471"}}, {"seed": 472, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0472"}}, {"seed": 473, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0473"}}, {"seed": 474, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0474"}}, {"seed": 475, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0475"}}, {"seed": 476, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0476"}}, {"seed": 477, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0477"}}, {"seed": 478, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0478"}}, {"seed": 479, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0479"}}, {"seed": 480, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0480"}}, {"seed": 481, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0481"}}, {"seed": 482, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0482"}}, {"seed": 483, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0483"}}, {"seed": 484, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0484"}}, {"seed": 485, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0485"}}, {"seed": 486, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0486"}}, {"seed": 487, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0487"}}, {"seed": 488, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0488"}}, {"seed": 489, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0489"}}, {"seed": 490, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0490"}}, {"seed": 491, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0491"}}, {"seed": 492, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0492"}}, {"seed": 493, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0493"}}, {"seed": 494, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0494"}}, {"seed": 495, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0495"}}, {"seed": 496, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0496"}}, {"seed": 497, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0497"}}, {"seed": 498, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0498"}}, {"seed": 499, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0499"}}, {"seed": 500, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0500"}}, {"seed": 501, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0501"}}, {"seed": 502, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0502"}}, {"seed": 503, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0503"}}, {"seed": 504, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0504"}}, {"seed": 505, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0505"}}, {"seed": 506, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0506"}}, {"seed": 507, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0507"}}, {"seed": 508, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0508"}}, {"seed": 509, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0509"}}, {"seed": 510, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0510"}}, {"seed": 511, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0511"}}, {"seed": 512, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0512"}}, {"seed": 513, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0513"}}, {"seed": 514, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0514"}}, {"seed": 515, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0515"}}, {"seed": 516, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0516"}}, {"seed": 517, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0517"}}, {"seed": 518, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0518"}}, {"seed": 519, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0519"}}, {"seed": 520, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0520"}}, {"seed": 521, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0521"}}, {"seed": 522, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0522"}}, {"seed": 523, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0523"}}, {"seed": 524, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0524"}}, {"seed": 525, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0525"}}, {"seed": 526, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0526"}}, {"seed": 527, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0527"}}, {"seed": 528, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0528"}}, {"seed": 529, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0529"}}, {"seed": 530, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0530"}}, {"seed": 531, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0531"}}, {"seed": 532, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0532"}}, {"seed": 533, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0533"}}, {"seed": 534, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0534"}}, {"seed": 535, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0535"}}, {"seed": 536, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0536"}}, {"seed": 537, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0537"}}, {"seed": 538, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0538"}}, {"seed": 539, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0539"}}, {"seed": 540, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0540"}}, {"seed": 541, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0541"}}, {"seed": 542, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0542"}}, {"seed": 543, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0543"}}, {"seed": 544, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0544"}}, {"seed": 545, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0545"}}, {"seed": 546, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0546"}}, {"seed": 547, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0547"}}, {"seed": 548, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0548"}}, {"seed": 549, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0549"}}, {"seed": 550, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0550"}}, {"seed": 551, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0551"}}, {"seed": 552, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0552"}}, {"seed": 553, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0553"}}, {"seed": 554, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0554"}}, {"seed": 555, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0555"}}, {"seed": 556, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0556"}}, {"seed": 557, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0557"}}, {"seed": 558, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0558"}}, {"seed": 559, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0559"}}, {"seed": 560, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0560"}}, {"seed": 561, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0561"}}, {"seed": 562, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0562"}}, {"seed": 563, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0563"}}, {"seed": 564, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0564"}}, {"seed": 565, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0565"}}, {"seed": 566, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0566"}}, {"seed": 567, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0567"}}, {"seed": 568, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0568"}}, {"seed": 569, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0569"}}, {"seed": 570, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0570"}}, {"seed": 571, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0571"}}, {"seed": 572, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0572"}}, {"seed": 573, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0573"}}, {"seed": 574, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0574"}}, {"seed": 575, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0575"}}, {"seed": 576, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0576"}}, {"seed": 577, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0577"}}, {"seed": 578, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0578"}}, {"seed": 579, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0579"}}, {"seed": 580, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0580"}}, {"seed": 581, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0581"}}, {"seed": 582, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0582"}}, {"seed": 583, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0583"}}, {"seed": 584, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0584"}}, {"seed": 585, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0585"}}, {"seed": 586, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0586"}}, {"seed": 587, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0587"}}, {"seed": 588, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0588"}}, {"seed": 589, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0589"}}, {"seed": 590, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0590"}}, {"seed": 591, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0591"}}, {"seed": 592, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0592"}}, {"seed": 593, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0593"}}, {"seed": 594, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0594"}}, {"seed": 595, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0595"}}, {"seed": 596, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0596"}}, {"seed": 597, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0597"}}, {"seed": 598, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0598"}}, {"seed": 599, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0599"}}, {"seed": 600, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0600"}}, {"seed": 601, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0601"}}, {"seed": 602, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0602"}}, {"seed": 603, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0603"}}, {"seed": 604, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0604"}}, {"seed": 605, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0605"}}, {"seed": 606, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0606"}}, {"seed": 607, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0607"}}, {"seed": 608, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0608"}}, {"seed": 609, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0609"}}, {"seed": 610, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0610"}}, {"seed": 611, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0611"}}, {"seed": 612, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0612"}}, {"seed": 613, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0613"}}, {"seed": 614, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0614"}}, {"seed": 615, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0615"}}, {"seed": 616, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0616"}}, {"seed": 617, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0617"}}, {"seed": 618, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0618"}}, {"seed": 619, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0619"}}, {"seed": 620, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0620"}}, {"seed": 621, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0621"}}, {"seed": 622, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0622"}}, {"seed": 623, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0623"}}, {"seed": 624, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0624"}}, {"seed": 625, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0625"}}, {"seed": 626, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0626"}}, {"seed": 627, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0627"}}, {"seed": 628, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0628"}}, {"seed": 629, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0629"}}, {"seed": 630, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0630"}}, {"seed": 631, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0631"}}, {"seed": 632, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0632"}}, {"seed": 633, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0633"}}, {"seed": 634, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0634"}}, {"seed": 635, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0635"}}, {"seed": 636, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0636"}}, {"seed": 637, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0637"}}, {"seed": 638, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0638"}}, {"seed": 639, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0639"}}, {"seed": 640, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0640"}}, {"seed": 641, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0641"}}, {"seed": 642, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0642"}}, {"seed": 643, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0643"}}, {"seed": 644, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0644"}}, {"seed": 645, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0645"}}, {"seed": 646, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0646"}}, {"seed": 647, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0647"}}, {"seed": 648, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0648"}}, {"seed": 649, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0649"}}, {"seed": 650, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0650"}}, {"seed": 651, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0651"}}, {"seed": 652, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0652"}}, {"seed": 653, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0653"}}, {"seed": 654, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0654"}}, {"seed": 655, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0655"}}, {"seed": 656, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0656"}}, {"seed": 657, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0657"}}, {"seed": 658, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0658"}}, {"seed": 659, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0659"}}, {"seed": 660, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0660"}}, {"seed": 661, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0661"}}, {"seed": 662, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0662"}}, {"seed": 663, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0663"}}, {"seed": 664, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0664"}}, {"seed": 665, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0665"}}, {"seed": 666, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0666"}}, {"seed": 667, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0667"}}, {"seed": 668, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0668"}}, {"seed": 669, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0669"}}, {"seed": 670, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0670"}}, {"seed": 671, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0671"}}, {"seed": 672, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0672"}}, {"seed": 673, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0673"}}, {"seed": 674, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0674"}}, {"seed": 675, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0675"}}, {"seed": 676, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0676"}}, {"seed": 677, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0677"}}, {"seed": 678, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0678"}}, {"seed": 679, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0679"}}, {"seed": 680, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0680"}}, {"seed": 681, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0681"}}, {"seed": 682, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0682"}}, {"seed": 683, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0683"}}, {"seed": 684, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0684"}}, {"seed": 685, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0685"}}, {"seed": 686, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0686"}}, {"seed": 687, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0687"}}, {"seed": 688, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0688"}}, {"seed": 689, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0689"}}, {"seed": 690, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0690"}}, {"seed": 691, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0691"}}, {"seed": 692, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0692"}}, {"seed": 693, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0693"}}, {"seed": 694, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0694"}}, {"seed": 695, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0695"}}, {"seed": 696, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0696"}}, {"seed": 697, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0697"}}, {"seed": 698, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0698"}}, {"seed": 699, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0699"}}, {"seed": 700, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0700"}}, {"seed": 701, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0701"}}, {"seed": 702, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0702"}}, {"seed": 703, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0703"}}, {"seed": 704, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0704"}}, {"seed": 705, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0705"}}, {"seed": 706, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0706"}}, {"seed": 707, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0707"}}, {"seed": 708, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0708"}}, {"seed": 709, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0709"}}, {"seed": 710, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0710"}}, {"seed": 711, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0711"}}, {"seed": 712, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0712"}}, {"seed": 713, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0713"}}, {"seed": 714, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0714"}}, {"seed": 715, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0715"}}, {"seed": 716, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0716"}}, {"seed": 717, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0717"}}, {"seed": 718, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0718"}}, {"seed": 719, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0719"}}, {"seed": 720, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0720"}}, {"seed": 721, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0721"}}, {"seed": 722, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0722"}}, {"seed": 723, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0723"}}, {"seed": 724, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0724"}}, {"seed": 725, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0725"}}, {"seed": 726, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0726"}}, {"seed": 727, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0727"}}, {"seed": 728, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0728"}}, {"seed": 729, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0729"}}, {"seed": 730, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0730"}}, {"seed": 731, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0731"}}, {"seed": 732, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0732"}}, {"seed": 733, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0733"}}, {"seed": 734, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0734"}}, {"seed": 735, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0735"}}, {"seed": 736, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0736"}}, {"seed": 737, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0737"}}, {"seed": 738, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0738"}}, {"seed": 739, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0739"}}, {"seed": 740, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0740"}}, {"seed": 741, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0741"}}, {"seed": 742, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0742"}}, {"seed": 743, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0743"}}, {"seed": 744, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0744"}}, {"seed": 745, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0745"}}, {"seed": 746, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0746"}}, {"seed": 747, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0747"}}, {"seed": 748, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0748"}}, {"seed": 749, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0749"}}, {"seed": 750, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0750"}}, {"seed": 751, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0751"}}, {"seed": 752, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0752"}}, {"seed": 753, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0753"}}, {"seed": 754, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0754"}}, {"seed": 755, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0755"}}, {"seed": 756, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0756"}}, {"seed": 757, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0757"}}, {"seed": 758, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0758"}}, {"seed": 759, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0759"}}, {"seed": 760, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0760"}}, {"seed": 761, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0761"}}, {"seed": 762, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0762"}}, {"seed": 763, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0763"}}, {"seed": 764, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0764"}}, {"seed": 765, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0765"}}, {"seed": 766, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0766"}}, {"seed": 767, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0767"}}, {"seed": 768, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0768"}}, {"seed": 769, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0769"}}, {"seed": 770, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0770"}}, {"seed": 771, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0771"}}, {"seed": 772, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0772"}}, {"seed": 773, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0773"}}, {"seed": 774, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0774"}}, {"seed": 775, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0775"}}, {"seed": 776, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0776"}}, {"seed": 777, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0777"}}, {"seed": 778, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0778"}}, {"seed": 779, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0779"}}, {"seed": 780, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0780"}}, {"seed": 781, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0781"}}, {"seed": 782, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0782"}}, {"seed": 783, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0783"}}, {"seed": 784, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0784"}}, {"seed": 785, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0785"}}, {"seed": 786, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0786"}}, {"seed": 787, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0787"}}, {"seed": 788, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0788"}}, {"seed": 789, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0789"}}, {"seed": 790, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0790"}}, {"seed": 791, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0791"}}, {"seed": 792, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0792"}}, {"seed": 793, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0793"}}, {"seed": 794, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0794"}}, {"seed": 795, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0795"}}, {"seed": 796, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0796"}}, {"seed": 797, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0797"}}, {"seed": 798, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0798"}}, {"seed": 799, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0799"}}, {"seed": 800, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0800"}}, {"seed": 801, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0801"}}, {"seed": 802, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0802"}}, {"seed": 803, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0803"}}, {"seed": 804, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0804"}}, {"seed": 805, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0805"}}, {"seed": 806, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0806"}}, {"seed": 807, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0807"}}, {"seed": 808, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0808"}}, {"seed": 809, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0809"}}, {"seed": 810, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0810"}}, {"seed": 811, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0811"}}, {"seed": 812, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0812"}}, {"seed": 813, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0813"}}, {"seed": 814, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0814"}}, {"seed": 815, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0815"}}, {"seed": 816, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0816"}}, {"seed": 817, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0817"}}, {"seed": 818, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0818"}}, {"seed": 819, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0819"}}, {"seed": 820, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0820"}}, {"seed": 821, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0821"}}, {"seed": 822, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0822"}}, {"seed": 823, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0823"}}, {"seed": 824, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0824"}}, {"seed": 825, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0825"}}, {"seed": 826, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0826"}}, {"seed": 827, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0827"}}, {"seed": 828, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0828"}}, {"seed": 829, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0829"}}, {"seed": 830, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0830"}}, {"seed": 831, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0831"}}, {"seed": 832, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0832"}}, {"seed": 833, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0833"}}, {"seed": 834, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0834"}}, {"seed": 835, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0835"}}, {"seed": 836, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0836"}}, {"seed": 837, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0837"}}, {"seed": 838, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0838"}}, {"seed": 839, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0839"}}, {"seed": 840, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0840"}}, {"seed": 841, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0841"}}, {"seed": 842, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0842"}}, {"seed": 843, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0843"}}, {"seed": 844, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0844"}}, {"seed": 845, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0845"}}, {"seed": 846, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0846"}}, {"seed": 847, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0847"}}, {"seed": 848, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0848"}}, {"seed": 849, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0849"}}, {"seed": 850, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0850"}}, {"seed": 851, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0851"}}, {"seed": 852, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0852"}}, {"seed": 853, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0853"}}, {"seed": 854, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0854"}}, {"seed": 855, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0855"}}, {"seed": 856, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0856"}}, {"seed": 857, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0857"}}, {"seed": 858, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0858"}}, {"seed": 859, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0859"}}, {"seed": 860, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0860"}}, {"seed": 861, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0861"}}, {"seed": 862, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0862"}}, {"seed": 863, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0863"}}, {"seed": 864, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0864"}}, {"seed": 865, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0865"}}, {"seed": 866, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0866"}}, {"seed": 867, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0867"}}, {"seed": 868, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0868"}}, {"seed": 869, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0869"}}, {"seed": 870, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0870"}}, {"seed": 871, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0871"}}, {"seed": 872, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0872"}}, {"seed": 873, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0873"}}, {"seed": 874, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0874"}}, {"seed": 875, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0875"}}, {"seed": 876, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0876"}}, {"seed": 877, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0877"}}, {"seed": 878, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0878"}}, {"seed": 879, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0879"}}, {"seed": 880, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0880"}}, {"seed": 881, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0881"}}, {"seed": 882, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0882"}}, {"seed": 883, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0883"}}, {"seed": 884, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0884"}}, {"seed": 885, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0885"}}, {"seed": 886, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0886"}}, {"seed": 887, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0887"}}, {"seed": 888, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0888"}}, {"seed": 889, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0889"}}, {"seed": 890, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0890"}}, {"seed": 891, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0891"}}, {"seed": 892, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0892"}}, {"seed": 893, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0893"}}, {"seed": 894, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0894"}}, {"seed": 895, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0895"}}, {"seed": 896, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0896"}}, {"seed": 897, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0897"}}, {"seed": 898, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0898"}}, {"seed": 899, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0899"}}, {"seed": 900, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0900"}}, {"seed": 901, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0901"}}, {"seed": 902, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0902"}}, {"seed": 903, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0903"}}, {"seed": 904, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0904"}}, {"seed": 905, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0905"}}, {"seed": 906, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0906"}}, {"seed": 907, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0907"}}, {"seed": 908, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0908"}}, {"seed": 909, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0909"}}, {"seed": 910, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0910"}}, {"seed": 911, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0911"}}, {"seed": 912, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0912"}}, {"seed": 913, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0913"}}, {"seed": 914, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0914"}}, {"seed": 915, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0915"}}, {"seed": 916, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0916"}}, {"seed": 917, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0917"}}, {"seed": 918, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0918"}}, {"seed": 919, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0919"}}, {"seed": 920, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0920"}}, {"seed": 921, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0921"}}, {"seed": 922, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0922"}}, {"seed": 923, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0923"}}, {"seed": 924, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0924"}}, {"seed": 925, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0925"}}, {"seed": 926, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0926"}}, {"seed": 927, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0927"}}, {"seed": 928, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0928"}}, {"seed": 929, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0929"}}, {"seed": 930, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0930"}}, {"seed": 931, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0931"}}, {"seed": 932, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0932"}}, {"seed": 933, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0933"}}, {"seed": 934, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0934"}}, {"seed": 935, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0935"}}, {"seed": 936, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0936"}}, {"seed": 937, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0937"}}, {"seed": 938, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0938"}}, {"seed": 939, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0939"}}, {"seed": 940, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0940"}}, {"seed": 941, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0941"}}, {"seed": 942, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0942"}}, {"seed": 943, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0943"}}, {"seed": 944, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0944"}}, {"seed": 945, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0945"}}, {"seed": 946, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0946"}}, {"seed": 947, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0947"}}, {"seed": 948, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0948"}}, {"seed": 949, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0949"}}, {"seed": 950, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0950"}}, {"seed": 951, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0951"}}, {"seed": 952, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0952"}}, {"seed": 953, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0953"}}, {"seed": 954, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0954"}}, {"seed": 955, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0955"}}, {"seed": 956, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0956"}}, {"seed": 957, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0957"}}, {"seed": 958, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0958"}}, {"seed": 959, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0959"}}, {"seed": 960, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0960"}}, {"seed": 961, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0961"}}, {"seed": 962, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0962"}}, {"seed": 963, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0963"}}, {"seed": 964, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0964"}}, {"seed": 965, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0965"}}, {"seed": 966, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0966"}}, {"seed": 967, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0967"}}, {"seed": 968, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0968"}}, {"seed": 969, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0969"}}, {"seed": 970, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0970"}}, {"seed": 971, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0971"}}, {"seed": 972, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0972"}}, {"seed": 973, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0973"}}, {"seed": 974, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0974"}}, {"seed": 975, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0975"}}, {"seed": 976, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0976"}}, {"seed": 977, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0977"}}, {"seed": 978, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0978"}}, {"seed": 979, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0979"}}, {"seed": 980, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0980"}}, {"seed": 981, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0981"}}, {"seed": 982, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0982"}}, {"seed": 983, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0983"}}, {"seed": 984, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0984"}}, {"seed": 985, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0985"}}, {"seed": 986, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0986"}}, {"seed": 987, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0987"}}, {"seed": 988, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0988"}}, {"seed": 989, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0989"}}, {"seed": 990, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0990"}}, {"seed": 991, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0991"}}, {"seed": 992, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0992"}}, {"seed": 993, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0993"}}, {"seed": 994, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0994"}}, {"seed": 995, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0995"}}, {"seed": 996, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0996"}}, {"seed": 997, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0997"}}, {"seed": 998, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0998"}}, {"seed": 999, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0999"}}]}, {"title": "Finding the GCD", "slug": "N3", "description": "\n I can compute the greatest common divisor (GCD) of two numbers using the listing and prime factorization methods.\n ", "template": "\n\n \n \n

Find {{listing_prob}} using the listing method (sometimes called the set intersection method). You must show correct lists and a final answer.

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Divisors of {{listing_a}}: {{listing_list_a}}

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Divisors of {{listing_b}}: {{listing_list_b}}

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The largest divisor appearing in both lists simultaneously is {{listing_gcd}}, so {{listing_prob}} = {{listing_gcd}}

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Find {{factorization_prob}} using the prime factorization method. You must show your factorization(s) before giving the final answer.

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Prime factorization of {{factorization_a}}: {{factorization_mult_a}}

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Prime factorization of {{factorization_b}}: {{factorization_mult_b}}

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Multiplying together all common factors gives us {{factorization_mult_gcd}}, so {{factorization_prob}} = {{factorization_gcd}}

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\n", "exercises": [{"seed": 0, "data": {"listing_a": "30", "listing_b": "40", "listing_prob": "\\text{GCD}(30,40)", "listing_list_a": "1, 2, 3, 5, 6, 10, 15, 30", "listing_list_b": "1, 2, 4, 5, 8, 10, 20, 40", "listing_gcd": "10", "listing_gcd_type": "share composite", "factorization_a": "360", "factorization_b": "500", "factorization_prob": "\\text{GCD}(360,500)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 5 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 2 \\times 5", "factorization_gcd": "20", "factorization_type": "b not prefactored, a_b kernel 20", "__seed__": "0000"}}, {"seed": 1, "data": {"listing_a": "18", "listing_b": "30", "listing_prob": "\\text{GCD}(18,30)", "listing_list_a": "1, 2, 3, 6, 9, 18", "listing_list_b": "1, 2, 3, 5, 6, 10, 15, 30", "listing_gcd": "6", "listing_gcd_type": "share composite", "factorization_a": "210", "factorization_b": "294", "factorization_prob": "\\text{GCD}(210,294)", "factorization_mult_a": "2 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_gcd": "2 \\times 3 \\times 7", "factorization_gcd": "42", "factorization_type": "b not prefactored, a_b kernel 14", "__seed__": "0001"}}, {"seed": 2, "data": {"listing_a": "68", "listing_b": "75", "listing_prob": "\\text{GCD}(68,75)", "listing_list_a": "1, 2, 4, 17, 34, 68", "listing_list_b": "1, 3, 5, 15, 25, 75", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "125", "factorization_b": "5^4", "factorization_prob": "\\text{GCD}(125,5^4)", "factorization_mult_a": "5 \\times 5 \\times 5", "factorization_mult_b": "5 \\times 5 \\times 5 \\times 5", "factorization_mult_gcd": "5 \\times 5 \\times 5", "factorization_gcd": "125", "factorization_type": "b prefactored, a_b kernel 125", "__seed__": "0002"}}, {"seed": 3, "data": {"listing_a": "42", "listing_b": "98", "listing_prob": "\\text{GCD}(42,98)", 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"listing_gcd_type": "share prime", "factorization_a": "100", "factorization_b": "2^2 \\times 5^2 \\times 7", "factorization_prob": "\\text{GCD}(100,2^2 \\times 5^2 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 5 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 5 \\times 5", "factorization_gcd": "100", "factorization_type": "b prefactored, a_b kernel 10", "__seed__": "0978"}}, {"seed": 979, "data": {"listing_a": "66", "listing_b": "99", "listing_prob": "\\text{GCD}(66,99)", "listing_list_a": "1, 2, 3, 6, 11, 22, 33, 66", "listing_list_b": "1, 3, 9, 11, 33, 99", "listing_gcd": "33", "listing_gcd_type": "share composite", "factorization_a": "189", "factorization_b": "2 \\times 3^2 \\times 5 \\times 7", "factorization_prob": "\\text{GCD}(189,2 \\times 3^2 \\times 5 \\times 7)", "factorization_mult_a": "3 \\times 3 \\times 3 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "3 \\times 3 \\times 7", "factorization_gcd": "63", "factorization_type": "b prefactored, a_b kernel 63", "__seed__": "0979"}}, {"seed": 980, "data": {"listing_a": "30", "listing_b": "91", "listing_prob": "\\text{GCD}(30,91)", "listing_list_a": "1, 2, 3, 5, 6, 10, 15, 30", "listing_list_b": "1, 7, 13, 91", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "72", "factorization_b": "2^3 \\times 3 \\times 7", "factorization_prob": "\\text{GCD}(72,2^3 \\times 3 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 2 \\times 3", "factorization_gcd": "24", "factorization_type": "b prefactored, a_b kernel 6", "__seed__": "0980"}}, {"seed": 981, "data": {"listing_a": "42", "listing_b": "78", "listing_prob": "\\text{GCD}(42,78)", "listing_list_a": "1, 2, 3, 6, 7, 14, 21, 42", "listing_list_b": "1, 2, 3, 6, 13, 26, 39, 78", "listing_gcd": "6", "listing_gcd_type": "share composite", "factorization_a": "300", "factorization_b": "2 \\times 3^2 \\times 5^2", "factorization_prob": "\\text{GCD}(300,2 \\times 3^2 \\times 5^2)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 3 \\times 5 \\times 5", "factorization_gcd": "150", "factorization_type": "b prefactored, a_b kernel 30", "__seed__": "0981"}}, {"seed": 982, "data": {"listing_a": "76", "listing_b": "92", "listing_prob": "\\text{GCD}(76,92)", "listing_list_a": "1, 2, 4, 19, 38, 76", "listing_list_b": "1, 2, 4, 23, 46, 92", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "294", "factorization_b": "2 \\times 5 \\times 7 \\times 11", "factorization_prob": "\\text{GCD}(294,2 \\times 5 \\times 7 \\times 11)", "factorization_mult_a": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_b": "2 \\times 5 \\times 7 \\times 11", "factorization_mult_gcd": "2 \\times 7", "factorization_gcd": "14", "factorization_type": "b prefactored, a_b kernel 14", "__seed__": "0982"}}, {"seed": 983, "data": {"listing_a": "20", "listing_b": "81", "listing_prob": "\\text{GCD}(20,81)", "listing_list_a": "1, 2, 4, 5, 10, 20", "listing_list_b": "1, 3, 9, 27, 81", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "70", "factorization_b": "350", "factorization_prob": "\\text{GCD}(70,350)", "factorization_mult_a": "2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 5 \\times 7", "factorization_gcd": "70", "factorization_type": "b not prefactored, a_b kernel 70", "__seed__": "0983"}}, {"seed": 984, "data": {"listing_a": "50", "listing_b": "75", "listing_prob": "\\text{GCD}(50,75)", "listing_list_a": "1, 2, 5, 10, 25, 50", "listing_list_b": "1, 3, 5, 15, 25, 75", "listing_gcd": "25", "listing_gcd_type": "share composite", "factorization_a": "120", "factorization_b": "2^3 \\times 3 \\times 5 \\times 7", "factorization_prob": "\\text{GCD}(120,2^3 \\times 3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 2 \\times 3 \\times 5", "factorization_gcd": "120", "factorization_type": "b prefactored, a_b kernel 4", "__seed__": "0984"}}, {"seed": 985, "data": {"listing_a": "22", "listing_b": "64", "listing_prob": "\\text{GCD}(22,64)", "listing_list_a": "1, 2, 11, 22", "listing_list_b": "1, 2, 4, 8, 16, 32, 64", "listing_gcd": "2", "listing_gcd_type": "share prime", "factorization_a": "360", "factorization_b": "2 \\times 3^4", "factorization_prob": "\\text{GCD}(360,2 \\times 3^4)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 3 \\times 3", "factorization_mult_gcd": "2 \\times 3 \\times 3", "factorization_gcd": "18", "factorization_type": "b prefactored, a_b kernel 9", "__seed__": "0985"}}, {"seed": 986, "data": {"listing_a": "32", "listing_b": "91", "listing_prob": "\\text{GCD}(32,91)", "listing_list_a": "1, 2, 4, 8, 16, 32", "listing_list_b": "1, 7, 13, 91", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "126", "factorization_b": "2^3 \\times 3^2 \\times 7", "factorization_prob": "\\text{GCD}(126,2^3 \\times 3^2 \\times 7)", "factorization_mult_a": "2 \\times 3 \\times 3 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 3 \\times 3 \\times 7", "factorization_gcd": "126", "factorization_type": "b prefactored, a_b kernel 42", "__seed__": "0986"}}, {"seed": 987, "data": {"listing_a": "15", "listing_b": "45", "listing_prob": "\\text{GCD}(15,45)", "listing_list_a": "1, 3, 5, 15", "listing_list_b": "1, 3, 5, 9, 15, 45", "listing_gcd": "15", "listing_gcd_type": "multiple", "factorization_a": "140", "factorization_b": "2^3 \\times 5 \\times 7", "factorization_prob": "\\text{GCD}(140,2^3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 5 \\times 7", "factorization_gcd": "140", "factorization_type": "b prefactored, a_b kernel 20", "__seed__": "0987"}}, {"seed": 988, "data": {"listing_a": "51", "listing_b": "95", "listing_prob": "\\text{GCD}(51,95)", "listing_list_a": "1, 3, 17, 51", "listing_list_b": "1, 5, 19, 95", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "180", "factorization_b": "252", "factorization_prob": "\\text{GCD}(180,252)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 3 \\times 3", "factorization_gcd": "36", "factorization_type": "b not prefactored, a_b kernel 9", "__seed__": "0988"}}, {"seed": 989, "data": {"listing_a": "65", "listing_b": "92", "listing_prob": "\\text{GCD}(65,92)", "listing_list_a": "1, 5, 13, 65", "listing_list_b": "1, 2, 4, 23, 46, 92", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "315", "factorization_b": "3 \\times 5^2 \\times 7", "factorization_prob": "\\text{GCD}(315,3 \\times 5^2 \\times 7)", "factorization_mult_a": "3 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "3 \\times 5 \\times 5 \\times 7", "factorization_mult_gcd": "3 \\times 5 \\times 7", "factorization_gcd": "105", "factorization_type": "b prefactored, a_b kernel 15", "__seed__": "0989"}}, {"seed": 990, "data": {"listing_a": "45", "listing_b": "99", "listing_prob": "\\text{GCD}(45,99)", "listing_list_a": "1, 3, 5, 9, 15, 45", "listing_list_b": "1, 3, 9, 11, 33, 99", "listing_gcd": "9", "listing_gcd_type": "share composite", "factorization_a": "108", "factorization_b": "540", "factorization_prob": "\\text{GCD}(108,540)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 3 \\times 3", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 3 \\times 3 \\times 5", "factorization_mult_gcd": "2 \\times 2 \\times 3 \\times 3 \\times 3", "factorization_gcd": "108", "factorization_type": "b not prefactored, a_b kernel 9", "__seed__": "0990"}}, {"seed": 991, "data": {"listing_a": "28", "listing_b": "64", "listing_prob": "\\text{GCD}(28,64)", "listing_list_a": "1, 2, 4, 7, 14, 28", "listing_list_b": "1, 2, 4, 8, 16, 32, 64", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "126", "factorization_b": "189", "factorization_prob": "\\text{GCD}(126,189)", "factorization_mult_a": "2 \\times 3 \\times 3 \\times 7", "factorization_mult_b": "3 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "3 \\times 3 \\times 7", "factorization_gcd": "63", "factorization_type": "b not prefactored, a_b kernel 63", "__seed__": "0991"}}, {"seed": 992, "data": {"listing_a": "44", "listing_b": "76", "listing_prob": "\\text{GCD}(44,76)", "listing_list_a": "1, 2, 4, 11, 22, 44", "listing_list_b": "1, 2, 4, 19, 38, 76", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "220", "factorization_b": "420", "factorization_prob": "\\text{GCD}(220,420)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 11", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 5", "factorization_gcd": "20", "factorization_type": "b not prefactored, a_b kernel 10", "__seed__": "0992"}}, {"seed": 993, "data": {"listing_a": "12", "listing_b": "92", "listing_prob": "\\text{GCD}(12,92)", "listing_list_a": "1, 2, 3, 4, 6, 12", "listing_list_b": "1, 2, 4, 23, 46, 92", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "294", "factorization_b": "2^5 \\times 3 \\times 7", "factorization_prob": "\\text{GCD}(294,2^5 \\times 3 \\times 7)", "factorization_mult_a": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 3 \\times 7", "factorization_gcd": "42", "factorization_type": "b prefactored, a_b kernel 7", "__seed__": "0993"}}, {"seed": 994, "data": {"listing_a": "8", "listing_b": "44", "listing_prob": "\\text{GCD}(8,44)", "listing_list_a": "1, 2, 4, 8", "listing_list_b": "1, 2, 4, 11, 22, 44", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "140", "factorization_b": "450", "factorization_prob": "\\text{GCD}(140,450)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 5", "factorization_gcd": "10", "factorization_type": "b not prefactored, a_b kernel 2", "__seed__": "0994"}}, {"seed": 995, "data": {"listing_a": "88", "listing_b": "94", "listing_prob": "\\text{GCD}(88,94)", "listing_list_a": "1, 2, 4, 8, 11, 22, 44, 88", "listing_list_b": "1, 2, 47, 94", "listing_gcd": "2", "listing_gcd_type": "share prime", "factorization_a": "96", "factorization_b": "400", "factorization_prob": "\\text{GCD}(96,400)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 2 \\times 2 \\times 2", "factorization_gcd": "16", "factorization_type": "b not prefactored, a_b kernel 4", "__seed__": "0995"}}, {"seed": 996, "data": {"listing_a": "30", "listing_b": "70", "listing_prob": "\\text{GCD}(30,70)", "listing_list_a": "1, 2, 3, 5, 6, 10, 15, 30", "listing_list_b": "1, 2, 5, 7, 10, 14, 35, 70", "listing_gcd": "10", "listing_gcd_type": "share composite", "factorization_a": "315", "factorization_b": "2 \\times 3^2 \\times 5^2", "factorization_prob": "\\text{GCD}(315,2 \\times 3^2 \\times 5^2)", "factorization_mult_a": "3 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_gcd": "3 \\times 3 \\times 5", "factorization_gcd": "45", "factorization_type": "b prefactored, a_b kernel 45", "__seed__": "0996"}}, {"seed": 997, "data": {"listing_a": "8", "listing_b": "44", "listing_prob": "\\text{GCD}(8,44)", "listing_list_a": "1, 2, 4, 8", "listing_list_b": "1, 2, 4, 11, 22, 44", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "420", "factorization_b": "2^2 \\times 3^3 \\times 7", "factorization_prob": "\\text{GCD}(420,2^2 \\times 3^3 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 3 \\times 7", "factorization_gcd": "84", "factorization_type": "b prefactored, a_b kernel 4", "__seed__": "0997"}}, {"seed": 998, "data": {"listing_a": "52", "listing_b": "88", "listing_prob": "\\text{GCD}(52,88)", "listing_list_a": "1, 2, 4, 13, 26, 52", "listing_list_b": "1, 2, 4, 8, 11, 22, 44, 88", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "360", "factorization_b": "588", "factorization_prob": "\\text{GCD}(360,588)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 7 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 3", "factorization_gcd": "12", "factorization_type": "b not prefactored, a_b kernel 6", "__seed__": "0998"}}, {"seed": 999, "data": {"listing_a": "12", "listing_b": "30", "listing_prob": "\\text{GCD}(12,30)", "listing_list_a": "1, 2, 3, 4, 6, 12", "listing_list_b": "1, 2, 3, 5, 6, 10, 15, 30", "listing_gcd": "6", "listing_gcd_type": "share composite", "factorization_a": "315", "factorization_b": "420", "factorization_prob": "\\text{GCD}(315,420)", "factorization_mult_a": "3 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "3 \\times 5 \\times 7", "factorization_gcd": "105", "factorization_type": "b not prefactored, a_b kernel 21", "__seed__": "0999"}}]}, {"title": "Finding the LCM", "slug": "N4", "description": "\n I can compute the least common multiple (LCM) of two numbers using the listing and prime factorization methods.\n ", "template": "\n\n \n \n

Find {{listing_prob}} using the listing method (sometimes called the set intersection method). You must show correct lists and a final answer.

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\n \n

(Some) multiples of {{listing_a}}: {{listing_list_a}}

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(Some) multiples of {{listing_b}}: {{listing_list_b}}

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The smallest nonzero multiple appearing in both lists simultaneously is {{listing_lcm}}, so {{listing_prob}} = {{listing_lcm}}

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\n
\n \n \n \n

Find {{factorization_prob}} using the prime factorization method. You must show your factorizations before giving the final answer. You may leave your answer in factored form.

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\n \n

Prime factorization of {{factorization_a}}: {{factorization_mult_a}}

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Prime factorization of {{factorization_b}}: {{factorization_mult_b}}

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Multiplying together all prime factors of {{factorization_a}} and {{factorization_b}}, then removing the overlapping prime factors gives us {{factorization_mult_lcm}}, so {{factorization_prob}} = {{factorization_lcm}}

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\n
\n
\n", "exercises": [{"seed": 0, "data": {"listing_a": "21", "listing_b": "6", "listing_prob": "\\text{LCM}(21,6)", "listing_list_a": "21, 42, 63, 84, 105...", "listing_list_b": "6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90...", "listing_lcm": "42", "factorization_a": "350", "factorization_b": "375", "factorization_prob": "\\text{LCM}(350,375)", "factorization_mult_a": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_b": "3 \\times 5 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 3 \\times 5 \\times 5 \\times 5 \\times 7", "factorization_lcm": "5250", "factorization_type": "b not prefactored, a_b kernel 25", "__seed__": "0000"}}, {"seed": 1, "data": {"listing_a": "14", "listing_b": "8", "listing_prob": "\\text{LCM}(14,8)", "listing_list_a": "14, 28, 42, 56, 70, 84, 98, 112, 126...", "listing_list_b": "8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120...", "listing_lcm": "56", "factorization_a": "147", "factorization_b": "378", "factorization_prob": "\\text{LCM}(147,378)", "factorization_mult_a": "3 \\times 7 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 3 \\times 7", "factorization_mult_lcm": "2 \\times 3 \\times 3 \\times 3 \\times 7 \\times 7", "factorization_lcm": "2646", "factorization_type": "b not prefactored, a_b kernel 21", "__seed__": "0001"}}, {"seed": 2, "data": {"listing_a": "35", "listing_b": "30", "listing_prob": "\\text{LCM}(35,30)", "listing_list_a": "35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455...", "listing_list_b": "30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450...", "listing_lcm": "210", "factorization_a": "105", "factorization_b": "2^4 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(105,2^4 \\times 5 \\times 7)", "factorization_mult_a": "3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5 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988, "data": {"listing_a": "56", "listing_b": "35", "listing_prob": "\\text{LCM}(56,35)", "listing_list_a": "56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616...", "listing_list_b": "35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455, 490, 525, 560, 595...", "listing_lcm": "280", "factorization_a": "231", "factorization_b": "2 \\times 3 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(231,2 \\times 3 \\times 5 \\times 7)", "factorization_mult_a": "3 \\times 7 \\times 11", "factorization_mult_b": "2 \\times 3 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 3 \\times 5 \\times 7 \\times 11", "factorization_lcm": "2310", "factorization_type": "b prefactored, a_b kernel 21", "__seed__": "0988"}}, {"seed": 989, "data": {"listing_a": "70", "listing_b": "49", "listing_prob": "\\text{LCM}(70,49)", "listing_list_a": "70, 140, 210, 280, 350, 420, 490, 560, 630, 700, 770, 840, 910, 980, 1050...", "listing_list_b": "49, 98, 147, 196, 245, 294, 343, 392, 441, 490, 539, 588, 637, 686, 735, 784, 833, 882, 931, 980, 1029...", "listing_lcm": "490", "factorization_a": "84", "factorization_b": "2^2 \\times 5 \\times 7^2", "factorization_prob": "\\text{LCM}(84,2^2 \\times 5 \\times 7^2)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 5 \\times 7 \\times 7", "factorization_mult_lcm": "2 \\times 2 \\times 3 \\times 5 \\times 7 \\times 7", "factorization_lcm": "2940", "factorization_type": "b prefactored, a_b kernel 14", "__seed__": "0989"}}, {"seed": 990, "data": {"listing_a": "68", "listing_b": "17", "listing_prob": "\\text{LCM}(68,17)", "listing_list_a": "68, 136, 204...", "listing_list_b": "17, 34, 51, 68, 85, 102, 119, 136, 153...", "listing_lcm": "68", "factorization_a": "220", "factorization_b": "330", "factorization_prob": "\\text{LCM}(220,330)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 11", "factorization_mult_b": "2 \\times 3 \\times 5 \\times 11", "factorization_mult_lcm": "2 \\times 2 \\times 3 \\times 5 \\times 11", "factorization_lcm": "660", "factorization_type": "b not prefactored, a_b kernel 22", "__seed__": "0990"}}, {"seed": 991, "data": {"listing_a": "72", "listing_b": "48", "listing_prob": "\\text{LCM}(72,48)", "listing_list_a": "72, 144, 216, 288, 360...", "listing_list_b": "48, 96, 144, 192, 240, 288, 336...", "listing_lcm": "144", "factorization_a": "420", "factorization_b": "600", "factorization_prob": "\\text{LCM}(420,600)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5 \\times 7", "factorization_lcm": "4200", "factorization_type": "b not prefactored, a_b kernel 12", "__seed__": "0991"}}, {"seed": 992, "data": {"listing_a": "8", "listing_b": "6", "listing_prob": "\\text{LCM}(8,6)", "listing_list_a": "8, 16, 24, 32, 40, 48, 56...", "listing_list_b": "6, 12, 18, 24, 30, 36, 42, 48, 54...", "listing_lcm": "24", "factorization_a": "360", "factorization_b": "2^3 \\times 3^2 \\times 11", "factorization_prob": "\\text{LCM}(360,2^3 \\times 3^2 \\times 11)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 11", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5 \\times 11", "factorization_lcm": "3960", "factorization_type": "b prefactored, a_b kernel 2", "__seed__": "0992"}}, {"seed": 993, "data": {"listing_a": "15", "listing_b": "12", "listing_prob": "\\text{LCM}(15,12)", "listing_list_a": "15, 30, 45, 60, 75, 90, 105, 120, 135...", "listing_list_b": "12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132...", "listing_lcm": "60", "factorization_a": "480", "factorization_b": "2 \\times 3 \\times 7 \\times 11", "factorization_prob": "\\text{LCM}(480,2 \\times 3 \\times 7 \\times 11)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 7 \\times 11", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 7 \\times 11", "factorization_lcm": "36960", "factorization_type": "b prefactored, a_b kernel 6", "__seed__": "0993"}}, {"seed": 994, "data": {"listing_a": "64", "listing_b": "8", "listing_prob": "\\text{LCM}(64,8)", "listing_list_a": "64, 128, 192...", "listing_list_b": "8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136...", "listing_lcm": "64", "factorization_a": "350", "factorization_b": "2^3 \\times 3 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(350,2^3 \\times 3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5 \\times 7", "factorization_lcm": "4200", "factorization_type": "b prefactored, a_b kernel 70", "__seed__": "0994"}}, {"seed": 995, "data": {"listing_a": "70", "listing_b": "10", "listing_prob": "\\text{LCM}(70,10)", "listing_list_a": "70, 140, 210...", "listing_list_b": "10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150...", "listing_lcm": "70", "factorization_a": "350", "factorization_b": "490", "factorization_prob": "\\text{LCM}(350,490)", "factorization_mult_a": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 5 \\times 7 \\times 7", "factorization_mult_lcm": "2 \\times 5 \\times 5 \\times 7 \\times 7", "factorization_lcm": "2450", "factorization_type": "b not prefactored, a_b kernel 35", "__seed__": "0995"}}, {"seed": 996, "data": {"listing_a": "63", "listing_b": "45", "listing_prob": "\\text{LCM}(63,45)", "listing_list_a": "63, 126, 189, 252, 315, 378, 441, 504, 567, 630, 693...", "listing_list_b": "45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675...", "listing_lcm": "315", "factorization_a": "300", "factorization_b": "450", "factorization_prob": "\\text{LCM}(300,450)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_lcm": "900", "factorization_type": "b not prefactored, a_b kernel 50", "__seed__": "0996"}}, {"seed": 997, "data": {"listing_a": "70", "listing_b": "30", "listing_prob": "\\text{LCM}(70,30)", "listing_list_a": "70, 140, 210, 280, 350, 420, 490...", "listing_list_b": "30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450...", "listing_lcm": "210", "factorization_a": "140", "factorization_b": "400", "factorization_prob": "\\text{LCM}(140,400)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5 \\times 7", "factorization_lcm": "2800", "factorization_type": "b not prefactored, a_b kernel 20", "__seed__": "0997"}}, {"seed": 998, "data": {"listing_a": "70", "listing_b": "20", "listing_prob": "\\text{LCM}(70,20)", "listing_list_a": "70, 140, 210, 280, 350...", "listing_list_b": "20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300...", "listing_lcm": "140", "factorization_a": "294", "factorization_b": "3^3 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(294,3^3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_b": "3 \\times 3 \\times 3 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 3 \\times 3 \\times 3 \\times 5 \\times 7 \\times 7", "factorization_lcm": "13230", "factorization_type": "b prefactored, a_b kernel 21", "__seed__": "0998"}}, {"seed": 999, "data": {"listing_a": "56", "listing_b": "49", "listing_prob": "\\text{LCM}(56,49)", "listing_list_a": "56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784, 840...", "listing_list_b": "49, 98, 147, 196, 245, 294, 343, 392, 441, 490, 539, 588, 637, 686, 735, 784, 833...", "listing_lcm": "392", "factorization_a": "400", "factorization_b": "2^2 \\times 3 \\times 5^2", "factorization_prob": "\\text{LCM}(400,2^2 \\times 3 \\times 5^2)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_lcm": "1200", "factorization_type": "b prefactored, a_b kernel 4", "__seed__": "0999"}}]}, {"title": "Equivalent Fractions", "slug": "F1", "description": "\n I can convert fractions to different forms (including simplest form), and determine if two fractions are equivalent.\n ", "template": "\n\n \n \n

Write {{simplify_prob}} in simplest form.

\n
\n \n

The above simplifies to {{simplify_ans}}, after pulling out {{factors_sequence}} from both the numerator and denominator.

\n
\n
\n \n \n \n

Convert {{convert_prob}} to {{convert_type}}.

\n
\n \n

{{convert_ans}}

\n
\n
\n\n \n \n

Determine if {{equiv_prob_ab}} \\text{ and } {{equiv_prob_cd}} and are equivalent fractions. You may use any method of your choosing, but you must show correct work in order to pass.

\n
\n \n

The fraction {{equiv_prob_ab}} simplifies to {{equiv_ans_ab}}.

\n

The fraction {{equiv_prob_cd}} simplifies to {{equiv_ans_cd}}.

\n

{{equiv_ans_supp_1}}

\n

Alternatively, we see that the product of one pair of diagonal entries is {{equiv_prob_a}} \\times {{equiv_prob_d}} = {{equiv_ans_axd}} while the other diagonal product is {{equiv_prob_b}} \\times {{equiv_prob_c}} = {{equiv_ans_bxc}} {{equiv_ans_supp_2}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"simplify_prob": "\\dfrac{49}{196}", "simplify_ans": "\\dfrac{1}{4}", "factors_list": ["7", "7"], "factors_sequence": "7 and 7", "convert_prob": "\\dfrac{61}{15}", "convert_type": "a mixed number", "convert_ans": "4\\frac{1}{15}", "equiv_prob_a": "18", "equiv_prob_b": "30", "equiv_prob_c": "14", "equiv_prob_d": "27", "equiv_prob_ab": "\\dfrac{18}{30}", "equiv_prob_cd": "\\dfrac{14}{27}", "equiv_ans_ab": "\\dfrac{3}{5}", "equiv_ans_cd": "\\dfrac{14}{27}", "equiv_ans_axd": "486", "equiv_ans_bxc": "420", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0000"}}, {"seed": 1, "data": {"simplify_prob": "\\dfrac{22}{330}", "simplify_ans": "\\dfrac{1}{15}", "factors_list": ["2", "11"], "factors_sequence": "2 and 11", "convert_prob": "\\dfrac{25}{11}", "convert_type": "a mixed number", "convert_ans": "2\\frac{3}{11}", "equiv_prob_a": "48", "equiv_prob_b": "60", "equiv_prob_c": "36", "equiv_prob_d": "45", "equiv_prob_ab": "\\dfrac{48}{60}", "equiv_prob_cd": "\\dfrac{36}{45}", "equiv_ans_ab": "\\dfrac{4}{5}", "equiv_ans_cd": "\\dfrac{4}{5}", "equiv_ans_axd": "2160", "equiv_ans_bxc": "2160", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0001"}}, {"seed": 2, "data": {"simplify_prob": "\\dfrac{252}{273}", "simplify_ans": "\\dfrac{12}{13}", "factors_list": ["3", "7"], "factors_sequence": "3 and 7", "convert_prob": "7\\frac{9}{13}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{100}{13}", "equiv_prob_a": "20", "equiv_prob_b": "80", "equiv_prob_c": "22", "equiv_prob_d": "83", "equiv_prob_ab": "\\dfrac{20}{80}", "equiv_prob_cd": "\\dfrac{22}{83}", "equiv_ans_ab": "\\dfrac{1}{4}", "equiv_ans_cd": "\\dfrac{22}{83}", "equiv_ans_axd": "1660", "equiv_ans_bxc": "1760", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0002"}}, {"seed": 3, "data": {"simplify_prob": "\\dfrac{24}{120}", "simplify_ans": "\\dfrac{1}{5}", "factors_list": ["2", "2", "2", "3"], "factors_sequence": "2, 2, 2, and 3", "convert_prob": "\\dfrac{81}{14}", "convert_type": "a mixed number", "convert_ans": "5\\frac{11}{14}", "equiv_prob_a": "90", "equiv_prob_b": "108", "equiv_prob_c": "110", "equiv_prob_d": "132", "equiv_prob_ab": "\\dfrac{90}{108}", "equiv_prob_cd": "\\dfrac{110}{132}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{5}{6}", "equiv_ans_axd": "11880", "equiv_ans_bxc": "11880", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0003"}}, {"seed": 4, "data": {"simplify_prob": "\\dfrac{45}{180}", "simplify_ans": "\\dfrac{1}{4}", "factors_list": ["3", "3", "5"], "factors_sequence": "3, 3, and 5", "convert_prob": "\\dfrac{11}{5}", "convert_type": "a mixed number", "convert_ans": "2\\frac{1}{5}", "equiv_prob_a": "15", "equiv_prob_b": "45", "equiv_prob_c": "21", "equiv_prob_d": "51", "equiv_prob_ab": "\\dfrac{15}{45}", "equiv_prob_cd": "\\dfrac{21}{51}", "equiv_ans_ab": "\\dfrac{1}{3}", "equiv_ans_cd": "\\dfrac{7}{17}", "equiv_ans_axd": "765", "equiv_ans_bxc": "945", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0004"}}, {"seed": 5, "data": {"simplify_prob": "\\dfrac{70}{84}", "simplify_ans": "\\dfrac{5}{6}", "factors_list": ["2", "7"], "factors_sequence": "2 and 7", "convert_prob": "2\\frac{1}{4}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{9}{4}", "equiv_prob_a": "2", "equiv_prob_b": "11", "equiv_prob_c": "3", "equiv_prob_d": "11", "equiv_prob_ab": "\\dfrac{2}{11}", "equiv_prob_cd": "\\dfrac{3}{11}", "equiv_ans_ab": "\\dfrac{2}{11}", "equiv_ans_cd": "\\dfrac{3}{11}", "equiv_ans_axd": "22", "equiv_ans_bxc": "33", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0005"}}, {"seed": 6, "data": {"simplify_prob": "\\dfrac{33}{231}", "simplify_ans": "\\dfrac{1}{7}", "factors_list": ["3", "11"], "factors_sequence": "3 and 11", "convert_prob": "8\\frac{7}{8}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{71}{8}", "equiv_prob_a": "81", "equiv_prob_b": "90", "equiv_prob_c": "77", "equiv_prob_d": "85", "equiv_prob_ab": "\\dfrac{81}{90}", "equiv_prob_cd": "\\dfrac{77}{85}", "equiv_ans_ab": "\\dfrac{9}{10}", "equiv_ans_cd": "\\dfrac{77}{85}", "equiv_ans_axd": "6885", "equiv_ans_bxc": "6930", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0006"}}, {"seed": 7, "data": {"simplify_prob": "\\dfrac{25}{375}", "simplify_ans": "\\dfrac{1}{15}", "factors_list": ["5", "5"], "factors_sequence": "5 and 5", "convert_prob": "\\dfrac{65}{11}", "convert_type": "a mixed number", "convert_ans": "5\\frac{10}{11}", "equiv_prob_a": "45", "equiv_prob_b": "60", "equiv_prob_c": "57", "equiv_prob_d": "76", "equiv_prob_ab": "\\dfrac{45}{60}", "equiv_prob_cd": "\\dfrac{57}{76}", "equiv_ans_ab": "\\dfrac{3}{4}", "equiv_ans_cd": "\\dfrac{3}{4}", "equiv_ans_axd": "3420", "equiv_ans_bxc": "3420", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0007"}}, {"seed": 8, "data": {"simplify_prob": "\\dfrac{21}{105}", "simplify_ans": "\\dfrac{1}{5}", "factors_list": ["3", "7"], "factors_sequence": "3 and 7", "convert_prob": "4\\frac{5}{7}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{33}{7}", "equiv_prob_a": "126", "equiv_prob_b": "198", "equiv_prob_c": "154", "equiv_prob_d": "242", "equiv_prob_ab": "\\dfrac{126}{198}", "equiv_prob_cd": "\\dfrac{154}{242}", "equiv_ans_ab": "\\dfrac{7}{11}", "equiv_ans_cd": "\\dfrac{7}{11}", "equiv_ans_axd": "30492", "equiv_ans_bxc": "30492", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0008"}}, {"seed": 9, "data": {"simplify_prob": "\\dfrac{99}{154}", "simplify_ans": "\\dfrac{9}{14}", "factors_list": ["11"], "factors_sequence": "11", "convert_prob": "\\dfrac{107}{14}", "convert_type": "a mixed number", "convert_ans": "7\\frac{9}{14}", "equiv_prob_a": "25", "equiv_prob_b": "70", "equiv_prob_c": "26", "equiv_prob_d": "72", "equiv_prob_ab": "\\dfrac{25}{70}", "equiv_prob_cd": "\\dfrac{26}{72}", "equiv_ans_ab": "\\dfrac{5}{14}", "equiv_ans_cd": "\\dfrac{13}{36}", "equiv_ans_axd": "1800", "equiv_ans_bxc": "1820", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0009"}}, {"seed": 10, "data": {"simplify_prob": "\\dfrac{14}{105}", "simplify_ans": "\\dfrac{2}{15}", "factors_list": ["7"], "factors_sequence": "7", "convert_prob": "\\dfrac{23}{3}", "convert_type": "a mixed number", "convert_ans": "7\\frac{2}{3}", "equiv_prob_a": "154", "equiv_prob_b": "182", "equiv_prob_c": "165", "equiv_prob_d": "195", "equiv_prob_ab": "\\dfrac{154}{182}", "equiv_prob_cd": "\\dfrac{165}{195}", "equiv_ans_ab": "\\dfrac{11}{13}", "equiv_ans_cd": "\\dfrac{11}{13}", "equiv_ans_axd": "30030", "equiv_ans_bxc": "30030", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0010"}}, {"seed": 11, "data": {"simplify_prob": "\\dfrac{54}{324}", "simplify_ans": "\\dfrac{1}{6}", "factors_list": ["2", "3", "3", "3"], "factors_sequence": "2, 3, 3, and 3", "convert_prob": "4\\frac{5}{7}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{33}{7}", "equiv_prob_a": "55", "equiv_prob_b": "66", "equiv_prob_c": "48", "equiv_prob_d": "60", "equiv_prob_ab": "\\dfrac{55}{66}", "equiv_prob_cd": "\\dfrac{48}{60}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{4}{5}", "equiv_ans_axd": "3300", "equiv_ans_bxc": "3168", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0011"}}, {"seed": 12, "data": {"simplify_prob": "\\dfrac{180}{280}", "simplify_ans": "\\dfrac{9}{14}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "\\dfrac{23}{6}", "convert_type": "a mixed number", "convert_ans": "3\\frac{5}{6}", "equiv_prob_a": "70", "equiv_prob_b": "130", "equiv_prob_c": "56", "equiv_prob_d": "104", "equiv_prob_ab": "\\dfrac{70}{130}", "equiv_prob_cd": "\\dfrac{56}{104}", "equiv_ans_ab": "\\dfrac{7}{13}", "equiv_ans_cd": "\\dfrac{7}{13}", "equiv_ans_axd": "7280", "equiv_ans_bxc": "7280", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows 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"\\dfrac{5}{55}", "equiv_prob_cd": "\\dfrac{9}{57}", "equiv_ans_ab": "\\dfrac{1}{11}", "equiv_ans_cd": "\\dfrac{3}{19}", "equiv_ans_axd": "285", "equiv_ans_bxc": "495", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0977"}}, {"seed": 978, "data": {"simplify_prob": "\\dfrac{42}{196}", "simplify_ans": "\\dfrac{3}{14}", "factors_list": ["2", "7"], "factors_sequence": "2 and 7", "convert_prob": "4\\frac{1}{9}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{37}{9}", "equiv_prob_a": "20", "equiv_prob_b": "200", "equiv_prob_c": "17", "equiv_prob_d": "170", "equiv_prob_ab": "\\dfrac{20}{200}", "equiv_prob_cd": "\\dfrac{17}{170}", "equiv_ans_ab": "\\dfrac{1}{10}", "equiv_ans_cd": "\\dfrac{1}{10}", "equiv_ans_axd": "3400", "equiv_ans_bxc": "3400", "equiv_ans_supp_1": "The fractions are equivalent, 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"\\dfrac{120}{195}", "simplify_ans": "\\dfrac{8}{13}", "factors_list": ["3", "5"], "factors_sequence": "3 and 5", "convert_prob": "\\dfrac{29}{4}", "convert_type": "a mixed number", "convert_ans": "7\\frac{1}{4}", "equiv_prob_a": "15", "equiv_prob_b": "45", "equiv_prob_c": "11", "equiv_prob_d": "33", "equiv_prob_ab": "\\dfrac{15}{45}", "equiv_prob_cd": "\\dfrac{11}{33}", "equiv_ans_ab": "\\dfrac{1}{3}", "equiv_ans_cd": "\\dfrac{1}{3}", "equiv_ans_axd": "495", "equiv_ans_bxc": "495", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0980"}}, {"seed": 981, "data": {"simplify_prob": "\\dfrac{66}{396}", "simplify_ans": "\\dfrac{1}{6}", "factors_list": ["2", "3", "11"], "factors_sequence": "2, 3, and 11", "convert_prob": "\\dfrac{26}{7}", "convert_type": "a mixed number", "convert_ans": "3\\frac{5}{7}", "equiv_prob_a": "100", "equiv_prob_b": "160", "equiv_prob_c": "115", "equiv_prob_d": "184", "equiv_prob_ab": "\\dfrac{100}{160}", "equiv_prob_cd": "\\dfrac{115}{184}", "equiv_ans_ab": "\\dfrac{5}{8}", "equiv_ans_cd": "\\dfrac{5}{8}", "equiv_ans_axd": "18400", "equiv_ans_bxc": "18400", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0981"}}, {"seed": 982, "data": {"simplify_prob": "\\dfrac{286}{330}", "simplify_ans": "\\dfrac{13}{15}", "factors_list": ["2", "11"], "factors_sequence": "2 and 11", "convert_prob": "\\dfrac{38}{9}", "convert_type": "a mixed number", "convert_ans": "4\\frac{2}{9}", "equiv_prob_a": "18", "equiv_prob_b": "33", "equiv_prob_c": "22", "equiv_prob_d": "39", "equiv_prob_ab": "\\dfrac{18}{33}", "equiv_prob_cd": "\\dfrac{22}{39}", "equiv_ans_ab": "\\dfrac{6}{11}", "equiv_ans_cd": "\\dfrac{22}{39}", "equiv_ans_axd": "702", "equiv_ans_bxc": "726", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0982"}}, {"seed": 983, "data": {"simplify_prob": "\\dfrac{36}{504}", "simplify_ans": "\\dfrac{1}{14}", "factors_list": ["2", "2", "3", "3"], "factors_sequence": "2, 2, 3, and 3", "convert_prob": "6\\frac{4}{9}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{58}{9}", "equiv_prob_a": "40", "equiv_prob_b": "48", "equiv_prob_c": "46", "equiv_prob_d": "56", "equiv_prob_ab": "\\dfrac{40}{48}", "equiv_prob_cd": "\\dfrac{46}{56}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{23}{28}", "equiv_ans_axd": "2240", "equiv_ans_bxc": "2208", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0983"}}, {"seed": 984, "data": {"simplify_prob": "\\dfrac{40}{220}", "simplify_ans": "\\dfrac{2}{11}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "6\\frac{9}{11}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{75}{11}", "equiv_prob_a": "65", "equiv_prob_b": "75", "equiv_prob_c": "39", "equiv_prob_d": "45", "equiv_prob_ab": "\\dfrac{65}{75}", "equiv_prob_cd": "\\dfrac{39}{45}", "equiv_ans_ab": "\\dfrac{13}{15}", "equiv_ans_cd": "\\dfrac{13}{15}", "equiv_ans_axd": "2925", "equiv_ans_bxc": "2925", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0984"}}, {"seed": 985, "data": {"simplify_prob": "\\dfrac{110}{264}", "simplify_ans": "\\dfrac{5}{12}", "factors_list": ["2", "11"], "factors_sequence": "2 and 11", "convert_prob": "\\dfrac{91}{15}", "convert_type": "a mixed number", "convert_ans": "6\\frac{1}{15}", "equiv_prob_a": "36", "equiv_prob_b": "42", "equiv_prob_c": "24", "equiv_prob_d": "28", "equiv_prob_ab": "\\dfrac{36}{42}", "equiv_prob_cd": "\\dfrac{24}{28}", "equiv_ans_ab": "\\dfrac{6}{7}", "equiv_ans_cd": "\\dfrac{6}{7}", "equiv_ans_axd": "1008", "equiv_ans_bxc": "1008", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0985"}}, {"seed": 986, "data": {"simplify_prob": "\\dfrac{165}{495}", "simplify_ans": "\\dfrac{1}{3}", "factors_list": ["3", "5", "11"], "factors_sequence": "3, 5, and 11", "convert_prob": "\\dfrac{23}{9}", "convert_type": "a mixed number", "convert_ans": "2\\frac{5}{9}", "equiv_prob_a": "42", "equiv_prob_b": "78", "equiv_prob_c": "56", "equiv_prob_d": "104", "equiv_prob_ab": "\\dfrac{42}{78}", "equiv_prob_cd": "\\dfrac{56}{104}", "equiv_ans_ab": "\\dfrac{7}{13}", "equiv_ans_cd": "\\dfrac{7}{13}", "equiv_ans_axd": "4368", "equiv_ans_bxc": "4368", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0986"}}, {"seed": 987, "data": {"simplify_prob": "\\dfrac{160}{300}", "simplify_ans": "\\dfrac{8}{15}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "\\dfrac{79}{10}", "convert_type": "a mixed number", "convert_ans": "7\\frac{9}{10}", "equiv_prob_a": "70", "equiv_prob_b": "105", "equiv_prob_c": "62", "equiv_prob_d": "93", "equiv_prob_ab": "\\dfrac{70}{105}", "equiv_prob_cd": "\\dfrac{62}{93}", "equiv_ans_ab": "\\dfrac{2}{3}", "equiv_ans_cd": "\\dfrac{2}{3}", "equiv_ans_axd": "6510", "equiv_ans_bxc": "6510", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0987"}}, {"seed": 988, "data": {"simplify_prob": "\\dfrac{44}{396}", "simplify_ans": "\\dfrac{1}{9}", "factors_list": ["2", "2", "11"], "factors_sequence": "2, 2, and 11", "convert_prob": "6\\frac{8}{9}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{62}{9}", "equiv_prob_a": "75", "equiv_prob_b": "200", "equiv_prob_c": "69", "equiv_prob_d": "184", "equiv_prob_ab": "\\dfrac{75}{200}", "equiv_prob_cd": "\\dfrac{69}{184}", "equiv_ans_ab": "\\dfrac{3}{8}", "equiv_ans_cd": "\\dfrac{3}{8}", "equiv_ans_axd": "13800", "equiv_ans_bxc": "13800", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0988"}}, {"seed": 989, "data": {"simplify_prob": "\\dfrac{77}{231}", "simplify_ans": "\\dfrac{1}{3}", "factors_list": ["7", "11"], "factors_sequence": "7 and 11", "convert_prob": "\\dfrac{11}{4}", "convert_type": "a mixed number", "convert_ans": "2\\frac{3}{4}", "equiv_prob_a": "40", "equiv_prob_b": "56", "equiv_prob_c": "60", "equiv_prob_d": "84", "equiv_prob_ab": "\\dfrac{40}{56}", "equiv_prob_cd": "\\dfrac{60}{84}", "equiv_ans_ab": "\\dfrac{5}{7}", "equiv_ans_cd": "\\dfrac{5}{7}", "equiv_ans_axd": "3360", "equiv_ans_bxc": "3360", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0989"}}, {"seed": 990, "data": {"simplify_prob": "\\dfrac{120}{480}", "simplify_ans": "\\dfrac{1}{4}", "factors_list": ["2", "2", "2", "3", "5"], "factors_sequence": "2, 2, 2, 3, and 5", "convert_prob": "\\dfrac{91}{11}", "convert_type": "a mixed number", "convert_ans": "8\\frac{3}{11}", "equiv_prob_a": "5", "equiv_prob_b": "45", "equiv_prob_c": "12", "equiv_prob_d": "51", "equiv_prob_ab": "\\dfrac{5}{45}", "equiv_prob_cd": "\\dfrac{12}{51}", "equiv_ans_ab": "\\dfrac{1}{9}", "equiv_ans_cd": "\\dfrac{4}{17}", "equiv_ans_axd": "255", "equiv_ans_bxc": "540", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0990"}}, {"seed": 991, "data": {"simplify_prob": "\\dfrac{231}{308}", "simplify_ans": "\\dfrac{3}{4}", "factors_list": ["7", "11"], "factors_sequence": "7 and 11", "convert_prob": "\\dfrac{23}{4}", "convert_type": "a mixed number", "convert_ans": "5\\frac{3}{4}", "equiv_prob_a": "6", "equiv_prob_b": "28", "equiv_prob_c": "1", "equiv_prob_d": "21", "equiv_prob_ab": "\\dfrac{6}{28}", "equiv_prob_cd": "\\dfrac{1}{21}", "equiv_ans_ab": "\\dfrac{3}{14}", "equiv_ans_cd": "\\dfrac{1}{21}", "equiv_ans_axd": "126", "equiv_ans_bxc": "28", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0991"}}, {"seed": 992, "data": {"simplify_prob": "\\dfrac{495}{585}", "simplify_ans": "\\dfrac{11}{13}", "factors_list": ["3", "3", "5"], "factors_sequence": "3, 3, and 5", "convert_prob": "\\dfrac{43}{12}", "convert_type": "a mixed number", "convert_ans": "3\\frac{7}{12}", "equiv_prob_a": "25", "equiv_prob_b": "75", "equiv_prob_c": "24", "equiv_prob_d": "72", "equiv_prob_ab": "\\dfrac{25}{75}", "equiv_prob_cd": "\\dfrac{24}{72}", "equiv_ans_ab": "\\dfrac{1}{3}", "equiv_ans_cd": "\\dfrac{1}{3}", "equiv_ans_axd": "1800", "equiv_ans_bxc": "1800", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0992"}}, {"seed": 993, "data": {"simplify_prob": "\\dfrac{220}{240}", "simplify_ans": "\\dfrac{11}{12}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "5\\frac{3}{10}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{53}{10}", "equiv_prob_a": "50", "equiv_prob_b": "65", "equiv_prob_c": "47", "equiv_prob_d": "60", "equiv_prob_ab": "\\dfrac{50}{65}", "equiv_prob_cd": "\\dfrac{47}{60}", "equiv_ans_ab": "\\dfrac{10}{13}", "equiv_ans_cd": "\\dfrac{47}{60}", "equiv_ans_axd": "3000", "equiv_ans_bxc": "3055", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0993"}}, {"seed": 994, "data": {"simplify_prob": "\\dfrac{216}{288}", "simplify_ans": "\\dfrac{3}{4}", "factors_list": ["2", "2", "2", "3", "3"], "factors_sequence": "2, 2, 2, 3, and 3", "convert_prob": "\\dfrac{88}{13}", "convert_type": "a mixed number", "convert_ans": "6\\frac{10}{13}", "equiv_prob_a": "75", "equiv_prob_b": "200", "equiv_prob_c": "78", "equiv_prob_d": "208", "equiv_prob_ab": "\\dfrac{75}{200}", "equiv_prob_cd": "\\dfrac{78}{208}", "equiv_ans_ab": "\\dfrac{3}{8}", "equiv_ans_cd": "\\dfrac{3}{8}", "equiv_ans_axd": "15600", "equiv_ans_bxc": "15600", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0994"}}, {"seed": 995, "data": {"simplify_prob": "\\dfrac{231}{315}", "simplify_ans": "\\dfrac{11}{15}", "factors_list": ["3", "7"], "factors_sequence": "3 and 7", "convert_prob": "7\\frac{5}{6}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{47}{6}", "equiv_prob_a": "21", "equiv_prob_b": "49", "equiv_prob_c": "12", "equiv_prob_d": "28", "equiv_prob_ab": "\\dfrac{21}{49}", "equiv_prob_cd": "\\dfrac{12}{28}", "equiv_ans_ab": "\\dfrac{3}{7}", "equiv_ans_cd": "\\dfrac{3}{7}", "equiv_ans_axd": "588", "equiv_ans_bxc": "588", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0995"}}, {"seed": 996, "data": {"simplify_prob": "\\dfrac{378}{546}", "simplify_ans": "\\dfrac{9}{13}", "factors_list": ["2", "3", "7"], "factors_sequence": "2, 3, and 7", "convert_prob": "\\dfrac{33}{13}", "convert_type": "a mixed number", "convert_ans": "2\\frac{7}{13}", "equiv_prob_a": "4", "equiv_prob_b": "36", "equiv_prob_c": "8", "equiv_prob_d": "38", "equiv_prob_ab": "\\dfrac{4}{36}", "equiv_prob_cd": "\\dfrac{8}{38}", "equiv_ans_ab": "\\dfrac{1}{9}", "equiv_ans_cd": "\\dfrac{4}{19}", "equiv_ans_axd": "152", "equiv_ans_bxc": "288", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0996"}}, {"seed": 997, "data": {"simplify_prob": "\\dfrac{44}{528}", "simplify_ans": "\\dfrac{1}{12}", "factors_list": ["2", "2", "11"], "factors_sequence": "2, 2, and 11", "convert_prob": "5\\frac{1}{3}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{16}{3}", "equiv_prob_a": "100", "equiv_prob_b": "120", "equiv_prob_c": "90", "equiv_prob_d": "108", "equiv_prob_ab": "\\dfrac{100}{120}", "equiv_prob_cd": "\\dfrac{90}{108}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{5}{6}", "equiv_ans_axd": "10800", "equiv_ans_bxc": "10800", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0997"}}, {"seed": 998, "data": {"simplify_prob": "\\dfrac{352}{572}", "simplify_ans": "\\dfrac{8}{13}", "factors_list": ["2", "2", "11"], "factors_sequence": "2, 2, and 11", "convert_prob": "5\\frac{2}{5}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{27}{5}", "equiv_prob_a": "45", "equiv_prob_b": "50", "equiv_prob_c": "46", "equiv_prob_d": "53", "equiv_prob_ab": "\\dfrac{45}{50}", "equiv_prob_cd": "\\dfrac{46}{53}", "equiv_ans_ab": "\\dfrac{9}{10}", "equiv_ans_cd": "\\dfrac{46}{53}", "equiv_ans_axd": "2385", "equiv_ans_bxc": "2300", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0998"}}, {"seed": 999, "data": {"simplify_prob": "\\dfrac{150}{500}", "simplify_ans": "\\dfrac{3}{10}", "factors_list": ["2", "5", "5"], "factors_sequence": "2, 5, and 5", "convert_prob": "5\\frac{1}{4}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{21}{4}", "equiv_prob_a": "64", "equiv_prob_b": "176", "equiv_prob_c": "76", "equiv_prob_d": "209", "equiv_prob_ab": "\\dfrac{64}{176}", "equiv_prob_cd": "\\dfrac{76}{209}", "equiv_ans_ab": "\\dfrac{4}{11}", "equiv_ans_cd": "\\dfrac{4}{11}", "equiv_ans_axd": "13376", "equiv_ans_bxc": "13376", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0999"}}]}, {"title": "Modeling Fractions", "slug": "F2", "description": "\n I can construct both number line and area models for fractions.\n ", "template": "\n\n \n \n

\\begin{CD} A @>a>> B \\\\ @VbVV @AAcA \\\\ C @= D \\end{CD}

\n
\n \n

This is a test.

\n
\n
\n \n
\n", "exercises": [{"seed": 0, "data": {"__seed__": "0000"}}, {"seed": 1, "data": {"__seed__": "0001"}}, {"seed": 2, "data": {"__seed__": "0002"}}, {"seed": 3, "data": {"__seed__": "0003"}}, {"seed": 4, "data": {"__seed__": "0004"}}, {"seed": 5, "data": {"__seed__": "0005"}}, {"seed": 6, "data": {"__seed__": "0006"}}, {"seed": 7, "data": {"__seed__": "0007"}}, {"seed": 8, "data": {"__seed__": "0008"}}, {"seed": 9, "data": {"__seed__": "0009"}}, {"seed": 10, "data": {"__seed__": "0010"}}, {"seed": 11, "data": {"__seed__": "0011"}}, {"seed": 12, "data": {"__seed__": "0012"}}, {"seed": 13, "data": {"__seed__": "0013"}}, {"seed": 14, "data": {"__seed__": "0014"}}, {"seed": 15, "data": {"__seed__": "0015"}}, {"seed": 16, "data": {"__seed__": "0016"}}, {"seed": 17, "data": {"__seed__": "0017"}}, {"seed": 18, "data": {"__seed__": "0018"}}, {"seed": 19, "data": {"__seed__": "0019"}}, {"seed": 20, "data": {"__seed__": "0020"}}, {"seed": 21, "data": {"__seed__": "0021"}}, {"seed": 22, "data": {"__seed__": "0022"}}, {"seed": 23, "data": {"__seed__": "0023"}}, {"seed": 24, "data": {"__seed__": "0024"}}, {"seed": 25, "data": {"__seed__": "0025"}}, {"seed": 26, "data": {"__seed__": "0026"}}, {"seed": 27, "data": {"__seed__": "0027"}}, {"seed": 28, "data": {"__seed__": "0028"}}, {"seed": 29, "data": {"__seed__": "0029"}}, {"seed": 30, "data": {"__seed__": "0030"}}, {"seed": 31, "data": {"__seed__": "0031"}}, {"seed": 32, "data": {"__seed__": "0032"}}, {"seed": 33, "data": {"__seed__": "0033"}}, {"seed": 34, "data": {"__seed__": "0034"}}, {"seed": 35, "data": {"__seed__": "0035"}}, {"seed": 36, "data": {"__seed__": "0036"}}, {"seed": 37, "data": {"__seed__": "0037"}}, {"seed": 38, "data": {"__seed__": "0038"}}, {"seed": 39, "data": {"__seed__": "0039"}}, {"seed": 40, "data": {"__seed__": "0040"}}, {"seed": 41, "data": {"__seed__": "0041"}}, {"seed": 42, "data": {"__seed__": "0042"}}, {"seed": 43, "data": {"__seed__": "0043"}}, {"seed": 44, "data": {"__seed__": "0044"}}, {"seed": 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{"__seed__": "0861"}}, {"seed": 862, "data": {"__seed__": "0862"}}, {"seed": 863, "data": {"__seed__": "0863"}}, {"seed": 864, "data": {"__seed__": "0864"}}, {"seed": 865, "data": {"__seed__": "0865"}}, {"seed": 866, "data": {"__seed__": "0866"}}, {"seed": 867, "data": {"__seed__": "0867"}}, {"seed": 868, "data": {"__seed__": "0868"}}, {"seed": 869, "data": {"__seed__": "0869"}}, {"seed": 870, "data": {"__seed__": "0870"}}, {"seed": 871, "data": {"__seed__": "0871"}}, {"seed": 872, "data": {"__seed__": "0872"}}, {"seed": 873, "data": {"__seed__": "0873"}}, {"seed": 874, "data": {"__seed__": "0874"}}, {"seed": 875, "data": {"__seed__": "0875"}}, {"seed": 876, "data": {"__seed__": "0876"}}, {"seed": 877, "data": {"__seed__": "0877"}}, {"seed": 878, "data": {"__seed__": "0878"}}, {"seed": 879, "data": {"__seed__": "0879"}}, {"seed": 880, "data": {"__seed__": "0880"}}, {"seed": 881, "data": {"__seed__": "0881"}}, {"seed": 882, "data": {"__seed__": "0882"}}, {"seed": 883, "data": {"__seed__": "0883"}}, {"seed": 884, "data": {"__seed__": "0884"}}, {"seed": 885, "data": {"__seed__": "0885"}}, {"seed": 886, "data": {"__seed__": "0886"}}, {"seed": 887, "data": {"__seed__": "0887"}}, {"seed": 888, "data": {"__seed__": "0888"}}, {"seed": 889, "data": {"__seed__": "0889"}}, {"seed": 890, "data": {"__seed__": "0890"}}, {"seed": 891, "data": {"__seed__": "0891"}}, {"seed": 892, "data": {"__seed__": "0892"}}, {"seed": 893, "data": {"__seed__": "0893"}}, {"seed": 894, "data": {"__seed__": "0894"}}, {"seed": 895, "data": {"__seed__": "0895"}}, {"seed": 896, "data": {"__seed__": "0896"}}, {"seed": 897, "data": {"__seed__": "0897"}}, {"seed": 898, "data": {"__seed__": "0898"}}, {"seed": 899, "data": {"__seed__": "0899"}}, {"seed": 900, "data": {"__seed__": "0900"}}, {"seed": 901, "data": {"__seed__": "0901"}}, {"seed": 902, "data": {"__seed__": "0902"}}, {"seed": 903, "data": {"__seed__": "0903"}}, {"seed": 904, "data": {"__seed__": "0904"}}, {"seed": 905, "data": {"__seed__": "0905"}}, {"seed": 906, "data": {"__seed__": "0906"}}, {"seed": 907, "data": {"__seed__": "0907"}}, {"seed": 908, "data": {"__seed__": "0908"}}, {"seed": 909, "data": {"__seed__": "0909"}}, {"seed": 910, "data": {"__seed__": "0910"}}, {"seed": 911, "data": {"__seed__": "0911"}}, {"seed": 912, "data": {"__seed__": "0912"}}, {"seed": 913, "data": {"__seed__": "0913"}}, {"seed": 914, "data": {"__seed__": "0914"}}, {"seed": 915, "data": {"__seed__": "0915"}}, {"seed": 916, "data": {"__seed__": "0916"}}, {"seed": 917, "data": {"__seed__": "0917"}}, {"seed": 918, "data": {"__seed__": "0918"}}, {"seed": 919, "data": {"__seed__": "0919"}}, {"seed": 920, "data": {"__seed__": "0920"}}, {"seed": 921, "data": {"__seed__": "0921"}}, {"seed": 922, "data": {"__seed__": "0922"}}, {"seed": 923, "data": {"__seed__": "0923"}}, {"seed": 924, "data": {"__seed__": "0924"}}, {"seed": 925, "data": {"__seed__": "0925"}}, {"seed": 926, "data": {"__seed__": "0926"}}, {"seed": 927, "data": {"__seed__": "0927"}}, {"seed": 928, "data": {"__seed__": "0928"}}, {"seed": 929, "data": {"__seed__": "0929"}}, {"seed": 930, "data": {"__seed__": "0930"}}, {"seed": 931, "data": {"__seed__": "0931"}}, {"seed": 932, "data": {"__seed__": "0932"}}, {"seed": 933, "data": {"__seed__": "0933"}}, {"seed": 934, "data": {"__seed__": "0934"}}, {"seed": 935, "data": {"__seed__": "0935"}}, {"seed": 936, "data": {"__seed__": "0936"}}, {"seed": 937, "data": {"__seed__": "0937"}}, {"seed": 938, "data": {"__seed__": "0938"}}, {"seed": 939, "data": {"__seed__": "0939"}}, {"seed": 940, "data": {"__seed__": "0940"}}, {"seed": 941, "data": {"__seed__": "0941"}}, {"seed": 942, "data": {"__seed__": "0942"}}, {"seed": 943, "data": {"__seed__": "0943"}}, {"seed": 944, "data": {"__seed__": "0944"}}, {"seed": 945, "data": {"__seed__": "0945"}}, {"seed": 946, "data": {"__seed__": "0946"}}, {"seed": 947, "data": {"__seed__": "0947"}}, {"seed": 948, "data": {"__seed__": "0948"}}, {"seed": 949, "data": {"__seed__": "0949"}}, {"seed": 950, "data": {"__seed__": "0950"}}, {"seed": 951, "data": {"__seed__": "0951"}}, {"seed": 952, "data": {"__seed__": "0952"}}, {"seed": 953, "data": {"__seed__": "0953"}}, {"seed": 954, "data": {"__seed__": "0954"}}, {"seed": 955, "data": {"__seed__": "0955"}}, {"seed": 956, "data": {"__seed__": "0956"}}, {"seed": 957, "data": {"__seed__": "0957"}}, {"seed": 958, "data": {"__seed__": "0958"}}, {"seed": 959, "data": {"__seed__": "0959"}}, {"seed": 960, "data": {"__seed__": "0960"}}, {"seed": 961, "data": {"__seed__": "0961"}}, {"seed": 962, "data": {"__seed__": "0962"}}, {"seed": 963, "data": {"__seed__": "0963"}}, {"seed": 964, "data": {"__seed__": "0964"}}, {"seed": 965, "data": {"__seed__": "0965"}}, {"seed": 966, "data": {"__seed__": "0966"}}, {"seed": 967, "data": {"__seed__": "0967"}}, {"seed": 968, "data": {"__seed__": "0968"}}, {"seed": 969, "data": {"__seed__": "0969"}}, {"seed": 970, "data": {"__seed__": "0970"}}, {"seed": 971, "data": {"__seed__": "0971"}}, {"seed": 972, "data": {"__seed__": "0972"}}, {"seed": 973, "data": {"__seed__": "0973"}}, {"seed": 974, "data": {"__seed__": "0974"}}, {"seed": 975, "data": {"__seed__": "0975"}}, {"seed": 976, "data": {"__seed__": "0976"}}, {"seed": 977, "data": {"__seed__": "0977"}}, {"seed": 978, "data": {"__seed__": "0978"}}, {"seed": 979, "data": {"__seed__": "0979"}}, {"seed": 980, "data": {"__seed__": "0980"}}, {"seed": 981, "data": {"__seed__": "0981"}}, {"seed": 982, "data": {"__seed__": "0982"}}, {"seed": 983, "data": {"__seed__": "0983"}}, {"seed": 984, "data": {"__seed__": "0984"}}, {"seed": 985, "data": {"__seed__": "0985"}}, {"seed": 986, "data": {"__seed__": "0986"}}, {"seed": 987, "data": {"__seed__": "0987"}}, {"seed": 988, "data": {"__seed__": "0988"}}, {"seed": 989, "data": {"__seed__": "0989"}}, {"seed": 990, "data": {"__seed__": "0990"}}, {"seed": 991, "data": {"__seed__": "0991"}}, {"seed": 992, "data": {"__seed__": "0992"}}, {"seed": 993, "data": {"__seed__": "0993"}}, {"seed": 994, "data": {"__seed__": "0994"}}, {"seed": 995, "data": {"__seed__": "0995"}}, {"seed": 996, "data": {"__seed__": "0996"}}, {"seed": 997, "data": {"__seed__": "0997"}}, {"seed": 998, "data": {"__seed__": "0998"}}, {"seed": 999, "data": {"__seed__": "0999"}}]}, {"title": "Decimal Place Values", "slug": "D1", "description": "\n I can identify place values in decimal numbers using both numerical notation and English words, and represent decimal numbers using base-ten blocks.\n ", "template": "\n\n \n \n

Consider the number {{pv_dec_string}}. Identify and name each of the place values used in this number. Write these names using both a numerical label (e.g. ``10s'') and an English-word label (e.g. ``tens'').

\n
\n \n

{{pv_ans_text}}

\n
\n
\n \n \n

Using {{units_block_choice}} to represent the units, draw a base-ten block representation of the number {{blocks_dec}}.

\n
\n \n

{{blocks_ans_text}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"pv_dec_string": "992,477.06389", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.153", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0000"}}, {"seed": 1, "data": {"pv_dec_string": "407.326049", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0001"}}, {"seed": 2, "data": {"pv_dec_string": "655,514.5852", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 6 small cubes", "__seed__": "0002"}}, {"seed": 3, "data": {"pv_dec_string": "4,587,850.6053", "pv_ans_text": "4 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0003"}}, {"seed": 4, "data": {"pv_dec_string": "97,816.15361", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.21", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 1 longs, and 0 small cubes", "__seed__": "0004"}}, {"seed": 5, "data": {"pv_dec_string": "6,992,669.2169", "pv_ans_text": "6 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 3 small cubes", "__seed__": "0005"}}, {"seed": 6, "data": {"pv_dec_string": "340,774.7684", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0006"}}, {"seed": 7, "data": {"pv_dec_string": "694.001913", "pv_ans_text": "6 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.224", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0007"}}, {"seed": 8, "data": {"pv_dec_string": "16,796.13469", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 5 small cubes", "__seed__": "0008"}}, {"seed": 9, "data": {"pv_dec_string": "674.260836", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 2 small cubes", "__seed__": "0009"}}, {"seed": 10, "data": {"pv_dec_string": "13,886.67734", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.12", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0010"}}, {"seed": 11, "data": {"pv_dec_string": "200,967.34713", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 3 small cubes", "__seed__": "0011"}}, {"seed": 12, "data": {"pv_dec_string": "4,836.450036", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.633", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 3 small cubes", "__seed__": "0012"}}, {"seed": 13, "data": {"pv_dec_string": "8,292.218899", "pv_ans_text": "8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.240", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0013"}}, {"seed": 14, "data": {"pv_dec_string": "9,992.054838", "pv_ans_text": "9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.63", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0014"}}, {"seed": 15, "data": {"pv_dec_string": "429,974.7998", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.451", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0015"}}, {"seed": 16, "data": {"pv_dec_string": "2,964,739.9292", "pv_ans_text": "2 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.015", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 1 longs, and 5 small cubes", "__seed__": "0016"}}, {"seed": 17, "data": {"pv_dec_string": "321.376057", "pv_ans_text": "3 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.14", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0017"}}, {"seed": 18, "data": {"pv_dec_string": "533,698.3724", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0018"}}, {"seed": 19, "data": {"pv_dec_string": "403.393733", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.15", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0019"}}, {"seed": 20, "data": {"pv_dec_string": "7,102.50037", "pv_ans_text": "7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.146", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 4 longs, and 6 small cubes", "__seed__": "0020"}}, {"seed": 21, "data": {"pv_dec_string": "757,776.806", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.134", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0021"}}, {"seed": 22, "data": {"pv_dec_string": "1,875.973392", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 2 small cubes", "__seed__": "0022"}}, {"seed": 23, "data": {"pv_dec_string": "62,079.615021", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.16", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0023"}}, {"seed": 24, "data": {"pv_dec_string": "648,443.4976", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.430", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0024"}}, {"seed": 25, "data": {"pv_dec_string": "518,926.7324", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.564", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 6 longs, and 4 small cubes", "__seed__": "0025"}}, {"seed": 26, "data": {"pv_dec_string": "932,406.3667", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0026"}}, {"seed": 27, "data": {"pv_dec_string": "7,523,929.0946", "pv_ans_text": "7 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.451", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0027"}}, {"seed": 28, "data": {"pv_dec_string": "393.686779", "pv_ans_text": "3 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.234", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0028"}}, {"seed": 29, "data": {"pv_dec_string": "865,762.2975", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.262", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 6 longs, and 2 small cubes", "__seed__": "0029"}}, {"seed": 30, "data": {"pv_dec_string": "26,417.687065", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0030"}}, {"seed": 31, "data": {"pv_dec_string": "22,341.288174", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.26", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0031"}}, {"seed": 32, "data": {"pv_dec_string": "19,278.04694", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.31", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0032"}}, {"seed": 33, "data": {"pv_dec_string": "473.688155", "pv_ans_text": "4 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0033"}}, {"seed": 34, "data": {"pv_dec_string": "87,402.01659", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.113", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0034"}}, {"seed": 35, "data": {"pv_dec_string": "1,647.31928", "pv_ans_text": "1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0035"}}, {"seed": 36, "data": {"pv_dec_string": "30,516.27952", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 2 small cubes", "__seed__": "0036"}}, {"seed": 37, "data": {"pv_dec_string": "4,832.889082", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0037"}}, {"seed": 38, "data": {"pv_dec_string": "1,772.8065", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 3 small cubes", "__seed__": "0038"}}, {"seed": 39, "data": {"pv_dec_string": "53,264.993479", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.126", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 2 longs, and 6 small cubes", "__seed__": "0039"}}, {"seed": 40, "data": {"pv_dec_string": "4,365,297.7812", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.241", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0040"}}, {"seed": 41, "data": {"pv_dec_string": "1,627,100.3801", "pv_ans_text": "1 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.265", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 6 longs, and 5 small cubes", "__seed__": "0041"}}, {"seed": 42, "data": {"pv_dec_string": "46,964.342", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 1 small cubes", "__seed__": "0042"}}, {"seed": 43, "data": {"pv_dec_string": "90,651.17785", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 4 small cubes", "__seed__": "0043"}}, {"seed": 44, "data": {"pv_dec_string": "4,338.44775", "pv_ans_text": "4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0044"}}, {"seed": 45, "data": {"pv_dec_string": "29,941.92678", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 2 small cubes", "__seed__": "0045"}}, {"seed": 46, "data": {"pv_dec_string": "584.98676", "pv_ans_text": "5 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0046"}}, {"seed": 47, "data": {"pv_dec_string": "72,433.651132", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0047"}}, {"seed": 48, "data": {"pv_dec_string": "31,395.34096", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 3 small cubes", "__seed__": "0048"}}, {"seed": 49, "data": {"pv_dec_string": "28,014.611323", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0049"}}, {"seed": 50, "data": {"pv_dec_string": "561,464.9278", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0050"}}, {"seed": 51, "data": {"pv_dec_string": "607,373.5177", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0051"}}, {"seed": 52, "data": {"pv_dec_string": "677.960078", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.013", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 1 longs, and 3 small cubes", "__seed__": "0052"}}, {"seed": 53, "data": {"pv_dec_string": "2,306.097075", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.362", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 6 longs, and 2 small cubes", "__seed__": "0053"}}, {"seed": 54, "data": {"pv_dec_string": "4,583,257.7742", "pv_ans_text": "4 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0054"}}, {"seed": 55, "data": {"pv_dec_string": "8,493,583.9491", "pv_ans_text": "8 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 6 small cubes", "__seed__": "0055"}}, {"seed": 56, "data": {"pv_dec_string": "2,824.80616", "pv_ans_text": "2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.31", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0056"}}, {"seed": 57, "data": {"pv_dec_string": "1,996.503918", "pv_ans_text": "1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.56", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0057"}}, {"seed": 58, "data": {"pv_dec_string": "29,343.38975", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.603", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 0 longs, and 3 small cubes", "__seed__": "0058"}}, {"seed": 59, "data": {"pv_dec_string": "500.83225", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.44", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0059"}}, {"seed": 60, "data": {"pv_dec_string": "53,268.40304", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.35", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0060"}}, {"seed": 61, "data": {"pv_dec_string": "39,264.05101", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.311", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0061"}}, {"seed": 62, "data": {"pv_dec_string": "39,576.04037", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0062"}}, {"seed": 63, "data": {"pv_dec_string": "42,364.61019", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.04", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0063"}}, {"seed": 64, "data": {"pv_dec_string": "88,652.682255", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.20", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0064"}}, {"seed": 65, "data": {"pv_dec_string": "4,318,513.329", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.22", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0065"}}, {"seed": 66, "data": {"pv_dec_string": "7,608.50823", "pv_ans_text": "7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0066"}}, {"seed": 67, "data": {"pv_dec_string": "402,497.43346", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 4 small cubes", "__seed__": "0067"}}, {"seed": 68, "data": {"pv_dec_string": "81,717.0742", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.62", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0068"}}, {"seed": 69, "data": {"pv_dec_string": "11,777.7422", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.344", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 4 longs, and 4 small cubes", "__seed__": "0069"}}, {"seed": 70, "data": {"pv_dec_string": "198.476117", "pv_ans_text": "1 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0070"}}, {"seed": 71, "data": {"pv_dec_string": "5,762.167245", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.05", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0071"}}, {"seed": 72, "data": {"pv_dec_string": "9,985.07097", "pv_ans_text": "9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.24", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0072"}}, {"seed": 73, "data": {"pv_dec_string": "838.930614", "pv_ans_text": "8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 1 small cubes", "__seed__": "0073"}}, {"seed": 74, "data": {"pv_dec_string": "12,380.0968", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 1 small cubes", "__seed__": "0074"}}, {"seed": 75, "data": {"pv_dec_string": "317,095.06179", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.306", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 0 longs, and 6 small cubes", "__seed__": "0075"}}, {"seed": 76, "data": {"pv_dec_string": "963,711.43543", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.32", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0076"}}, {"seed": 77, "data": {"pv_dec_string": "538,227.05194", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.453", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 3 small cubes", "__seed__": "0077"}}, {"seed": 78, "data": {"pv_dec_string": "895,304.3003", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0078"}}, {"seed": 79, "data": {"pv_dec_string": "238,893.14091", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 2 small cubes", "__seed__": "0079"}}, {"seed": 80, "data": {"pv_dec_string": "598.858435", "pv_ans_text": "5 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.11", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0080"}}, {"seed": 81, "data": {"pv_dec_string": "691,126.56081", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0081"}}, {"seed": 82, "data": {"pv_dec_string": "1,349.94995", "pv_ans_text": "1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.63", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0082"}}, {"seed": 83, "data": {"pv_dec_string": "16,436.00905", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0083"}}, {"seed": 84, "data": {"pv_dec_string": "9,922,335.7236", "pv_ans_text": "9 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.515", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 1 longs, and 5 small cubes", "__seed__": "0084"}}, {"seed": 85, "data": {"pv_dec_string": "40,408.248368", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.66", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0085"}}, {"seed": 86, "data": {"pv_dec_string": "7,394,699.9594", "pv_ans_text": "7 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 3 small cubes", "__seed__": "0086"}}, {"seed": 87, "data": {"pv_dec_string": "38,101.34148", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.24", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0087"}}, {"seed": 88, "data": {"pv_dec_string": "730,383.1446", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.16", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0088"}}, {"seed": 89, "data": {"pv_dec_string": "3,684,109.2976", "pv_ans_text": "3 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.233", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 3 small cubes", "__seed__": "0089"}}, {"seed": 90, "data": {"pv_dec_string": "361.330321", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.604", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0090"}}, {"seed": 91, "data": {"pv_dec_string": "1,784.76868", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0091"}}, {"seed": 92, "data": {"pv_dec_string": "1,741.448746", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0092"}}, {"seed": 93, "data": {"pv_dec_string": "19,117.6684", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.161", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0093"}}, {"seed": 94, "data": {"pv_dec_string": "17,738.11201", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0094"}}, {"seed": 95, "data": {"pv_dec_string": "678,951.98415", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 4 small cubes", "__seed__": "0095"}}, {"seed": 96, "data": {"pv_dec_string": "545,144.93441", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 4 small cubes", "__seed__": "0096"}}, {"seed": 97, "data": {"pv_dec_string": "651.907127", "pv_ans_text": "6 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.61", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0097"}}, {"seed": 98, "data": {"pv_dec_string": "5,194.720551", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.463", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0098"}}, {"seed": 99, "data": {"pv_dec_string": "704,813.24581", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0099"}}, {"seed": 100, "data": {"pv_dec_string": "37,416.4489", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.06", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0100"}}, {"seed": 101, "data": {"pv_dec_string": "475,481.6849", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0101"}}, {"seed": 102, "data": {"pv_dec_string": "5,514,913.2553", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 3 small cubes", "__seed__": "0102"}}, {"seed": 103, "data": {"pv_dec_string": "354,128.4416", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.314", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 1 longs, and 4 small cubes", "__seed__": "0103"}}, {"seed": 104, "data": {"pv_dec_string": "9,369,564.9145", "pv_ans_text": "9 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.56", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0104"}}, {"seed": 105, "data": {"pv_dec_string": "146.611524", "pv_ans_text": "1 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.66", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0105"}}, {"seed": 106, "data": {"pv_dec_string": "8,168,300.1658", "pv_ans_text": "8 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.165", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 6 longs, and 5 small cubes", "__seed__": "0106"}}, {"seed": 107, "data": {"pv_dec_string": "825,480.7", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.604", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0107"}}, {"seed": 108, "data": {"pv_dec_string": "1,120,336.1523", "pv_ans_text": "1 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0108"}}, {"seed": 109, "data": {"pv_dec_string": "922,023.3657", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 4 small cubes", "__seed__": "0109"}}, {"seed": 110, "data": {"pv_dec_string": "6,553,961.9043", "pv_ans_text": "6 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0110"}}, {"seed": 111, "data": {"pv_dec_string": "63,430.1771", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 6 small cubes", "__seed__": "0111"}}, {"seed": 112, "data": {"pv_dec_string": "790.801038", "pv_ans_text": "7 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.566", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0112"}}, {"seed": 113, "data": {"pv_dec_string": "2,758,652.7832", "pv_ans_text": "2 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0113"}}, {"seed": 114, "data": {"pv_dec_string": "2,610.802021", "pv_ans_text": "2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.22", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0114"}}, {"seed": 115, "data": {"pv_dec_string": "2,173.03828", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.60", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0115"}}, {"seed": 116, "data": {"pv_dec_string": "1,143,995.8764", "pv_ans_text": "1 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.536", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0116"}}, {"seed": 117, "data": {"pv_dec_string": "86,295.873746", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0117"}}, {"seed": 118, "data": {"pv_dec_string": "1,074.74787", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 3 small cubes", "__seed__": "0118"}}, {"seed": 119, "data": {"pv_dec_string": "32,025.1136", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.364", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 4 small cubes", "__seed__": "0119"}}, {"seed": 120, "data": {"pv_dec_string": "60,558.5821", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.015", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 1 longs, and 5 small cubes", "__seed__": "0120"}}, {"seed": 121, "data": {"pv_dec_string": "9,055,350.9353", "pv_ans_text": "9 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0121"}}, {"seed": 122, "data": {"pv_dec_string": "17,264.53662", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 5 small cubes", "__seed__": "0122"}}, {"seed": 123, "data": {"pv_dec_string": "6,089.24182", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.66", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0123"}}, {"seed": 124, "data": {"pv_dec_string": "5,521.426033", "pv_ans_text": "5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.430", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0124"}}, {"seed": 125, "data": {"pv_dec_string": "1,506.46677", "pv_ans_text": "1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0125"}}, {"seed": 126, "data": {"pv_dec_string": "7,943.989748", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 1 small cubes", "__seed__": "0126"}}, {"seed": 127, "data": {"pv_dec_string": "348.861057", "pv_ans_text": "3 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.16", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0127"}}, {"seed": 128, "data": {"pv_dec_string": "508.721162", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0128"}}, {"seed": 129, "data": {"pv_dec_string": "81,520.795543", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.306", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 0 longs, and 6 small cubes", "__seed__": "0129"}}, {"seed": 130, "data": {"pv_dec_string": "2,424,866.5305", "pv_ans_text": "2 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.544", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0130"}}, {"seed": 131, "data": {"pv_dec_string": "3,738.07431", "pv_ans_text": "3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0131"}}, {"seed": 132, "data": {"pv_dec_string": "79,859.81686", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 5 small cubes", "__seed__": "0132"}}, {"seed": 133, "data": {"pv_dec_string": "135.78469", "pv_ans_text": "1 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.10", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0133"}}, {"seed": 134, "data": {"pv_dec_string": "921,114.91765", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0134"}}, {"seed": 135, "data": {"pv_dec_string": "217,096.71213", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0135"}}, {"seed": 136, "data": {"pv_dec_string": "742.233794", "pv_ans_text": "7 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.550", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0136"}}, {"seed": 137, "data": {"pv_dec_string": "377,543.2664", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 5 small cubes", "__seed__": "0137"}}, {"seed": 138, "data": {"pv_dec_string": "17,393.5119", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0138"}}, {"seed": 139, "data": {"pv_dec_string": "139,552.22393", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.62", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0139"}}, {"seed": 140, "data": {"pv_dec_string": "131,974.77339", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0140"}}, {"seed": 141, "data": {"pv_dec_string": "32,993.85506", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0141"}}, {"seed": 142, "data": {"pv_dec_string": "782,543.5039", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0142"}}, {"seed": 143, "data": {"pv_dec_string": "8,782.928117", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.00", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0143"}}, {"seed": 144, "data": {"pv_dec_string": "801.422686", "pv_ans_text": "8 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.544", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0144"}}, {"seed": 145, "data": {"pv_dec_string": "146,558.48407", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.542", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 4 longs, and 2 small cubes", "__seed__": "0145"}}, {"seed": 146, "data": {"pv_dec_string": "3,561.99045", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0146"}}, {"seed": 147, "data": {"pv_dec_string": "95,070.8742", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0147"}}, {"seed": 148, "data": {"pv_dec_string": "591.678943", "pv_ans_text": "5 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.10", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0148"}}, {"seed": 149, "data": {"pv_dec_string": "251.188032", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.616", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 6 small cubes", "__seed__": "0149"}}, {"seed": 150, "data": {"pv_dec_string": "755,019.1749", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0150"}}, {"seed": 151, "data": {"pv_dec_string": "2,307.36289", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 5 small cubes", "__seed__": "0151"}}, {"seed": 152, "data": {"pv_dec_string": "853,661.8932", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0152"}}, {"seed": 153, "data": {"pv_dec_string": "348.098958", "pv_ans_text": "3 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.34", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0153"}}, {"seed": 154, "data": {"pv_dec_string": "232,561.49625", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.03", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0154"}}, {"seed": 155, "data": {"pv_dec_string": "809,625.9976", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 1 small cubes", "__seed__": "0155"}}, {"seed": 156, "data": {"pv_dec_string": "1,886,731.1576", "pv_ans_text": "1 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 6 small cubes", "__seed__": "0156"}}, {"seed": 157, "data": {"pv_dec_string": "19,482.63463", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.415", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 5 small cubes", "__seed__": "0157"}}, {"seed": 158, "data": {"pv_dec_string": "797,252.81572", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.224", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0158"}}, {"seed": 159, "data": {"pv_dec_string": "208,795.207", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.34", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0159"}}, {"seed": 160, "data": {"pv_dec_string": "63,788.374884", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.63", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0160"}}, {"seed": 161, "data": {"pv_dec_string": "446,595.0882", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.534", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0161"}}, {"seed": 162, "data": {"pv_dec_string": "4,085,404.0564", "pv_ans_text": "4 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 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", "blocks_dec": "3.034", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 3 longs, and 4 small cubes", "__seed__": "0163"}}, {"seed": 164, "data": {"pv_dec_string": "464,691.50463", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 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", "blocks_dec": "5.46", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0165"}}, {"seed": 166, "data": {"pv_dec_string": "3,292.65328", "pv_ans_text": "3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 4 small cubes", "__seed__": "0166"}}, {"seed": 167, "data": {"pv_dec_string": "6,444.2347", "pv_ans_text": "6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0167"}}, {"seed": 168, "data": {"pv_dec_string": "397,771.3654", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0168"}}, {"seed": 169, "data": {"pv_dec_string": "440,874.04981", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 4 small cubes", "__seed__": "0169"}}, {"seed": 170, "data": {"pv_dec_string": "702.275877", "pv_ans_text": "7 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 6 small cubes", "__seed__": "0170"}}, {"seed": 171, "data": {"pv_dec_string": "439,196.34765", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 1 small cubes", "__seed__": "0171"}}, {"seed": 172, "data": {"pv_dec_string": "172,827.98063", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.63", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0172"}}, {"seed": 173, "data": {"pv_dec_string": "59,430.690775", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.24", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0173"}}, {"seed": 174, "data": {"pv_dec_string": "9,206,151.9238", "pv_ans_text": "9 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 1 small cubes", "__seed__": "0174"}}, {"seed": 175, "data": {"pv_dec_string": "565,717.1749", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.53", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0175"}}, {"seed": 176, "data": {"pv_dec_string": "6,669.935279", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 1 small cubes", "__seed__": "0176"}}, {"seed": 177, "data": {"pv_dec_string": "653,422.3815", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0177"}}, {"seed": 178, "data": {"pv_dec_string": "63,720.404288", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 6 small cubes", "__seed__": "0178"}}, {"seed": 179, "data": {"pv_dec_string": "446,117.8821", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.025", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 2 longs, and 5 small cubes", "__seed__": "0179"}}, {"seed": 180, "data": {"pv_dec_string": "93,714.896177", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 6 small cubes", "__seed__": "0180"}}, {"seed": 181, "data": {"pv_dec_string": "4,034.214866", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0181"}}, {"seed": 182, "data": {"pv_dec_string": "939,595.2103", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 2 small cubes", "__seed__": "0182"}}, {"seed": 183, "data": {"pv_dec_string": "867.897767", "pv_ans_text": "8 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.30", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 0 longs, and 0 small cubes", "__seed__": "0183"}}, {"seed": 184, "data": {"pv_dec_string": "714,989.6004", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.16", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0184"}}, {"seed": 185, "data": {"pv_dec_string": "7,397.31053", "pv_ans_text": "7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0185"}}, {"seed": 186, "data": {"pv_dec_string": "855,049.70785", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.03", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0186"}}, {"seed": 187, "data": {"pv_dec_string": "27,074.4289", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 3 small cubes", "__seed__": "0187"}}, {"seed": 188, "data": {"pv_dec_string": "305,479.18946", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 1 small cubes", "__seed__": "0188"}}, {"seed": 189, "data": {"pv_dec_string": "61,086.6555", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.312", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0189"}}, {"seed": 190, "data": {"pv_dec_string": "18,785.46418", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 4 small cubes", "__seed__": "0190"}}, {"seed": 191, "data": {"pv_dec_string": "53,953.13492", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.300", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 0 longs, and 0 small cubes", "__seed__": "0191"}}, {"seed": 192, "data": {"pv_dec_string": "5,564.895669", "pv_ans_text": "5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.65", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0192"}}, {"seed": 193, "data": {"pv_dec_string": "20,370.729659", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 6 small cubes", "__seed__": "0193"}}, {"seed": 194, "data": {"pv_dec_string": "3,497,430.0103", "pv_ans_text": "3 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 5 small cubes", "__seed__": "0194"}}, {"seed": 195, "data": {"pv_dec_string": "31,204.889874", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.12", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0195"}}, {"seed": 196, "data": {"pv_dec_string": "916.502371", "pv_ans_text": "9 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.65", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0196"}}, {"seed": 197, "data": {"pv_dec_string": "361,005.9684", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 1 small cubes", "__seed__": "0197"}}, {"seed": 198, "data": {"pv_dec_string": "1,280.0394", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.43", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0198"}}, {"seed": 199, "data": {"pv_dec_string": "49,236.8765", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0199"}}, {"seed": 200, "data": {"pv_dec_string": "36,164.155811", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 3 small cubes", "__seed__": "0200"}}, {"seed": 201, "data": {"pv_dec_string": "141,633.03461", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 5 small cubes", "__seed__": "0201"}}, {"seed": 202, "data": {"pv_dec_string": "78,265.838708", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 1 small cubes", "__seed__": "0202"}}, {"seed": 203, "data": {"pv_dec_string": "7,097.591915", "pv_ans_text": "7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0203"}}, {"seed": 204, "data": {"pv_dec_string": "760,516.68857", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 1 small cubes", "__seed__": "0204"}}, {"seed": 205, "data": {"pv_dec_string": "1,339.348294", "pv_ans_text": "1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.26", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0205"}}, {"seed": 206, "data": {"pv_dec_string": "72,966.6456", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0206"}}, {"seed": 207, "data": {"pv_dec_string": "50,515.059225", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0207"}}, {"seed": 208, "data": {"pv_dec_string": "675,164.07828", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.143", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 4 longs, and 3 small cubes", "__seed__": "0208"}}, {"seed": 209, "data": {"pv_dec_string": "3,079.218936", "pv_ans_text": "3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 4 small cubes", "__seed__": "0209"}}, {"seed": 210, "data": {"pv_dec_string": "95,835.28609", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.665", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0210"}}, {"seed": 211, "data": {"pv_dec_string": "4,589.65289", "pv_ans_text": "4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.02", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 2 longs, and 0 small cubes", "__seed__": "0211"}}, {"seed": 212, "data": {"pv_dec_string": "9,844,117.7118", "pv_ans_text": "9 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.46", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0212"}}, {"seed": 213, "data": {"pv_dec_string": "57,837.0853", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 4 small cubes", "__seed__": "0213"}}, {"seed": 214, "data": {"pv_dec_string": "428,785.1069", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0214"}}, {"seed": 215, "data": {"pv_dec_string": "3,954.284377", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 2 small cubes", "__seed__": "0215"}}, {"seed": 216, "data": {"pv_dec_string": "690,787.15009", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.040", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0216"}}, {"seed": 217, "data": {"pv_dec_string": "280.062014", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.11", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0217"}}, {"seed": 218, "data": {"pv_dec_string": "507,104.7536", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.03", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0218"}}, {"seed": 219, "data": {"pv_dec_string": "1,033,045.991", "pv_ans_text": "1 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.31", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0219"}}, {"seed": 220, "data": {"pv_dec_string": "45,550.36887", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.13", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0220"}}, {"seed": 221, "data": {"pv_dec_string": "608,576.79856", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 2 small cubes", "__seed__": "0221"}}, {"seed": 222, "data": {"pv_dec_string": "1,234.74873", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 6 small cubes", "__seed__": "0222"}}, {"seed": 223, "data": {"pv_dec_string": "5,992.298601", "pv_ans_text": "5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.15", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0223"}}, {"seed": 224, "data": {"pv_dec_string": "86,567.120505", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.46", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0224"}}, {"seed": 225, "data": {"pv_dec_string": "9,029.670799", "pv_ans_text": "9 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0225"}}, {"seed": 226, "data": {"pv_dec_string": "6,035.75122", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0226"}}, {"seed": 227, "data": {"pv_dec_string": "91,518.29691", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.303", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0227"}}, {"seed": 228, "data": {"pv_dec_string": "74,232.118502", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.31", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0228"}}, {"seed": 229, "data": {"pv_dec_string": "23,134.9109", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0229"}}, {"seed": 230, "data": {"pv_dec_string": "588,589.15646", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 3 small cubes", "__seed__": "0230"}}, {"seed": 231, "data": {"pv_dec_string": "5,045.795989", "pv_ans_text": "5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.416", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 6 small cubes", "__seed__": "0231"}}, {"seed": 232, "data": {"pv_dec_string": "5,166,778.1676", "pv_ans_text": "5 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.150", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0232"}}, {"seed": 233, "data": {"pv_dec_string": "469.049134", "pv_ans_text": "4 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.500", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0233"}}, {"seed": 234, "data": {"pv_dec_string": "44,040.6109", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.060", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0234"}}, {"seed": 235, "data": {"pv_dec_string": "81,644.30839", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 3 small cubes", "__seed__": "0235"}}, {"seed": 236, "data": {"pv_dec_string": "8,091,026.1451", "pv_ans_text": "8 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 5 small cubes", "__seed__": "0236"}}, {"seed": 237, "data": {"pv_dec_string": "5,500,895.2311", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0237"}}, {"seed": 238, "data": {"pv_dec_string": "875.375074", "pv_ans_text": "8 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 2 small cubes", "__seed__": "0238"}}, {"seed": 239, "data": {"pv_dec_string": "1,118.07175", "pv_ans_text": "1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.36", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0239"}}, {"seed": 240, "data": {"pv_dec_string": "62,427.782455", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 1 small cubes", "__seed__": "0240"}}, {"seed": 241, "data": {"pv_dec_string": "63,714.75679", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.426", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 6 small cubes", "__seed__": "0241"}}, {"seed": 242, "data": {"pv_dec_string": "4,041.128001", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0242"}}, {"seed": 243, "data": {"pv_dec_string": "4,086.860773", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0243"}}, {"seed": 244, "data": {"pv_dec_string": "44,184.638841", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0244"}}, {"seed": 245, "data": {"pv_dec_string": "227,279.27204", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0245"}}, {"seed": 246, "data": {"pv_dec_string": "55,024.6715", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.46", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0246"}}, {"seed": 247, "data": {"pv_dec_string": "18,562.3414", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.30", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 0 longs, and 0 small cubes", "__seed__": "0247"}}, {"seed": 248, "data": {"pv_dec_string": "93,051.29915", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.31", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0248"}}, {"seed": 249, "data": {"pv_dec_string": "611.014001", "pv_ans_text": "6 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 2 small cubes", "__seed__": "0249"}}, {"seed": 250, "data": {"pv_dec_string": "937.658327", "pv_ans_text": "9 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0250"}}, {"seed": 251, "data": {"pv_dec_string": "672,424.78711", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.26", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0251"}}, {"seed": 252, "data": {"pv_dec_string": "9,966,258.7348", "pv_ans_text": "9 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0252"}}, {"seed": 253, "data": {"pv_dec_string": "8,607.227104", "pv_ans_text": "8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0253"}}, {"seed": 254, "data": {"pv_dec_string": "2,607.40858", "pv_ans_text": "2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.35", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0254"}}, {"seed": 255, "data": {"pv_dec_string": "384,057.9664", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.63", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0255"}}, {"seed": 256, "data": {"pv_dec_string": "433,858.1331", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0256"}}, {"seed": 257, "data": {"pv_dec_string": "16,271.8748", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.246", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 6 small cubes", "__seed__": "0257"}}, {"seed": 258, "data": {"pv_dec_string": "5,787.9224", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 4 small cubes", "__seed__": "0258"}}, {"seed": 259, "data": {"pv_dec_string": "287,913.45535", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.02", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 2 longs, and 0 small cubes", "__seed__": "0259"}}, {"seed": 260, "data": {"pv_dec_string": "50,837.83808", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0260"}}, {"seed": 261, "data": {"pv_dec_string": "79,188.1195", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0261"}}, {"seed": 262, "data": {"pv_dec_string": "1,366.665786", "pv_ans_text": "1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.24", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0262"}}, {"seed": 263, "data": {"pv_dec_string": "905.249154", "pv_ans_text": "9 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.544", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0263"}}, {"seed": 264, "data": {"pv_dec_string": "8,718.507184", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0264"}}, {"seed": 265, "data": {"pv_dec_string": "4,476.526749", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 4 small cubes", "__seed__": "0265"}}, {"seed": 266, "data": {"pv_dec_string": "65,383.55575", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0266"}}, {"seed": 267, "data": {"pv_dec_string": "2,556.63999", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 1 small cubes", "__seed__": "0267"}}, {"seed": 268, "data": {"pv_dec_string": "47,373.3252", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0268"}}, {"seed": 269, "data": {"pv_dec_string": "19,855.691517", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0269"}}, {"seed": 270, "data": {"pv_dec_string": "3,366,482.7229", "pv_ans_text": "3 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 2 small cubes", "__seed__": "0270"}}, {"seed": 271, "data": {"pv_dec_string": "722,234.7187", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 2 small cubes", "__seed__": "0271"}}, {"seed": 272, "data": {"pv_dec_string": "56,675.668026", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.654", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 5 longs, and 4 small cubes", "__seed__": "0272"}}, {"seed": 273, "data": {"pv_dec_string": "778,107.8675", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.212", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 1 longs, and 2 small cubes", "__seed__": "0273"}}, {"seed": 274, "data": {"pv_dec_string": "705,983.66439", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 3 small cubes", "__seed__": "0274"}}, {"seed": 275, "data": {"pv_dec_string": "287,382.01694", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.235", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 3 longs, and 5 small cubes", "__seed__": "0275"}}, {"seed": 276, "data": {"pv_dec_string": "56,869.5718", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0276"}}, {"seed": 277, "data": {"pv_dec_string": "97,247.5486", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 3 small cubes", "__seed__": "0277"}}, {"seed": 278, "data": {"pv_dec_string": "2,085,046.8288", "pv_ans_text": "2 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0278"}}, {"seed": 279, "data": {"pv_dec_string": "581,544.6178", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.223", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 2 longs, and 3 small cubes", "__seed__": "0279"}}, {"seed": 280, "data": {"pv_dec_string": "46,653.258151", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.626", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 2 longs, and 6 small cubes", "__seed__": "0280"}}, {"seed": 281, "data": {"pv_dec_string": "87,851.31558", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 3 small cubes", "__seed__": "0281"}}, {"seed": 282, "data": {"pv_dec_string": "8,994.02985", "pv_ans_text": "8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.242", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 4 longs, and 2 small cubes", "__seed__": "0282"}}, {"seed": 283, "data": {"pv_dec_string": "19,399.0384", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0283"}}, {"seed": 284, "data": {"pv_dec_string": "531,868.6372", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 3 small cubes", "__seed__": "0284"}}, {"seed": 285, "data": {"pv_dec_string": "635,402.62683", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 3 small cubes", "__seed__": "0285"}}, {"seed": 286, "data": {"pv_dec_string": "18,974.0647", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0286"}}, {"seed": 287, "data": {"pv_dec_string": "29,862.6932", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.616", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 6 small cubes", "__seed__": "0287"}}, {"seed": 288, "data": {"pv_dec_string": "73,016.26659", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.662", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 6 longs, and 2 small cubes", "__seed__": "0288"}}, {"seed": 289, "data": {"pv_dec_string": "415.116114", "pv_ans_text": "4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 4 small cubes", "__seed__": "0289"}}, {"seed": 290, "data": {"pv_dec_string": "908.899032", "pv_ans_text": "9 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.11", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0290"}}, {"seed": 291, "data": {"pv_dec_string": "737,529.7304", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 1 small cubes", "__seed__": "0291"}}, {"seed": 292, "data": {"pv_dec_string": "80,017.7436", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0292"}}, {"seed": 293, "data": {"pv_dec_string": "194,929.5574", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.62", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0293"}}, {"seed": 294, "data": {"pv_dec_string": "57,526.18268", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.415", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 1 longs, and 5 small cubes", "__seed__": "0294"}}, {"seed": 295, "data": {"pv_dec_string": "251.40917", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.34", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0295"}}, {"seed": 296, "data": {"pv_dec_string": "158,840.1525", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 2 small cubes", "__seed__": "0296"}}, {"seed": 297, "data": {"pv_dec_string": "4,406,239.9244", "pv_ans_text": "4 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 1 small cubes", "__seed__": "0297"}}, {"seed": 298, "data": {"pv_dec_string": "6,919.47509", "pv_ans_text": "6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.465", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 5 small cubes", "__seed__": "0298"}}, {"seed": 299, "data": {"pv_dec_string": "1,996,463.4122", "pv_ans_text": "1 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0299"}}, {"seed": 300, "data": {"pv_dec_string": "3,306,529.6039", "pv_ans_text": "3 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0300"}}, {"seed": 301, "data": {"pv_dec_string": "9,934,637.3831", "pv_ans_text": "9 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.102", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0301"}}, {"seed": 302, "data": {"pv_dec_string": "34,154.622085", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0302"}}, {"seed": 303, "data": {"pv_dec_string": "91,391.01174", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 1 small cubes", "__seed__": "0303"}}, {"seed": 304, "data": {"pv_dec_string": "837,864.28645", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 6 small cubes", "__seed__": "0304"}}, {"seed": 305, "data": {"pv_dec_string": "8,314,981.8719", "pv_ans_text": "8 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0305"}}, {"seed": 306, "data": {"pv_dec_string": "43,152.36903", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.10", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0306"}}, {"seed": 307, "data": {"pv_dec_string": "7,847,046.2057", "pv_ans_text": "7 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 1 small cubes", "__seed__": "0307"}}, {"seed": 308, "data": {"pv_dec_string": "49,919.289", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.31", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0308"}}, {"seed": 309, "data": {"pv_dec_string": "307.592742", "pv_ans_text": "3 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.40", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0309"}}, {"seed": 310, "data": {"pv_dec_string": "3,528.18038", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 1 small cubes", "__seed__": "0310"}}, {"seed": 311, "data": {"pv_dec_string": "8,020.60862", "pv_ans_text": "8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0311"}}, {"seed": 312, "data": {"pv_dec_string": "9,456.09771", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.46", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0312"}}, {"seed": 313, "data": {"pv_dec_string": "985,838.6301", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0313"}}, {"seed": 314, "data": {"pv_dec_string": "337.797338", "pv_ans_text": "3 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 3 small cubes", "__seed__": "0314"}}, {"seed": 315, "data": {"pv_dec_string": "4,166.59545", "pv_ans_text": "4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.26", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0315"}}, {"seed": 316, "data": {"pv_dec_string": "12,577.54092", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0316"}}, {"seed": 317, "data": {"pv_dec_string": "13,220.5415", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 6 small cubes", "__seed__": "0317"}}, {"seed": 318, "data": {"pv_dec_string": "58,338.88669", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 3 small cubes", "__seed__": "0318"}}, {"seed": 319, "data": {"pv_dec_string": "85,766.84954", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.64", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0319"}}, {"seed": 320, "data": {"pv_dec_string": "7,806,121.5261", "pv_ans_text": "7 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.613", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 1 longs, and 3 small cubes", "__seed__": "0320"}}, {"seed": 321, "data": {"pv_dec_string": "769,698.6412", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.43", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0321"}}, {"seed": 322, "data": {"pv_dec_string": "3,129,439.7098", "pv_ans_text": "3 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0322"}}, {"seed": 323, "data": {"pv_dec_string": "495,622.67101", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0323"}}, {"seed": 324, "data": {"pv_dec_string": "342.756916", "pv_ans_text": "3 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.160", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0324"}}, {"seed": 325, "data": {"pv_dec_string": "62,897.08", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.123", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0325"}}, {"seed": 326, "data": {"pv_dec_string": "7,821.226341", "pv_ans_text": "7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 1 small cubes", "__seed__": "0326"}}, {"seed": 327, "data": {"pv_dec_string": "958,837.98104", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 4 small cubes", "__seed__": "0327"}}, {"seed": 328, "data": {"pv_dec_string": "831.123956", "pv_ans_text": "8 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 6 small cubes", "__seed__": "0328"}}, {"seed": 329, "data": {"pv_dec_string": "70,758.2605", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 3 small cubes", "__seed__": "0329"}}, {"seed": 330, "data": {"pv_dec_string": "73,660.7028", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0330"}}, {"seed": 331, "data": {"pv_dec_string": "82,040.70796", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.140", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0331"}}, {"seed": 332, "data": {"pv_dec_string": "136,738.7053", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.33", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0332"}}, {"seed": 333, "data": {"pv_dec_string": "394,186.16", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.60", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0333"}}, {"seed": 334, "data": {"pv_dec_string": "1,854.53683", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.425", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0334"}}, {"seed": 335, "data": {"pv_dec_string": "5,323.574836", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.12", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0335"}}, {"seed": 336, "data": {"pv_dec_string": "1,617.33557", "pv_ans_text": "1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.433", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 3 longs, and 3 small cubes", "__seed__": "0336"}}, {"seed": 337, "data": {"pv_dec_string": "29,346.217977", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0337"}}, {"seed": 338, "data": {"pv_dec_string": "3,681.92628", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 5 small cubes", "__seed__": "0338"}}, {"seed": 339, "data": {"pv_dec_string": "159.832643", "pv_ans_text": "1 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.311", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0339"}}, {"seed": 340, "data": {"pv_dec_string": "191,155.804", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.05", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0340"}}, {"seed": 341, "data": {"pv_dec_string": "506.376899", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 2 small cubes", "__seed__": "0341"}}, {"seed": 342, "data": {"pv_dec_string": "7,244,854.2629", "pv_ans_text": "7 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.244", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0342"}}, {"seed": 343, "data": {"pv_dec_string": "5,355.39343", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 2 small cubes", "__seed__": "0343"}}, {"seed": 344, "data": {"pv_dec_string": "43,089.6943", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.46", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0344"}}, {"seed": 345, "data": {"pv_dec_string": "939,701.9682", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 2 small cubes", "__seed__": "0345"}}, {"seed": 346, "data": {"pv_dec_string": "6,402.627215", "pv_ans_text": "6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.463", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0346"}}, {"seed": 347, "data": {"pv_dec_string": "648,592.0118", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.004", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 0 longs, and 4 small cubes", "__seed__": "0347"}}, {"seed": 348, "data": {"pv_dec_string": "5,702.79479", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.62", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0348"}}, {"seed": 349, "data": {"pv_dec_string": "30,566.7741", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.06", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0349"}}, {"seed": 350, "data": {"pv_dec_string": "90,954.943983", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.566", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0350"}}, {"seed": 351, "data": {"pv_dec_string": "3,268.53408", "pv_ans_text": "3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.06", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0351"}}, {"seed": 352, "data": {"pv_dec_string": "1,833.50005", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.242", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 2 small cubes", "__seed__": "0352"}}, {"seed": 353, "data": {"pv_dec_string": "963.52528", "pv_ans_text": "9 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0353"}}, {"seed": 354, "data": {"pv_dec_string": "584,839.5518", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.623", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0354"}}, {"seed": 355, "data": {"pv_dec_string": "31,549.846364", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.614", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 4 small cubes", "__seed__": "0355"}}, {"seed": 356, "data": {"pv_dec_string": "58,962.343596", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 5 small cubes", "__seed__": "0356"}}, {"seed": 357, "data": {"pv_dec_string": "314.075106", "pv_ans_text": "3 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0357"}}, {"seed": 358, "data": {"pv_dec_string": "168,277.72178", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.54", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0358"}}, {"seed": 359, "data": {"pv_dec_string": "11,488.9556", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0359"}}, {"seed": 360, "data": {"pv_dec_string": "6,601.72982", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 2 small cubes", "__seed__": "0360"}}, {"seed": 361, "data": {"pv_dec_string": "770,133.4157", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.20", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0361"}}, {"seed": 362, "data": {"pv_dec_string": "8,557,726.063", "pv_ans_text": "8 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.01", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0362"}}, {"seed": 363, "data": {"pv_dec_string": "436,203.12842", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0363"}}, {"seed": 364, "data": {"pv_dec_string": "7,979.32948", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.464", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 6 longs, and 4 small cubes", "__seed__": "0364"}}, {"seed": 365, "data": {"pv_dec_string": "703,984.5767", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.31", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0365"}}, {"seed": 366, "data": {"pv_dec_string": "91,406.1316", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0366"}}, {"seed": 367, "data": {"pv_dec_string": "91,352.01559", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.214", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 1 longs, and 4 small cubes", "__seed__": "0367"}}, {"seed": 368, "data": {"pv_dec_string": "39,688.5301", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 1 small cubes", "__seed__": "0368"}}, {"seed": 369, "data": {"pv_dec_string": "1,395,461.5225", "pv_ans_text": "1 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0369"}}, {"seed": 370, "data": {"pv_dec_string": "3,659.022855", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0370"}}, {"seed": 371, "data": {"pv_dec_string": "301,466.9024", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.463", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0371"}}, {"seed": 372, "data": {"pv_dec_string": "436,148.10088", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.46", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0372"}}, {"seed": 373, "data": {"pv_dec_string": "73,495.03998", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0373"}}, {"seed": 374, "data": {"pv_dec_string": "3,084,855.4168", "pv_ans_text": "3 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.46", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0374"}}, {"seed": 375, "data": {"pv_dec_string": "376,366.3907", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0375"}}, {"seed": 376, "data": {"pv_dec_string": "3,478,795.791", "pv_ans_text": "3 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0376"}}, {"seed": 377, "data": {"pv_dec_string": "770.07757", "pv_ans_text": "7 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0377"}}, {"seed": 378, "data": {"pv_dec_string": "13,749.270741", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0378"}}, {"seed": 379, "data": {"pv_dec_string": "789,641.52047", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.214", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 1 longs, and 4 small cubes", "__seed__": "0379"}}, {"seed": 380, "data": {"pv_dec_string": "98,768.04972", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 3 small cubes", "__seed__": "0380"}}, {"seed": 381, "data": {"pv_dec_string": "6,872,541.3881", "pv_ans_text": "6 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 2 small cubes", "__seed__": "0381"}}, {"seed": 382, "data": {"pv_dec_string": "442,077.3833", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 2 small cubes", "__seed__": "0382"}}, {"seed": 383, "data": {"pv_dec_string": "28,256.936626", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.616", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 1 longs, and 6 small cubes", "__seed__": "0383"}}, {"seed": 384, "data": {"pv_dec_string": "3,545.174991", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.44", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0384"}}, {"seed": 385, "data": {"pv_dec_string": "93,810.9747", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 1 small cubes", "__seed__": "0385"}}, {"seed": 386, "data": {"pv_dec_string": "7,956,511.4464", "pv_ans_text": "7 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.13", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0386"}}, {"seed": 387, "data": {"pv_dec_string": "71,934.26453", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0387"}}, {"seed": 388, "data": {"pv_dec_string": "893,196.9694", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.26", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0388"}}, {"seed": 389, "data": {"pv_dec_string": "96,232.60442", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 3 small cubes", "__seed__": "0389"}}, {"seed": 390, "data": {"pv_dec_string": "8,665,055.9222", "pv_ans_text": "8 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.045", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 4 longs, and 5 small cubes", "__seed__": "0390"}}, {"seed": 391, "data": {"pv_dec_string": "94,648.754846", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.53", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0391"}}, {"seed": 392, "data": {"pv_dec_string": "3,458.11545", "pv_ans_text": "3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.156", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 5 longs, and 6 small cubes", "__seed__": "0392"}}, {"seed": 393, "data": {"pv_dec_string": "328,367.468", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.631", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 1 small cubes", "__seed__": "0393"}}, {"seed": 394, "data": {"pv_dec_string": "246,120.6419", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.366", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 6 small cubes", "__seed__": "0394"}}, {"seed": 395, "data": {"pv_dec_string": "7,971,138.1513", "pv_ans_text": "7 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0395"}}, {"seed": 396, "data": {"pv_dec_string": "1,833.543391", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.046", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 6 small cubes", "__seed__": "0396"}}, {"seed": 397, "data": {"pv_dec_string": "4,813,145.9021", "pv_ans_text": "4 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.461", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 1 small cubes", "__seed__": "0397"}}, {"seed": 398, "data": {"pv_dec_string": "821,154.1434", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.62", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0398"}}, {"seed": 399, "data": {"pv_dec_string": "50,358.599067", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 2 small cubes", "__seed__": "0399"}}, {"seed": 400, "data": {"pv_dec_string": "90,877.12913", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.565", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0400"}}, {"seed": 401, "data": {"pv_dec_string": "179,604.8447", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.23", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0401"}}, {"seed": 402, "data": {"pv_dec_string": "294,353.222", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0402"}}, {"seed": 403, "data": {"pv_dec_string": "432,721.7921", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 2 small cubes", "__seed__": "0403"}}, {"seed": 404, "data": {"pv_dec_string": "633,415.0506", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.120", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0404"}}, {"seed": 405, "data": {"pv_dec_string": "460,524.61694", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.355", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0405"}}, {"seed": 406, "data": {"pv_dec_string": "46,597.550517", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.626", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 6 small cubes", "__seed__": "0406"}}, {"seed": 407, "data": {"pv_dec_string": "135,161.71229", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0407"}}, {"seed": 408, "data": {"pv_dec_string": "13,025.18901", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.35", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 5 small cubes", "__seed__": "0408"}}, {"seed": 409, "data": {"pv_dec_string": "7,398.082216", "pv_ans_text": "7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.24", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0409"}}, {"seed": 410, "data": {"pv_dec_string": "40,525.6441", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0410"}}, {"seed": 411, "data": {"pv_dec_string": "40,917.009", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.22", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0411"}}, {"seed": 412, "data": {"pv_dec_string": "8,093.205831", "pv_ans_text": "8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.40", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0412"}}, {"seed": 413, "data": {"pv_dec_string": "7,254.251038", "pv_ans_text": "7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 1 small cubes", "__seed__": "0413"}}, {"seed": 414, "data": {"pv_dec_string": "11,905.302735", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.52", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0414"}}, {"seed": 415, "data": {"pv_dec_string": "31,597.630808", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.51", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0415"}}, {"seed": 416, "data": {"pv_dec_string": "9,110.917", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 6 small cubes", "__seed__": "0416"}}, {"seed": 417, "data": {"pv_dec_string": "952,433.58204", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0417"}}, {"seed": 418, "data": {"pv_dec_string": "4,370.691508", "pv_ans_text": "4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0418"}}, {"seed": 419, "data": {"pv_dec_string": "12,416.06862", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.501", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 0 longs, and 1 small cubes", "__seed__": "0419"}}, {"seed": 420, "data": {"pv_dec_string": "23,471.8035", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0420"}}, {"seed": 421, "data": {"pv_dec_string": "135,009.55012", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.430", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0421"}}, {"seed": 422, "data": {"pv_dec_string": "18,298.469302", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.113", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0422"}}, {"seed": 423, "data": {"pv_dec_string": "91,289.3948", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 5 small cubes", "__seed__": "0423"}}, {"seed": 424, "data": {"pv_dec_string": "1,649.70177", "pv_ans_text": "1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 3 small cubes", "__seed__": "0424"}}, {"seed": 425, "data": {"pv_dec_string": "9,888.035495", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.322", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 2 longs, and 2 small cubes", "__seed__": "0425"}}, {"seed": 426, "data": {"pv_dec_string": "207,047.42745", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 5 small cubes", "__seed__": "0426"}}, {"seed": 427, "data": {"pv_dec_string": "3,959.3713", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.545", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0427"}}, {"seed": 428, "data": {"pv_dec_string": "4,852,182.8028", "pv_ans_text": "4 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.050", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0428"}}, {"seed": 429, "data": {"pv_dec_string": "9,459.922324", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.42", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0429"}}, {"seed": 430, "data": {"pv_dec_string": "113,181.5834", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.10", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0430"}}, {"seed": 431, "data": {"pv_dec_string": "10,636.2138", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0431"}}, {"seed": 432, "data": {"pv_dec_string": "223.05312", "pv_ans_text": "2 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0432"}}, {"seed": 433, "data": {"pv_dec_string": "593,607.83728", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.612", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 2 small cubes", "__seed__": "0433"}}, {"seed": 434, "data": {"pv_dec_string": "4,374,813.7708", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.341", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 4 longs, and 1 small cubes", "__seed__": "0434"}}, {"seed": 435, "data": {"pv_dec_string": "485,285.59605", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.44", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0435"}}, {"seed": 436, "data": {"pv_dec_string": "5,789.63937", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0436"}}, {"seed": 437, "data": {"pv_dec_string": "30,900.010713", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0437"}}, {"seed": 438, "data": {"pv_dec_string": "9,756.93983", "pv_ans_text": "9 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0438"}}, {"seed": 439, "data": {"pv_dec_string": "93,122.21482", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.46", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0439"}}, {"seed": 440, "data": {"pv_dec_string": "12,604.574773", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.405", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 0 longs, and 5 small cubes", "__seed__": "0440"}}, {"seed": 441, "data": {"pv_dec_string": "6,213.081556", "pv_ans_text": "6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0441"}}, {"seed": 442, "data": {"pv_dec_string": "1,383,900.638", "pv_ans_text": "1 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.455", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 5 longs, and 5 small cubes", "__seed__": "0442"}}, {"seed": 443, "data": {"pv_dec_string": "763,050.56284", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0443"}}, {"seed": 444, "data": {"pv_dec_string": "9,562.394475", "pv_ans_text": "9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0444"}}, {"seed": 445, "data": {"pv_dec_string": "3,934.5228", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 1 small cubes", "__seed__": "0445"}}, {"seed": 446, "data": {"pv_dec_string": "4,455.915745", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.10", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0446"}}, {"seed": 447, "data": {"pv_dec_string": "62,768.37707", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0447"}}, {"seed": 448, "data": {"pv_dec_string": "8,377.901792", "pv_ans_text": "8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0448"}}, {"seed": 449, "data": {"pv_dec_string": "11,770.642", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.233", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 3 longs, and 3 small cubes", "__seed__": "0449"}}, {"seed": 450, "data": {"pv_dec_string": "4,945.964246", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0450"}}, {"seed": 451, "data": {"pv_dec_string": "363.170173", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.560", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0451"}}, {"seed": 452, "data": {"pv_dec_string": "930,025.03687", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.336", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 3 longs, and 6 small cubes", "__seed__": "0452"}}, {"seed": 453, "data": {"pv_dec_string": "54,954.69099", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 3 small cubes", "__seed__": "0453"}}, {"seed": 454, "data": {"pv_dec_string": "353,087.4736", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 4 small cubes", "__seed__": "0454"}}, {"seed": 455, "data": {"pv_dec_string": "78,544.7066", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 4 small cubes", "__seed__": "0455"}}, {"seed": 456, "data": {"pv_dec_string": "17,631.470196", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0456"}}, {"seed": 457, "data": {"pv_dec_string": "6,611.799484", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.610", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0457"}}, {"seed": 458, "data": {"pv_dec_string": "301.573909", "pv_ans_text": "3 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.252", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0458"}}, {"seed": 459, "data": {"pv_dec_string": "4,907.371894", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0459"}}, {"seed": 460, "data": {"pv_dec_string": "4,818.668177", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0460"}}, {"seed": 461, "data": {"pv_dec_string": "731,224.4664", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 5 small cubes", "__seed__": "0461"}}, {"seed": 462, "data": {"pv_dec_string": "794,727.3181", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.133", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 3 small cubes", "__seed__": "0462"}}, {"seed": 463, "data": {"pv_dec_string": "98,397.1219", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 3 small cubes", "__seed__": "0463"}}, {"seed": 464, "data": {"pv_dec_string": "5,287.24558", "pv_ans_text": "5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.03", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0464"}}, {"seed": 465, "data": {"pv_dec_string": "3,447.611666", "pv_ans_text": "3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.516", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 1 longs, and 6 small cubes", "__seed__": "0465"}}, {"seed": 466, "data": {"pv_dec_string": "314,961.2457", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.520", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0466"}}, {"seed": 467, "data": {"pv_dec_string": "61,670.805018", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0467"}}, {"seed": 468, "data": {"pv_dec_string": "528,303.49747", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0468"}}, {"seed": 469, "data": {"pv_dec_string": "40,010.0853", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0469"}}, {"seed": 470, "data": {"pv_dec_string": "561,665.55232", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0470"}}, {"seed": 471, "data": {"pv_dec_string": "283,659.0039", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.23", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0471"}}, {"seed": 472, "data": {"pv_dec_string": "57,784.936701", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0472"}}, {"seed": 473, "data": {"pv_dec_string": "9,191.311321", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.60", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0473"}}, {"seed": 474, "data": {"pv_dec_string": "104,620.7243", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.566", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0474"}}, {"seed": 475, "data": {"pv_dec_string": "336,057.78824", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 6 small cubes", "__seed__": "0475"}}, {"seed": 476, "data": {"pv_dec_string": "207.314866", "pv_ans_text": "2 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0476"}}, {"seed": 477, "data": {"pv_dec_string": "176,336.0296", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 2 small cubes", "__seed__": "0477"}}, {"seed": 478, "data": {"pv_dec_string": "517.045891", "pv_ans_text": "5 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0478"}}, {"seed": 479, "data": {"pv_dec_string": "9,657,469.3516", "pv_ans_text": "9 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.11", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0479"}}, {"seed": 480, "data": {"pv_dec_string": "5,908,653.7197", "pv_ans_text": "5 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 3 small cubes", "__seed__": "0480"}}, {"seed": 481, "data": {"pv_dec_string": "1,751,872.1532", "pv_ans_text": "1 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 4 small cubes", "__seed__": "0481"}}, {"seed": 482, "data": {"pv_dec_string": "1,841,473.9819", "pv_ans_text": "1 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.645", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0482"}}, {"seed": 483, "data": {"pv_dec_string": "32,808.691136", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0483"}}, {"seed": 484, "data": {"pv_dec_string": "9,301,538.9075", "pv_ans_text": "9 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0484"}}, {"seed": 485, "data": {"pv_dec_string": "6,081.42154", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 5 small cubes", "__seed__": "0485"}}, {"seed": 486, "data": {"pv_dec_string": "5,174.075541", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 3 small cubes", "__seed__": "0486"}}, {"seed": 487, "data": {"pv_dec_string": "2,295.94507", "pv_ans_text": "2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0487"}}, {"seed": 488, "data": {"pv_dec_string": "131,405.2641", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.42", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0488"}}, {"seed": 489, "data": {"pv_dec_string": "2,259.10405", "pv_ans_text": "2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.514", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 1 longs, and 4 small cubes", "__seed__": "0489"}}, {"seed": 490, "data": {"pv_dec_string": "9,809.24314", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.56", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0490"}}, {"seed": 491, "data": {"pv_dec_string": "31,271.770901", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 4 small cubes", "__seed__": "0491"}}, {"seed": 492, "data": {"pv_dec_string": "6,808.545966", "pv_ans_text": "6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 2 small cubes", "__seed__": "0492"}}, {"seed": 493, "data": {"pv_dec_string": "73,587.9248", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.10", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0493"}}, {"seed": 494, "data": {"pv_dec_string": "673.074952", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.152", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 5 longs, and 2 small cubes", "__seed__": "0494"}}, {"seed": 495, "data": {"pv_dec_string": "68,942.351007", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0495"}}, {"seed": 496, "data": {"pv_dec_string": "981.201931", "pv_ans_text": "9 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.063", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 3 small cubes", "__seed__": "0496"}}, {"seed": 497, "data": {"pv_dec_string": "180,046.83061", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0497"}}, {"seed": 498, "data": {"pv_dec_string": "957,185.2138", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 6 small cubes", "__seed__": "0498"}}, {"seed": 499, "data": {"pv_dec_string": "55,822.217152", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0499"}}, {"seed": 500, "data": {"pv_dec_string": "393.249557", "pv_ans_text": "3 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.10", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0500"}}, {"seed": 501, "data": {"pv_dec_string": "525.260441", "pv_ans_text": "5 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 3 small cubes", "__seed__": "0501"}}, {"seed": 502, "data": {"pv_dec_string": "9,284.719835", "pv_ans_text": "9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.26", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0502"}}, {"seed": 503, "data": {"pv_dec_string": "52,968.280489", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0503"}}, {"seed": 504, "data": {"pv_dec_string": "46,624.47799", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0504"}}, {"seed": 505, "data": {"pv_dec_string": "8,668,903.0735", "pv_ans_text": "8 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.625", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 2 longs, and 5 small cubes", "__seed__": "0505"}}, {"seed": 506, "data": {"pv_dec_string": "6,355,809.0884", "pv_ans_text": "6 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0506"}}, {"seed": 507, "data": {"pv_dec_string": "605,626.49952", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.355", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0507"}}, {"seed": 508, "data": {"pv_dec_string": "31,072.5843", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.051", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 5 longs, and 1 small cubes", "__seed__": "0508"}}, {"seed": 509, "data": {"pv_dec_string": "106.507507", "pv_ans_text": "1 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.263", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 6 longs, and 3 small cubes", "__seed__": "0509"}}, {"seed": 510, "data": {"pv_dec_string": "3,825.133573", "pv_ans_text": "3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 3 small cubes", "__seed__": "0510"}}, {"seed": 511, "data": {"pv_dec_string": "69,882.688314", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.03", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0511"}}, {"seed": 512, "data": {"pv_dec_string": "320.778245", "pv_ans_text": "3 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0512"}}, {"seed": 513, "data": {"pv_dec_string": "37,337.873065", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0513"}}, {"seed": 514, "data": {"pv_dec_string": "48,751.8653", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.40", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0514"}}, {"seed": 515, "data": {"pv_dec_string": "329,347.1443", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.442", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 2 small cubes", "__seed__": "0515"}}, {"seed": 516, "data": {"pv_dec_string": "36,502.78607", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 6 small cubes", "__seed__": "0516"}}, {"seed": 517, "data": {"pv_dec_string": "86,988.9298", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0517"}}, {"seed": 518, "data": {"pv_dec_string": "5,807,616.0845", "pv_ans_text": "5 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.520", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0518"}}, {"seed": 519, "data": {"pv_dec_string": "790,364.3465", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.123", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0519"}}, {"seed": 520, "data": {"pv_dec_string": "94,879.422345", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.13", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0520"}}, {"seed": 521, "data": {"pv_dec_string": "657,517.0504", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0521"}}, {"seed": 522, "data": {"pv_dec_string": "113,605.09929", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.35", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0522"}}, {"seed": 523, "data": {"pv_dec_string": "5,625,138.9498", "pv_ans_text": "5 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.51", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0523"}}, {"seed": 524, "data": {"pv_dec_string": "726,972.14966", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.65", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0524"}}, {"seed": 525, "data": {"pv_dec_string": "864,528.62658", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0525"}}, {"seed": 526, "data": {"pv_dec_string": "7,792.397334", "pv_ans_text": "7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.32", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0526"}}, {"seed": 527, "data": {"pv_dec_string": "843.896157", "pv_ans_text": "8 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.022", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 2 longs, and 2 small cubes", "__seed__": "0527"}}, {"seed": 528, "data": {"pv_dec_string": "3,764,071.916", "pv_ans_text": "3 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.11", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0528"}}, {"seed": 529, "data": {"pv_dec_string": "33,591.39239", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.51", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0529"}}, {"seed": 530, "data": {"pv_dec_string": "7,683,109.0547", "pv_ans_text": "7 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.43", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0530"}}, {"seed": 531, "data": {"pv_dec_string": "33,433.133213", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.102", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0531"}}, {"seed": 532, "data": {"pv_dec_string": "625,911.367", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0532"}}, {"seed": 533, "data": {"pv_dec_string": "6,049.40335", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.05", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0533"}}, {"seed": 534, "data": {"pv_dec_string": "958,708.639", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.62", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0534"}}, {"seed": 535, "data": {"pv_dec_string": "4,844,827.4699", "pv_ans_text": "4 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 3 small cubes", "__seed__": "0535"}}, {"seed": 536, "data": {"pv_dec_string": "355,759.2494", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0536"}}, {"seed": 537, "data": {"pv_dec_string": "987.543269", "pv_ans_text": "9 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 4 small cubes", "__seed__": "0537"}}, {"seed": 538, "data": {"pv_dec_string": "6,018,104.3596", "pv_ans_text": "6 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0538"}}, {"seed": 539, "data": {"pv_dec_string": "1,897.308675", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.13", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0539"}}, {"seed": 540, "data": {"pv_dec_string": "17,423.841522", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0540"}}, {"seed": 541, "data": {"pv_dec_string": "533,317.1246", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 5 small cubes", "__seed__": "0541"}}, {"seed": 542, "data": {"pv_dec_string": "8,435,143.8569", "pv_ans_text": "8 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0542"}}, {"seed": 543, "data": {"pv_dec_string": "62,901.236794", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0543"}}, {"seed": 544, "data": {"pv_dec_string": "8,005.231529", "pv_ans_text": "8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 2 small cubes", "__seed__": "0544"}}, {"seed": 545, "data": {"pv_dec_string": "45,417.567107", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.54", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0545"}}, {"seed": 546, "data": {"pv_dec_string": "20,512.0156", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0546"}}, {"seed": 547, "data": {"pv_dec_string": "6,240.96098", "pv_ans_text": "6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.52", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0547"}}, {"seed": 548, "data": {"pv_dec_string": "427.029693", "pv_ans_text": "4 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.16", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0548"}}, {"seed": 549, "data": {"pv_dec_string": "297,341.89315", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.624", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 2 longs, and 4 small cubes", "__seed__": "0549"}}, {"seed": 550, "data": {"pv_dec_string": "2,304.64261", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.04", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0550"}}, {"seed": 551, "data": {"pv_dec_string": "14,031.625588", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0551"}}, {"seed": 552, "data": {"pv_dec_string": "113,924.67689", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 4 small cubes", "__seed__": "0552"}}, {"seed": 553, "data": {"pv_dec_string": "9,818.14194", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 6 small cubes", "__seed__": "0553"}}, {"seed": 554, "data": {"pv_dec_string": "9,823.833953", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.144", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0554"}}, {"seed": 555, "data": {"pv_dec_string": "4,847.914525", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.500", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0555"}}, {"seed": 556, "data": {"pv_dec_string": "60,323.880154", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0556"}}, {"seed": 557, "data": {"pv_dec_string": "1,852.55833", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.01", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0557"}}, {"seed": 558, "data": {"pv_dec_string": "553.886056", "pv_ans_text": "5 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.311", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0558"}}, {"seed": 559, "data": {"pv_dec_string": "889,320.5304", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.666", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 6 longs, and 6 small cubes", "__seed__": "0559"}}, {"seed": 560, "data": {"pv_dec_string": "4,497.5498", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.13", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0560"}}, {"seed": 561, "data": {"pv_dec_string": "110.416916", "pv_ans_text": "1 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.035", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 3 longs, and 5 small cubes", "__seed__": "0561"}}, {"seed": 562, "data": {"pv_dec_string": "9,518.34736", "pv_ans_text": "9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0562"}}, {"seed": 563, "data": {"pv_dec_string": "248,955.8881", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.65", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0563"}}, {"seed": 564, "data": {"pv_dec_string": "64,739.83175", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 2 small cubes", "__seed__": "0564"}}, {"seed": 565, "data": {"pv_dec_string": "616.862766", "pv_ans_text": "6 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.55", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0565"}}, {"seed": 566, "data": {"pv_dec_string": "347,704.69734", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.50", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0566"}}, {"seed": 567, "data": {"pv_dec_string": "958,282.40911", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0567"}}, {"seed": 568, "data": {"pv_dec_string": "4,914.300005", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0568"}}, {"seed": 569, "data": {"pv_dec_string": "58,437.11806", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.66", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0569"}}, {"seed": 570, "data": {"pv_dec_string": "88,213.6905", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 5 small cubes", "__seed__": "0570"}}, {"seed": 571, "data": {"pv_dec_string": "465.309376", "pv_ans_text": "4 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0571"}}, {"seed": 572, "data": {"pv_dec_string": "5,431,969.0855", "pv_ans_text": "5 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.54", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0572"}}, {"seed": 573, "data": {"pv_dec_string": "8,190.542288", "pv_ans_text": "8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0573"}}, {"seed": 574, "data": {"pv_dec_string": "90,550.3591", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 6 small cubes", "__seed__": "0574"}}, {"seed": 575, "data": {"pv_dec_string": "508,794.4673", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.03", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0575"}}, {"seed": 576, "data": {"pv_dec_string": "56,983.34399", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0576"}}, {"seed": 577, "data": {"pv_dec_string": "73,072.4084", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.36", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0577"}}, {"seed": 578, "data": {"pv_dec_string": "23,006.8314", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0578"}}, {"seed": 579, "data": {"pv_dec_string": "97,744.2217", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0579"}}, {"seed": 580, "data": {"pv_dec_string": "4,684.517749", "pv_ans_text": "4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.06", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0580"}}, {"seed": 581, "data": {"pv_dec_string": "984.456857", "pv_ans_text": "9 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.432", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 3 longs, and 2 small cubes", "__seed__": "0581"}}, {"seed": 582, "data": {"pv_dec_string": "742.553837", "pv_ans_text": "7 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 3 small cubes", "__seed__": "0582"}}, {"seed": 583, "data": {"pv_dec_string": "89,802.755738", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 5 small cubes", "__seed__": "0583"}}, {"seed": 584, "data": {"pv_dec_string": "713,427.6201", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 4 small cubes", "__seed__": "0584"}}, {"seed": 585, "data": {"pv_dec_string": "453,247.82696", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.36", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0585"}}, {"seed": 586, "data": {"pv_dec_string": "957,699.25476", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0586"}}, {"seed": 587, "data": {"pv_dec_string": "262,666.1511", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 5 small cubes", "__seed__": "0587"}}, {"seed": 588, "data": {"pv_dec_string": "6,867.32262", "pv_ans_text": "6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0588"}}, {"seed": 589, "data": {"pv_dec_string": "9,159.55203", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0589"}}, {"seed": 590, "data": {"pv_dec_string": "4,263.48154", "pv_ans_text": "4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0590"}}, {"seed": 591, "data": {"pv_dec_string": "729.99314", "pv_ans_text": "7 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 4 small cubes", "__seed__": "0591"}}, {"seed": 592, "data": {"pv_dec_string": "68,144.45219", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.42", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0592"}}, {"seed": 593, "data": {"pv_dec_string": "71,466.1901", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 2 small cubes", "__seed__": "0593"}}, {"seed": 594, "data": {"pv_dec_string": "4,437,488.3262", "pv_ans_text": "4 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0594"}}, {"seed": 595, "data": {"pv_dec_string": "685,495.54545", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.426", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 2 longs, and 6 small cubes", "__seed__": "0595"}}, {"seed": 596, "data": {"pv_dec_string": "7,996.970757", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.25", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0596"}}, {"seed": 597, "data": {"pv_dec_string": "363,619.7338", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.061", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 6 longs, and 1 small cubes", "__seed__": "0597"}}, {"seed": 598, "data": {"pv_dec_string": "1,303,850.6301", "pv_ans_text": "1 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.303", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0598"}}, {"seed": 599, "data": {"pv_dec_string": "42,526.15964", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 2 small cubes", "__seed__": "0599"}}, {"seed": 600, "data": {"pv_dec_string": "700,939.32591", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.161", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0600"}}, {"seed": 601, "data": {"pv_dec_string": "409.821554", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 4 small cubes", "__seed__": "0601"}}, {"seed": 602, "data": {"pv_dec_string": "656,251.17377", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.162", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 2 small cubes", "__seed__": "0602"}}, {"seed": 603, "data": {"pv_dec_string": "86,119.6943", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0603"}}, {"seed": 604, "data": {"pv_dec_string": "5,731.57209", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 6 small cubes", "__seed__": "0604"}}, {"seed": 605, "data": {"pv_dec_string": "792.48029", "pv_ans_text": "7 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 2 small cubes", "__seed__": "0605"}}, {"seed": 606, "data": {"pv_dec_string": "76,574.331288", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 1 small cubes", "__seed__": "0606"}}, {"seed": 607, "data": {"pv_dec_string": "258.098688", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.012", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 1 longs, and 2 small cubes", "__seed__": "0607"}}, {"seed": 608, "data": {"pv_dec_string": "98,943.88918", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0608"}}, {"seed": 609, "data": {"pv_dec_string": "13,562.57251", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 3 small cubes", "__seed__": "0609"}}, {"seed": 610, "data": {"pv_dec_string": "9,419.915559", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 4 small cubes", "__seed__": "0610"}}, {"seed": 611, "data": {"pv_dec_string": "2,252.84739", "pv_ans_text": "2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0611"}}, {"seed": 612, "data": {"pv_dec_string": "8,071,847.4454", "pv_ans_text": "8 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 2 small cubes", "__seed__": "0612"}}, {"seed": 613, "data": {"pv_dec_string": "3,913.813677", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.264", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 6 longs, and 4 small cubes", "__seed__": "0613"}}, {"seed": 614, "data": {"pv_dec_string": "83,545.6844", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0614"}}, {"seed": 615, "data": {"pv_dec_string": "2,553.13492", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0615"}}, {"seed": 616, "data": {"pv_dec_string": "5,919.19634", "pv_ans_text": "5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 2 small cubes", "__seed__": "0616"}}, {"seed": 617, "data": {"pv_dec_string": "3,514.99978", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.565", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0617"}}, {"seed": 618, "data": {"pv_dec_string": "504.608568", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 4 small cubes", "__seed__": "0618"}}, {"seed": 619, "data": {"pv_dec_string": "1,274,595.1134", "pv_ans_text": "1 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 5 small cubes", "__seed__": "0619"}}, {"seed": 620, "data": {"pv_dec_string": "96,703.2989", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.640", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0620"}}, {"seed": 621, "data": {"pv_dec_string": "7,332.97415", "pv_ans_text": "7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 1 small cubes", "__seed__": "0621"}}, {"seed": 622, "data": {"pv_dec_string": "3,986,949.2907", "pv_ans_text": "3 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0622"}}, {"seed": 623, "data": {"pv_dec_string": "72,052.82582", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 6 small cubes", "__seed__": "0623"}}, {"seed": 624, "data": {"pv_dec_string": "467.595195", "pv_ans_text": "4 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.51", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0624"}}, {"seed": 625, "data": {"pv_dec_string": "51,057.31084", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 5 small cubes", "__seed__": "0625"}}, {"seed": 626, "data": {"pv_dec_string": "8,191,172.611", "pv_ans_text": "8 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 1 small cubes", "__seed__": "0626"}}, {"seed": 627, "data": {"pv_dec_string": "463,448.128", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.241", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0627"}}, {"seed": 628, "data": {"pv_dec_string": "888.627853", "pv_ans_text": "8 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.015", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 1 longs, and 5 small cubes", "__seed__": "0628"}}, {"seed": 629, "data": {"pv_dec_string": "33,502.49337", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 6 small cubes", "__seed__": "0629"}}, {"seed": 630, "data": {"pv_dec_string": "14,189.02908", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.42", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0630"}}, {"seed": 631, "data": {"pv_dec_string": "8,734,999.7937", "pv_ans_text": "8 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 4 small cubes", "__seed__": "0631"}}, {"seed": 632, "data": {"pv_dec_string": "25,799.73402", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0632"}}, {"seed": 633, "data": {"pv_dec_string": "8,156.58495", "pv_ans_text": "8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.00", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0633"}}, {"seed": 634, "data": {"pv_dec_string": "594.359025", "pv_ans_text": "5 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0634"}}, {"seed": 635, "data": {"pv_dec_string": "858,733.43134", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.334", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0635"}}, {"seed": 636, "data": {"pv_dec_string": "91,443.83802", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.56", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0636"}}, {"seed": 637, "data": {"pv_dec_string": "71,228.18386", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0637"}}, {"seed": 638, "data": {"pv_dec_string": "688,681.6818", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 6 small cubes", "__seed__": "0638"}}, {"seed": 639, "data": {"pv_dec_string": "3,242,565.9735", "pv_ans_text": "3 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0639"}}, {"seed": 640, "data": {"pv_dec_string": "9,131,171.3091", "pv_ans_text": "9 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0640"}}, {"seed": 641, "data": {"pv_dec_string": "728,516.74", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.413", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 3 small cubes", "__seed__": "0641"}}, {"seed": 642, "data": {"pv_dec_string": "4,923.91238", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0642"}}, {"seed": 643, "data": {"pv_dec_string": "22,586.001197", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 4 small cubes", "__seed__": "0643"}}, {"seed": 644, "data": {"pv_dec_string": "9,620.98892", "pv_ans_text": "9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.212", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 1 longs, and 2 small cubes", "__seed__": "0644"}}, {"seed": 645, "data": {"pv_dec_string": "118,829.1737", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0645"}}, {"seed": 646, "data": {"pv_dec_string": "93,448.6691", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.11", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0646"}}, {"seed": 647, "data": {"pv_dec_string": "33,012.516218", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.00", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0647"}}, {"seed": 648, "data": {"pv_dec_string": "47,878.0181", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.22", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0648"}}, {"seed": 649, "data": {"pv_dec_string": "7,766,701.9477", "pv_ans_text": "7 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 3 small cubes", "__seed__": "0649"}}, {"seed": 650, "data": {"pv_dec_string": "737.875089", "pv_ans_text": "7 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0650"}}, {"seed": 651, "data": {"pv_dec_string": "3,709.83337", "pv_ans_text": "3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 1 small cubes", "__seed__": "0651"}}, {"seed": 652, "data": {"pv_dec_string": "93,861.780946", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 4 small cubes", "__seed__": "0652"}}, {"seed": 653, "data": {"pv_dec_string": "512,110.16362", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.050", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0653"}}, {"seed": 654, "data": {"pv_dec_string": "2,756.279067", "pv_ans_text": "2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.354", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0654"}}, {"seed": 655, "data": {"pv_dec_string": "66,891.9288", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.23", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0655"}}, {"seed": 656, "data": {"pv_dec_string": "5,257.32345", "pv_ans_text": "5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.40", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0656"}}, {"seed": 657, "data": {"pv_dec_string": "35,692.2933", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.006", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 0 longs, and 6 small cubes", "__seed__": "0657"}}, {"seed": 658, "data": {"pv_dec_string": "93,172.6873", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.653", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 5 longs, and 3 small cubes", "__seed__": "0658"}}, {"seed": 659, "data": {"pv_dec_string": "7,903.962854", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.62", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0659"}}, {"seed": 660, "data": {"pv_dec_string": "79,608.09259", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.332", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0660"}}, {"seed": 661, "data": {"pv_dec_string": "66,999.168999", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 5 small cubes", "__seed__": "0661"}}, {"seed": 662, "data": {"pv_dec_string": "7,991,951.8695", "pv_ans_text": "7 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0662"}}, {"seed": 663, "data": {"pv_dec_string": "4,069.711105", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.443", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0663"}}, {"seed": 664, "data": {"pv_dec_string": "62,282.0494", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.41", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0664"}}, {"seed": 665, "data": {"pv_dec_string": "6,520.935115", "pv_ans_text": "6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 6 small cubes", "__seed__": "0665"}}, {"seed": 666, "data": {"pv_dec_string": "33,068.92002", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.22", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0666"}}, {"seed": 667, "data": {"pv_dec_string": "18,992.541067", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.13", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0667"}}, {"seed": 668, "data": {"pv_dec_string": "933.422755", "pv_ans_text": "9 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.040", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0668"}}, {"seed": 669, "data": {"pv_dec_string": "317.980264", "pv_ans_text": "3 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0669"}}, {"seed": 670, "data": {"pv_dec_string": "41,190.313576", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 5 small cubes", "__seed__": "0670"}}, {"seed": 671, "data": {"pv_dec_string": "2,391,823.7938", "pv_ans_text": "2 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.35", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0671"}}, {"seed": 672, "data": {"pv_dec_string": "4,508.754409", "pv_ans_text": "4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.53", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0672"}}, {"seed": 673, "data": {"pv_dec_string": "22,578.3995", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0673"}}, {"seed": 674, "data": {"pv_dec_string": "830,563.22637", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.21", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 1 longs, and 0 small cubes", "__seed__": "0674"}}, {"seed": 675, "data": {"pv_dec_string": "30,209.35821", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0675"}}, {"seed": 676, "data": {"pv_dec_string": "319,452.8791", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.20", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0676"}}, {"seed": 677, "data": {"pv_dec_string": "761,730.6138", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0677"}}, {"seed": 678, "data": {"pv_dec_string": "82,901.52169", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 6 small cubes", "__seed__": "0678"}}, {"seed": 679, "data": {"pv_dec_string": "5,850.166181", "pv_ans_text": "5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.126", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 2 longs, and 6 small cubes", "__seed__": "0679"}}, {"seed": 680, "data": {"pv_dec_string": "939,275.63641", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 4 small cubes", "__seed__": "0680"}}, {"seed": 681, "data": {"pv_dec_string": "85,260.410559", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0681"}}, {"seed": 682, "data": {"pv_dec_string": "16,814.268625", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0682"}}, {"seed": 683, "data": {"pv_dec_string": "6,707.681542", "pv_ans_text": "6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.115", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 5 small cubes", "__seed__": "0683"}}, {"seed": 684, "data": {"pv_dec_string": "6,581.720731", "pv_ans_text": "6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.651", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0684"}}, {"seed": 685, "data": {"pv_dec_string": "90,792.8862", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0685"}}, {"seed": 686, "data": {"pv_dec_string": "487,557.1018", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.05", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0686"}}, {"seed": 687, "data": {"pv_dec_string": "339,860.9632", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.623", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0687"}}, {"seed": 688, "data": {"pv_dec_string": "732,552.8782", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 4 small cubes", "__seed__": "0688"}}, {"seed": 689, "data": {"pv_dec_string": "85,916.179", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.120", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0689"}}, {"seed": 690, "data": {"pv_dec_string": "9,524,548.7494", "pv_ans_text": "9 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.210", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 1 longs, and 0 small cubes", "__seed__": "0690"}}, {"seed": 691, "data": {"pv_dec_string": "9,245,805.5629", "pv_ans_text": "9 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0691"}}, {"seed": 692, "data": {"pv_dec_string": "899,553.64537", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0692"}}, {"seed": 693, "data": {"pv_dec_string": "247,043.0552", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 6 small cubes", "__seed__": "0693"}}, {"seed": 694, "data": {"pv_dec_string": "50,081.98468", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0694"}}, {"seed": 695, "data": {"pv_dec_string": "967,723.9863", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.04", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0695"}}, {"seed": 696, "data": {"pv_dec_string": "87,001.290583", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.611", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 1 longs, and 1 small cubes", "__seed__": "0696"}}, {"seed": 697, "data": {"pv_dec_string": "564.947175", "pv_ans_text": "5 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.20", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0697"}}, {"seed": 698, "data": {"pv_dec_string": "84,951.504433", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.621", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 2 longs, and 1 small cubes", "__seed__": "0698"}}, {"seed": 699, "data": {"pv_dec_string": "706,267.52101", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 2 small cubes", "__seed__": "0699"}}, {"seed": 700, "data": {"pv_dec_string": "494,606.301", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 2 small cubes", "__seed__": "0700"}}, {"seed": 701, "data": {"pv_dec_string": "6,457,746.8211", "pv_ans_text": "6 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.125", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 5 small cubes", "__seed__": "0701"}}, {"seed": 702, "data": {"pv_dec_string": "3,993.996908", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.431", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 3 longs, and 1 small cubes", "__seed__": "0702"}}, {"seed": 703, "data": {"pv_dec_string": "17,171.7979", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.661", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 6 longs, and 1 small cubes", "__seed__": "0703"}}, {"seed": 704, "data": {"pv_dec_string": "8,793.481122", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.23", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0704"}}, {"seed": 705, "data": {"pv_dec_string": "97,068.199189", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 4 small cubes", "__seed__": "0705"}}, {"seed": 706, "data": {"pv_dec_string": "761,500.6857", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.26", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0706"}}, {"seed": 707, "data": {"pv_dec_string": "81,558.63792", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.141", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 1 small cubes", "__seed__": "0707"}}, {"seed": 708, "data": {"pv_dec_string": "3,152.22462", "pv_ans_text": "3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.313", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 1 longs, and 3 small cubes", "__seed__": "0708"}}, {"seed": 709, "data": {"pv_dec_string": "39,177.75574", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0709"}}, {"seed": 710, "data": {"pv_dec_string": "7,657.31811", "pv_ans_text": "7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0710"}}, {"seed": 711, "data": {"pv_dec_string": "54,993.29184", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0711"}}, {"seed": 712, "data": {"pv_dec_string": "53,603.8012", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.043", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 4 longs, and 3 small cubes", "__seed__": "0712"}}, {"seed": 713, "data": {"pv_dec_string": "78,853.3397", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0713"}}, {"seed": 714, "data": {"pv_dec_string": "7,483,592.1798", "pv_ans_text": "7 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.12", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0714"}}, {"seed": 715, "data": {"pv_dec_string": "812,331.5141", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.35", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0715"}}, {"seed": 716, "data": {"pv_dec_string": "842,937.45048", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.434", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0716"}}, {"seed": 717, "data": {"pv_dec_string": "952,580.8636", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.20", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0717"}}, {"seed": 718, "data": {"pv_dec_string": "56,154.143008", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.360", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0718"}}, {"seed": 719, "data": {"pv_dec_string": "4,069.29044", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 6 small cubes", "__seed__": "0719"}}, {"seed": 720, "data": {"pv_dec_string": "43,802.5939", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.54", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0720"}}, {"seed": 721, "data": {"pv_dec_string": "36,201.78521", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0721"}}, {"seed": 722, "data": {"pv_dec_string": "4,929.640995", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.31", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0722"}}, {"seed": 723, "data": {"pv_dec_string": "74,581.800161", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0723"}}, {"seed": 724, "data": {"pv_dec_string": "379.792877", "pv_ans_text": "3 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.424", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0724"}}, {"seed": 725, "data": {"pv_dec_string": "431,519.67153", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0725"}}, {"seed": 726, "data": {"pv_dec_string": "242.350666", "pv_ans_text": "2 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0726"}}, {"seed": 727, "data": {"pv_dec_string": "5,012,323.9415", "pv_ans_text": "5 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 4 small cubes", "__seed__": "0727"}}, {"seed": 728, "data": {"pv_dec_string": "169.286858", "pv_ans_text": "1 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0728"}}, {"seed": 729, "data": {"pv_dec_string": "874,740.9987", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0729"}}, {"seed": 730, "data": {"pv_dec_string": "8,617.17652", "pv_ans_text": "8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.640", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0730"}}, {"seed": 731, "data": {"pv_dec_string": "401.984989", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.414", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 1 longs, and 4 small cubes", "__seed__": "0731"}}, {"seed": 732, "data": {"pv_dec_string": "37,724.2441", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.110", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0732"}}, {"seed": 733, "data": {"pv_dec_string": "66,725.0104", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 6 small cubes", "__seed__": "0733"}}, {"seed": 734, "data": {"pv_dec_string": "2,808.836224", "pv_ans_text": "2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.62", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0734"}}, {"seed": 735, "data": {"pv_dec_string": "340,234.6135", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.52", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0735"}}, {"seed": 736, "data": {"pv_dec_string": "665,992.2856", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.544", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0736"}}, {"seed": 737, "data": {"pv_dec_string": "195,322.36664", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.00", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0737"}}, {"seed": 738, "data": {"pv_dec_string": "4,358,542.4759", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.152", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 5 longs, and 2 small cubes", "__seed__": "0738"}}, {"seed": 739, "data": {"pv_dec_string": "5,683,739.0065", "pv_ans_text": "5 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0739"}}, {"seed": 740, "data": {"pv_dec_string": "1,761.956818", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.14", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0740"}}, {"seed": 741, "data": {"pv_dec_string": "206.837884", "pv_ans_text": "2 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.60", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0741"}}, {"seed": 742, "data": {"pv_dec_string": "4,771.093363", "pv_ans_text": "4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0742"}}, {"seed": 743, "data": {"pv_dec_string": "7,240.413262", "pv_ans_text": "7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0743"}}, {"seed": 744, "data": {"pv_dec_string": "8,386,835.872", "pv_ans_text": "8 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.00", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0744"}}, {"seed": 745, "data": {"pv_dec_string": "74,756.686781", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.35", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 5 small cubes", "__seed__": "0745"}}, {"seed": 746, "data": {"pv_dec_string": "537.914867", "pv_ans_text": "5 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0746"}}, {"seed": 747, "data": {"pv_dec_string": "1,036.36743", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.51", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0747"}}, {"seed": 748, "data": {"pv_dec_string": "6,950,461.4897", "pv_ans_text": "6 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0748"}}, {"seed": 749, "data": {"pv_dec_string": "5,817.526451", "pv_ans_text": "5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.56", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0749"}}, {"seed": 750, "data": {"pv_dec_string": "69,459.90945", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0750"}}, {"seed": 751, "data": {"pv_dec_string": "847.787409", "pv_ans_text": "8 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.46", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0751"}}, {"seed": 752, "data": {"pv_dec_string": "59,361.921332", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0752"}}, {"seed": 753, "data": {"pv_dec_string": "86,389.51687", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0753"}}, {"seed": 754, "data": {"pv_dec_string": "7,902.323125", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.124", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 2 longs, and 4 small cubes", "__seed__": "0754"}}, {"seed": 755, "data": {"pv_dec_string": "5,987,048.7444", "pv_ans_text": "5 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.343", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 4 longs, and 3 small cubes", "__seed__": "0755"}}, {"seed": 756, "data": {"pv_dec_string": "75,674.733", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.44", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0756"}}, {"seed": 757, "data": {"pv_dec_string": "98,087.0557", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0757"}}, {"seed": 758, "data": {"pv_dec_string": "7,884.50219", "pv_ans_text": "7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.42", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0758"}}, {"seed": 759, "data": {"pv_dec_string": "49,542.51327", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.240", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0759"}}, {"seed": 760, "data": {"pv_dec_string": "19,184.8258", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.15", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0760"}}, {"seed": 761, "data": {"pv_dec_string": "51,080.080568", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.10", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0761"}}, {"seed": 762, "data": {"pv_dec_string": "5,764,032.1888", "pv_ans_text": "5 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 6 small cubes", "__seed__": "0762"}}, {"seed": 763, "data": {"pv_dec_string": "533,443.29396", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 5 small cubes", "__seed__": "0763"}}, {"seed": 764, "data": {"pv_dec_string": "81,599.901247", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 5 small cubes", "__seed__": "0764"}}, {"seed": 765, "data": {"pv_dec_string": "6,628.527655", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.53", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0765"}}, {"seed": 766, "data": {"pv_dec_string": "20,928.773068", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0766"}}, {"seed": 767, "data": {"pv_dec_string": "24,955.55033", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.151", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 5 longs, and 1 small cubes", "__seed__": "0767"}}, {"seed": 768, "data": {"pv_dec_string": "26,755.261478", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0768"}}, {"seed": 769, "data": {"pv_dec_string": "6,826,814.1725", "pv_ans_text": "6 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.655", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 5 longs, and 5 small cubes", "__seed__": "0769"}}, {"seed": 770, "data": {"pv_dec_string": "82,909.6545", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 3 small cubes", "__seed__": "0770"}}, {"seed": 771, "data": {"pv_dec_string": "5,085.12886", "pv_ans_text": "5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.254", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 5 longs, and 4 small cubes", "__seed__": "0771"}}, {"seed": 772, "data": {"pv_dec_string": "4,450.976869", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 5 small cubes", "__seed__": "0772"}}, {"seed": 773, "data": {"pv_dec_string": "93,224.9635", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0773"}}, {"seed": 774, "data": {"pv_dec_string": "5,490.949572", "pv_ans_text": "5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.132", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 3 longs, and 2 small cubes", "__seed__": "0774"}}, {"seed": 775, "data": {"pv_dec_string": "249,418.07046", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0775"}}, {"seed": 776, "data": {"pv_dec_string": "76,928.682578", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0776"}}, {"seed": 777, "data": {"pv_dec_string": "79,521.4746", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.411", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 1 longs, and 1 small cubes", "__seed__": "0777"}}, {"seed": 778, "data": {"pv_dec_string": "7,217,279.2913", "pv_ans_text": "7 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0778"}}, {"seed": 779, "data": {"pv_dec_string": "37,351.74724", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 5 small cubes", "__seed__": "0779"}}, {"seed": 780, "data": {"pv_dec_string": "60,355.563083", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.61", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0780"}}, {"seed": 781, "data": {"pv_dec_string": "72,510.77394", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0781"}}, {"seed": 782, "data": {"pv_dec_string": "1,215.64469", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.356", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 5 longs, and 6 small cubes", "__seed__": "0782"}}, {"seed": 783, "data": {"pv_dec_string": "31,032.31364", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0783"}}, {"seed": 784, "data": {"pv_dec_string": "361,980.33679", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.542", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 4 longs, and 2 small cubes", "__seed__": "0784"}}, {"seed": 785, "data": {"pv_dec_string": "74,974.237335", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 1 small cubes", "__seed__": "0785"}}, {"seed": 786, "data": {"pv_dec_string": "5,176.2117", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.03", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0786"}}, {"seed": 787, "data": {"pv_dec_string": "1,189,449.2318", "pv_ans_text": "1 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.54", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0787"}}, {"seed": 788, "data": {"pv_dec_string": "11,213.06566", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.336", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 3 longs, and 6 small cubes", "__seed__": "0788"}}, {"seed": 789, "data": {"pv_dec_string": "762,862.1783", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 1 small cubes", "__seed__": "0789"}}, {"seed": 790, "data": {"pv_dec_string": "4,450,723.3507", "pv_ans_text": "4 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.161", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0790"}}, {"seed": 791, "data": {"pv_dec_string": "364.9546", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 3 small cubes", "__seed__": "0791"}}, {"seed": 792, "data": {"pv_dec_string": "217.069415", "pv_ans_text": "2 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0792"}}, {"seed": 793, "data": {"pv_dec_string": "50,945.8187", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 5 small cubes", "__seed__": "0793"}}, {"seed": 794, "data": {"pv_dec_string": "141,901.89934", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0794"}}, {"seed": 795, "data": {"pv_dec_string": "43,186.660148", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 1 small cubes", "__seed__": "0795"}}, {"seed": 796, "data": {"pv_dec_string": "137,851.7021", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 3 small cubes", "__seed__": "0796"}}, {"seed": 797, "data": {"pv_dec_string": "5,536.22213", "pv_ans_text": "5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 5 small cubes", "__seed__": "0797"}}, {"seed": 798, "data": {"pv_dec_string": "3,106.82246", "pv_ans_text": "3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.55", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0798"}}, {"seed": 799, "data": {"pv_dec_string": "3,521,844.4536", "pv_ans_text": "3 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.315", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 5 small cubes", "__seed__": "0799"}}, {"seed": 800, "data": {"pv_dec_string": "5,679.23631", "pv_ans_text": "5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 4 small cubes", "__seed__": "0800"}}, {"seed": 801, "data": {"pv_dec_string": "12,060.309532", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.53", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0801"}}, {"seed": 802, "data": {"pv_dec_string": "25,412.9946", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.64", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0802"}}, {"seed": 803, "data": {"pv_dec_string": "63,119.30709", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.12", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0803"}}, {"seed": 804, "data": {"pv_dec_string": "2,319.32316", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.216", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0804"}}, {"seed": 805, "data": {"pv_dec_string": "528.611971", "pv_ans_text": "5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.65", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0805"}}, {"seed": 806, "data": {"pv_dec_string": "4,222.44803", "pv_ans_text": "4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0806"}}, {"seed": 807, "data": {"pv_dec_string": "9,149.21273", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.22", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0807"}}, {"seed": 808, "data": {"pv_dec_string": "4,040.807341", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0808"}}, {"seed": 809, "data": {"pv_dec_string": "6,905,625.8948", "pv_ans_text": "6 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 2 small cubes", "__seed__": "0809"}}, {"seed": 810, "data": {"pv_dec_string": "3,495,953.8336", "pv_ans_text": "3 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.36", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0810"}}, {"seed": 811, "data": {"pv_dec_string": "47,839.835786", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0811"}}, {"seed": 812, "data": {"pv_dec_string": "9,154,959.8552", "pv_ans_text": "9 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0812"}}, {"seed": 813, "data": {"pv_dec_string": "314,495.91847", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 3 small cubes", "__seed__": "0813"}}, {"seed": 814, "data": {"pv_dec_string": "289.930605", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.63", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0814"}}, {"seed": 815, "data": {"pv_dec_string": "825,963.4766", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.16", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0815"}}, {"seed": 816, "data": {"pv_dec_string": "237.941262", "pv_ans_text": "2 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0816"}}, {"seed": 817, "data": {"pv_dec_string": "9,340.88687", "pv_ans_text": "9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.46", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0817"}}, {"seed": 818, "data": {"pv_dec_string": "94,426.0761", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.06", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0818"}}, {"seed": 819, "data": {"pv_dec_string": "360.260845", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.303", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0819"}}, {"seed": 820, "data": {"pv_dec_string": "286.688937", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.20", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0820"}}, {"seed": 821, "data": {"pv_dec_string": "2,158.943999", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.420", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0821"}}, {"seed": 822, "data": {"pv_dec_string": "57,481.5844", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 5 small cubes", "__seed__": "0822"}}, {"seed": 823, "data": {"pv_dec_string": "5,537,224.0507", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 6 small cubes", "__seed__": "0823"}}, {"seed": 824, "data": {"pv_dec_string": "24,528.3852", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 6 small cubes", "__seed__": "0824"}}, {"seed": 825, "data": {"pv_dec_string": "68,574.5651", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.61", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0825"}}, {"seed": 826, "data": {"pv_dec_string": "227,068.9355", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.114", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 4 small cubes", "__seed__": "0826"}}, {"seed": 827, "data": {"pv_dec_string": "8,730.023861", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0827"}}, {"seed": 828, "data": {"pv_dec_string": "79,031.768639", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0828"}}, {"seed": 829, "data": {"pv_dec_string": "239,935.63914", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.50", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0829"}}, {"seed": 830, "data": {"pv_dec_string": "2,934,528.6203", "pv_ans_text": "2 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0830"}}, {"seed": 831, "data": {"pv_dec_string": "896,738.241", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.304", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0831"}}, {"seed": 832, "data": {"pv_dec_string": "72,358.849275", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.01", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0832"}}, {"seed": 833, "data": {"pv_dec_string": "701.719424", "pv_ans_text": "7 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.101", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0833"}}, {"seed": 834, "data": {"pv_dec_string": "39,180.06854", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0834"}}, {"seed": 835, "data": {"pv_dec_string": "88,060.3143", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.330", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0835"}}, {"seed": 836, "data": {"pv_dec_string": "25,780.892389", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.35", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0836"}}, {"seed": 837, "data": {"pv_dec_string": "96,401.159261", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 3 small cubes", "__seed__": "0837"}}, {"seed": 838, "data": {"pv_dec_string": "470.628804", "pv_ans_text": "4 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 4 small cubes", "__seed__": "0838"}}, {"seed": 839, "data": {"pv_dec_string": "97,627.968335", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0839"}}, {"seed": 840, "data": {"pv_dec_string": "3,141,451.0023", "pv_ans_text": "3 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.154", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 5 longs, and 4 small cubes", "__seed__": "0840"}}, {"seed": 841, "data": {"pv_dec_string": "93,040.007926", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0841"}}, {"seed": 842, "data": {"pv_dec_string": "81,095.770751", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.041", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 1 small cubes", "__seed__": "0842"}}, {"seed": 843, "data": {"pv_dec_string": "645,005.069", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0843"}}, {"seed": 844, "data": {"pv_dec_string": "19,341.179", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.560", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0844"}}, {"seed": 845, "data": {"pv_dec_string": "764.960367", "pv_ans_text": "7 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.06", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0845"}}, {"seed": 846, "data": {"pv_dec_string": "7,623,486.4051", "pv_ans_text": "7 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.231", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 3 longs, and 1 small cubes", "__seed__": "0846"}}, {"seed": 847, "data": {"pv_dec_string": "2,929.397663", "pv_ans_text": "2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.415", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 5 small cubes", "__seed__": "0847"}}, {"seed": 848, "data": {"pv_dec_string": "8,838.84131", "pv_ans_text": "8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0848"}}, {"seed": 849, "data": {"pv_dec_string": "2,143.019342", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 1 small cubes", "__seed__": "0849"}}, {"seed": 850, "data": {"pv_dec_string": "43,485.55361", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0850"}}, {"seed": 851, "data": {"pv_dec_string": "3,141,471.7747", "pv_ans_text": "3 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0851"}}, {"seed": 852, "data": {"pv_dec_string": "366.081626", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.14", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0852"}}, {"seed": 853, "data": {"pv_dec_string": "76,660.90167", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.106", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 6 small cubes", "__seed__": "0853"}}, {"seed": 854, "data": {"pv_dec_string": "8,738,863.2886", "pv_ans_text": "8 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.134", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0854"}}, {"seed": 855, "data": {"pv_dec_string": "6,860.917275", "pv_ans_text": "6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.16", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0855"}}, {"seed": 856, "data": {"pv_dec_string": "7,058,415.8888", "pv_ans_text": "7 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.346", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0856"}}, {"seed": 857, "data": {"pv_dec_string": "1,056.246383", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 6 small cubes", "__seed__": "0857"}}, {"seed": 858, "data": {"pv_dec_string": "49,217.5895", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0858"}}, {"seed": 859, "data": {"pv_dec_string": "63,775.77899", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.54", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0859"}}, {"seed": 860, "data": {"pv_dec_string": "4,292.332829", "pv_ans_text": "4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.35", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 5 small cubes", "__seed__": "0860"}}, {"seed": 861, "data": {"pv_dec_string": "2,860,849.7696", "pv_ans_text": "2 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.435", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 3 longs, and 5 small cubes", "__seed__": "0861"}}, {"seed": 862, "data": {"pv_dec_string": "59,158.9345", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0862"}}, {"seed": 863, "data": {"pv_dec_string": "2,437.833286", "pv_ans_text": "2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.041", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 4 longs, and 1 small cubes", "__seed__": "0863"}}, {"seed": 864, "data": {"pv_dec_string": "7,907.06143", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.14", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0864"}}, {"seed": 865, "data": {"pv_dec_string": "5,806,329.2269", "pv_ans_text": "5 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0865"}}, {"seed": 866, "data": {"pv_dec_string": "76,300.30147", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0866"}}, {"seed": 867, "data": {"pv_dec_string": "564,909.6677", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 1 small cubes", "__seed__": "0867"}}, {"seed": 868, "data": {"pv_dec_string": "246,635.7395", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.52", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0868"}}, {"seed": 869, "data": {"pv_dec_string": "98,118.42689", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 5 small cubes", "__seed__": "0869"}}, {"seed": 870, "data": {"pv_dec_string": "2,199.05934", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 6 small cubes", "__seed__": "0870"}}, {"seed": 871, "data": {"pv_dec_string": "71,556.0343", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.24", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0871"}}, {"seed": 872, "data": {"pv_dec_string": "13,823.78826", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.61", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0872"}}, {"seed": 873, "data": {"pv_dec_string": "812,949.4641", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.01", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0873"}}, {"seed": 874, "data": {"pv_dec_string": "423,821.4807", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.640", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0874"}}, {"seed": 875, "data": {"pv_dec_string": "84,047.65976", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0875"}}, {"seed": 876, "data": {"pv_dec_string": "1,004.49533", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0876"}}, {"seed": 877, "data": {"pv_dec_string": "53,683.2606", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 4 small cubes", "__seed__": "0877"}}, {"seed": 878, "data": {"pv_dec_string": "629,607.87665", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 5 small cubes", "__seed__": "0878"}}, {"seed": 879, "data": {"pv_dec_string": "58,290.90895", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.462", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 2 small cubes", "__seed__": "0879"}}, {"seed": 880, "data": {"pv_dec_string": "286.457961", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.36", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0880"}}, {"seed": 881, "data": {"pv_dec_string": "4,827.75142", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0881"}}, {"seed": 882, "data": {"pv_dec_string": "523,490.0661", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 2 small cubes", "__seed__": "0882"}}, {"seed": 883, "data": {"pv_dec_string": "2,389.112245", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.45", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0883"}}, {"seed": 884, "data": {"pv_dec_string": "88,645.20293", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0884"}}, {"seed": 885, "data": {"pv_dec_string": "366,546.6353", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0885"}}, {"seed": 886, "data": {"pv_dec_string": "670.618051", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0886"}}, {"seed": 887, "data": {"pv_dec_string": "8,455.05376", "pv_ans_text": "8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0887"}}, {"seed": 888, "data": {"pv_dec_string": "843,156.4569", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 5 small cubes", "__seed__": "0888"}}, {"seed": 889, "data": {"pv_dec_string": "53,556.6062", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.26", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0889"}}, {"seed": 890, "data": {"pv_dec_string": "936,941.4462", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0890"}}, {"seed": 891, "data": {"pv_dec_string": "825,355.96755", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.24", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0891"}}, {"seed": 892, "data": {"pv_dec_string": "777,035.8932", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.60", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0892"}}, {"seed": 893, "data": {"pv_dec_string": "78,197.30602", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 2 small cubes", "__seed__": "0893"}}, {"seed": 894, "data": {"pv_dec_string": "212.661875", "pv_ans_text": "2 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.042", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 2 small cubes", "__seed__": "0894"}}, {"seed": 895, "data": {"pv_dec_string": "774.592938", "pv_ans_text": "7 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.563", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 6 longs, and 3 small cubes", "__seed__": "0895"}}, {"seed": 896, "data": {"pv_dec_string": "399.02823", "pv_ans_text": "3 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.452", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 2 small cubes", "__seed__": "0896"}}, {"seed": 897, "data": {"pv_dec_string": "9,404.114128", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0897"}}, {"seed": 898, "data": {"pv_dec_string": "8,762.405902", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.65", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0898"}}, {"seed": 899, "data": {"pv_dec_string": "53,858.22873", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0899"}}, {"seed": 900, "data": {"pv_dec_string": "5,855.016295", "pv_ans_text": "5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.03", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0900"}}, {"seed": 901, "data": {"pv_dec_string": "5,342.745307", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0901"}}, {"seed": 902, "data": {"pv_dec_string": "16,906.543097", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0902"}}, {"seed": 903, "data": {"pv_dec_string": "38,842.3546", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 6 small cubes", "__seed__": "0903"}}, {"seed": 904, "data": {"pv_dec_string": "1,791.97631", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0904"}}, {"seed": 905, "data": {"pv_dec_string": "25,049.17248", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.31", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0905"}}, {"seed": 906, "data": {"pv_dec_string": "488.553994", "pv_ans_text": "4 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0906"}}, {"seed": 907, "data": {"pv_dec_string": "49,435.9773", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.541", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 4 longs, and 1 small cubes", "__seed__": "0907"}}, {"seed": 908, "data": {"pv_dec_string": "1,793.640606", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.315", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 5 small cubes", "__seed__": "0908"}}, {"seed": 909, "data": {"pv_dec_string": "3,603.68699", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.53", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0909"}}, {"seed": 910, "data": {"pv_dec_string": "369.719855", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0910"}}, {"seed": 911, "data": {"pv_dec_string": "20,664.93707", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0911"}}, {"seed": 912, "data": {"pv_dec_string": "1,949.42253", "pv_ans_text": "1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.64", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0912"}}, {"seed": 913, "data": {"pv_dec_string": "2,506.185793", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 4 small cubes", "__seed__": "0913"}}, {"seed": 914, "data": {"pv_dec_string": "8,569.87741", "pv_ans_text": "8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0914"}}, {"seed": 915, "data": {"pv_dec_string": "92,356.81497", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.006", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 0 longs, and 6 small cubes", "__seed__": "0915"}}, {"seed": 916, "data": {"pv_dec_string": "613,460.6016", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.01", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0916"}}, {"seed": 917, "data": {"pv_dec_string": "6,952.544401", "pv_ans_text": "6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0917"}}, {"seed": 918, "data": {"pv_dec_string": "1,896.79976", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.20", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0918"}}, {"seed": 919, "data": {"pv_dec_string": "58,720.458901", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0919"}}, {"seed": 920, "data": {"pv_dec_string": "94,455.4786", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 5 small cubes", "__seed__": "0920"}}, {"seed": 921, "data": {"pv_dec_string": "401,914.6125", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.35", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0921"}}, {"seed": 922, "data": {"pv_dec_string": "235,612.61329", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.465", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 5 small cubes", "__seed__": "0922"}}, {"seed": 923, "data": {"pv_dec_string": "61,713.3033", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.14", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0923"}}, {"seed": 924, "data": {"pv_dec_string": "456,025.26972", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0924"}}, {"seed": 925, "data": {"pv_dec_string": "1,959,889.8676", "pv_ans_text": "1 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.20", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0925"}}, {"seed": 926, "data": {"pv_dec_string": "5,085,415.9562", "pv_ans_text": "5 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 1 small cubes", "__seed__": "0926"}}, {"seed": 927, "data": {"pv_dec_string": "586.677972", "pv_ans_text": "5 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.40", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0927"}}, {"seed": 928, "data": {"pv_dec_string": "76,740.269862", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0928"}}, {"seed": 929, "data": {"pv_dec_string": "25,188.4471", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0929"}}, {"seed": 930, "data": {"pv_dec_string": "9,273.148411", "pv_ans_text": "9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 5 small cubes", "__seed__": "0930"}}, {"seed": 931, "data": {"pv_dec_string": "83,935.9738", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.15", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0931"}}, {"seed": 932, "data": {"pv_dec_string": "3,647.14824", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0932"}}, {"seed": 933, "data": {"pv_dec_string": "440,838.21874", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.06", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0933"}}, {"seed": 934, "data": {"pv_dec_string": "288,575.91133", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0934"}}, {"seed": 935, "data": {"pv_dec_string": "332.125964", "pv_ans_text": "3 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.60", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0935"}}, {"seed": 936, "data": {"pv_dec_string": "196,526.143", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.406", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 0 longs, and 6 small cubes", "__seed__": "0936"}}, {"seed": 937, "data": {"pv_dec_string": "598,335.03118", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.41", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0937"}}, {"seed": 938, "data": {"pv_dec_string": "301,195.6591", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.062", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 2 small cubes", "__seed__": "0938"}}, {"seed": 939, "data": {"pv_dec_string": "107,943.1317", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.04", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0939"}}, {"seed": 940, "data": {"pv_dec_string": "80,682.696192", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 3 small cubes", "__seed__": "0940"}}, {"seed": 941, "data": {"pv_dec_string": "649,055.55455", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.11", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0941"}}, {"seed": 942, "data": {"pv_dec_string": "2,204,324.5056", "pv_ans_text": "2 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 5 small cubes", "__seed__": "0942"}}, {"seed": 943, "data": {"pv_dec_string": "148,050.6121", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0943"}}, {"seed": 944, "data": {"pv_dec_string": "6,382.324914", "pv_ans_text": "6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 2 small cubes", "__seed__": "0944"}}, {"seed": 945, "data": {"pv_dec_string": "7,854,818.115", "pv_ans_text": "7 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 5 small cubes", "__seed__": "0945"}}, {"seed": 946, "data": {"pv_dec_string": "478,402.0453", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0946"}}, {"seed": 947, "data": {"pv_dec_string": "692,095.86144", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0947"}}, {"seed": 948, "data": {"pv_dec_string": "56,532.04067", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0948"}}, {"seed": 949, "data": {"pv_dec_string": "5,198.972383", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.665", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0949"}}, {"seed": 950, "data": {"pv_dec_string": "49,236.38851", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.160", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0950"}}, {"seed": 951, "data": {"pv_dec_string": "9,325,367.1311", "pv_ans_text": "9 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 2 small cubes", "__seed__": "0951"}}, {"seed": 952, "data": {"pv_dec_string": "2,597.35258", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0952"}}, {"seed": 953, "data": {"pv_dec_string": "2,521,395.027", "pv_ans_text": "2 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.63", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0953"}}, {"seed": 954, "data": {"pv_dec_string": "5,344.965075", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0954"}}, {"seed": 955, "data": {"pv_dec_string": "43,743.352731", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0955"}}, {"seed": 956, "data": {"pv_dec_string": "16,233.134131", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.334", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0956"}}, {"seed": 957, "data": {"pv_dec_string": "403,988.8993", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.043", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 4 longs, and 3 small cubes", "__seed__": "0957"}}, {"seed": 958, "data": {"pv_dec_string": "5,178,719.7962", "pv_ans_text": "5 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.50", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0958"}}, {"seed": 959, "data": {"pv_dec_string": "94,499.24734", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0959"}}, {"seed": 960, "data": {"pv_dec_string": "430.555043", "pv_ans_text": "4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.03", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0960"}}, {"seed": 961, "data": {"pv_dec_string": "3,797.707445", "pv_ans_text": "3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0961"}}, {"seed": 962, "data": {"pv_dec_string": "2,742.71599", "pv_ans_text": "2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.23", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0962"}}, {"seed": 963, "data": {"pv_dec_string": "50,269.987299", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 5 small cubes", "__seed__": "0963"}}, {"seed": 964, "data": {"pv_dec_string": "7,654.194937", "pv_ans_text": "7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.434", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0964"}}, {"seed": 965, "data": {"pv_dec_string": "602,231.97942", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.232", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 3 longs, and 2 small cubes", "__seed__": "0965"}}, {"seed": 966, "data": {"pv_dec_string": "867.855769", "pv_ans_text": "8 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.23", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0966"}}, {"seed": 967, "data": {"pv_dec_string": "829,619.94884", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.503", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 0 longs, and 3 small cubes", "__seed__": "0967"}}, {"seed": 968, "data": {"pv_dec_string": "4,410.74516", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0968"}}, {"seed": 969, "data": {"pv_dec_string": "913,051.0574", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.44", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0969"}}, {"seed": 970, "data": {"pv_dec_string": "7,001,439.9936", "pv_ans_text": "7 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0970"}}, {"seed": 971, "data": {"pv_dec_string": "3,629.072512", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.405", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 0 longs, and 5 small cubes", "__seed__": "0971"}}, {"seed": 972, "data": {"pv_dec_string": "6,456,871.1775", "pv_ans_text": "6 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.16", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0972"}}, {"seed": 973, "data": {"pv_dec_string": "707.183939", "pv_ans_text": "7 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.324", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 2 longs, and 4 small cubes", "__seed__": "0973"}}, {"seed": 974, "data": {"pv_dec_string": "919,470.8577", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 2 small cubes", "__seed__": "0974"}}, {"seed": 975, "data": {"pv_dec_string": "83,995.2365", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0975"}}, {"seed": 976, "data": {"pv_dec_string": "883.808518", "pv_ans_text": "8 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.002", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 0 longs, and 2 small cubes", "__seed__": "0976"}}, {"seed": 977, "data": {"pv_dec_string": "326.666437", "pv_ans_text": "3 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0977"}}, {"seed": 978, "data": {"pv_dec_string": "854,271.11268", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.51", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0978"}}, {"seed": 979, "data": {"pv_dec_string": "375.041558", "pv_ans_text": "3 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.35", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0979"}}, {"seed": 980, "data": {"pv_dec_string": "597,573.9572", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0980"}}, {"seed": 981, "data": {"pv_dec_string": "852,764.91544", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0981"}}, {"seed": 982, "data": {"pv_dec_string": "28,736.0489", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 4 small cubes", "__seed__": "0982"}}, {"seed": 983, "data": {"pv_dec_string": "2,105,390.5284", "pv_ans_text": "2 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.352", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0983"}}, {"seed": 984, "data": {"pv_dec_string": "426,353.5172", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0984"}}, {"seed": 985, "data": {"pv_dec_string": "281,064.72956", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0985"}}, {"seed": 986, "data": {"pv_dec_string": "483.070621", "pv_ans_text": "4 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0986"}}, {"seed": 987, "data": {"pv_dec_string": "471,376.2368", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 1 small cubes", "__seed__": "0987"}}, {"seed": 988, "data": {"pv_dec_string": "5,579,835.0037", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 1 small cubes", "__seed__": "0988"}}, {"seed": 989, "data": {"pv_dec_string": "1,288.581401", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.05", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0989"}}, {"seed": 990, "data": {"pv_dec_string": "20,301.059", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 2 small cubes", "__seed__": "0990"}}, {"seed": 991, "data": {"pv_dec_string": "177,844.32588", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.06", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0991"}}, {"seed": 992, "data": {"pv_dec_string": "851,998.8156", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 1 small cubes", "__seed__": "0992"}}, {"seed": 993, "data": {"pv_dec_string": "25,312.27085", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.516", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 1 longs, and 6 small cubes", "__seed__": "0993"}}, {"seed": 994, "data": {"pv_dec_string": "118,665.1313", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.054", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 5 longs, and 4 small cubes", "__seed__": "0994"}}, {"seed": 995, "data": {"pv_dec_string": "257.933121", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 6 small cubes", "__seed__": "0995"}}, {"seed": 996, "data": {"pv_dec_string": "880.219698", "pv_ans_text": "8 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 3 small cubes", "__seed__": "0996"}}, {"seed": 997, "data": {"pv_dec_string": "218.936305", "pv_ans_text": "2 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0997"}}, {"seed": 998, "data": {"pv_dec_string": "8,597.980476", "pv_ans_text": "8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 2 small cubes", "__seed__": "0998"}}, {"seed": 999, "data": {"pv_dec_string": "97,727.7972", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.356", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 5 longs, and 6 small cubes", "__seed__": "0999"}}]}]} \ No newline at end of file +{"title": "MAT 106 - Number Systems and Operations - CheckIt Bank", "slug": "mat-106-bank", "url": "https://checkit.clontz.org", "generated_on": "2024-07-27T01:27:17.974057+00:00", "outcomes": [{"title": "Ancient Numeration Systems", "slug": "W1", "description": "\n I can convert the ancient Roman/Babylonian/Egyptian numeration systems to modern Hindu-Arabic base ten, and vice versa.\n ", "template": "\n\n \n \n

Convert {{to_a_modern}} to {{to_a_system}}.

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\n \n

{{to_a_ancient}}

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\n
\n \n \n

Convert the following {{to_m_system}} numeral to modern Hindu-Arabic base ten.

\n

{{to_m_ancient}}

\n
\n \n

{{to_m_modern}}

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\n
\n", "exercises": [{"seed": 0, "data": {"to_a_modern": "2,754", "to_a_system": "Roman", "to_a_ancient": "MMDCCLIV", "to_m_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udcf5\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_system": "ancient Babylonian", "to_m_modern": "122,433", "egy_test": false, "__seed__": "0000"}}, {"seed": 1, "data": {"to_a_modern": "112,495", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\u2003\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_ancient": "\ud80c\udc68\ud80c\udc68\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa", "to_m_system": "ancient Egyptian", "to_m_modern": "2,780,949", "egy_test": true, "__seed__": "0001"}}, {"seed": 2, "data": {"to_a_modern": "49,378", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_ancient": "MMCCCXCIV", "to_m_system": "Roman", "to_m_modern": "2,394", "egy_test": false, "__seed__": "0002"}}, {"seed": 3, "data": {"to_a_modern": "146,059", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_ancient": "MMMDXCIX", "to_m_system": "Roman", "to_m_modern": "3,599", "egy_test": false, "__seed__": "0003"}}, {"seed": 4, "data": {"to_a_modern": "48,297", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_ancient": "MIV", "to_m_system": "Roman", 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"\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udc79\u2003\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_system": "ancient Babylonian", "to_m_modern": "30,063", "egy_test": true, "__seed__": "0991"}}, {"seed": 992, "data": {"to_a_modern": "3,674,571", "to_a_system": "ancient Egyptian", "to_a_ancient": "\ud80c\udc68\ud80c\udc68\ud80c\udc68\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udffa", "to_m_ancient": 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"\ud80c\udc68\ud80c\udc68\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa", "to_m_system": "ancient Egyptian", "to_m_modern": "2,038,696", "egy_test": true, "__seed__": "0993"}}, {"seed": 994, "data": {"to_a_modern": "72,600", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udf0b\u2003\ud808\udf0b\u2003\ud808\udcf5", "to_m_ancient": "\ud80c\udc68\ud80c\udc68\ud80c\udd90\ud80c\udd90\ud80c\udd90\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa\ud80c\udffa", "to_m_system": "ancient Egyptian", "to_m_modern": "2,335,536", "egy_test": true, "__seed__": "0994"}}, {"seed": 995, "data": {"to_a_modern": "124,080", "to_a_system": "ancient Babylonian", "to_a_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udcf5", "to_m_ancient": "MDCXCIII", "to_m_system": "Roman", "to_m_modern": "1,693", "egy_test": false, "__seed__": "0995"}}, {"seed": 996, "data": {"to_a_modern": "88,128", "to_a_system": "ancient Babylonian", "to_a_ancient": 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"\ud80c\udc68\ud80c\udc68\ud80c\udc68\ud80c\udd90\ud80c\udd90\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\udcad\ud80c\uddbc\ud80c\uddbc\ud80c\uddbc\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf62\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udf86\ud80c\udffa\ud80c\udffa", "to_m_ancient": "\ud808\udf0b\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\u2003\ud808\udf0b\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79\ud808\udc79", "to_m_system": "ancient Babylonian", "to_m_modern": "97,457", "egy_test": true, "__seed__": "0999"}}]}, {"title": "Base-b Addition and Subtraction Algorithms", "slug": "W2", "description": "\n I can compute addition and subtraction of multi-digit base-b whole numbers using non-standard addition and subtraction algorithms.\n ", "template": "\n\n \n

Compute each of the following using the stated algorithm. You must show all calculations in the desired base, and not by converting between bases.

\n
\n \n \n

{{base_ten_prob}} ({{base_ten_alg}})

\n
\n \n

{{base_ten_ans}}

\n
\n
\n \n \n

{{base_b_prob}} ({{base_b_alg}})

\n
\n \n

{{base_b_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"base_ten_prob": "8986 + 2758", "base_ten_alg": "Lattice", "base_ten_ans": "11744", "base_b_prob": "1324_\\text{nine} - 1086_\\text{nine}", "base_b_alg": "Subtract from the Base", "base_b_ans": "227_\\text{nine}", "__seed__": "0000"}}, {"seed": 1, "data": {"base_ten_prob": "4168 - 3648", "base_ten_alg": "Equal Additions", "base_ten_ans": "520", "base_b_prob": "1410_\\text{eight} + 1456_\\text{eight}", "base_b_alg": "Partial Sums", "base_b_ans": "3066_\\text{eight}", "__seed__": "0001"}}, {"seed": 2, "data": {"base_ten_prob": "6846 - 6578", "base_ten_alg": "Subtract from the Base", "base_ten_ans": "268", "base_b_prob": "2507_\\text{eight} + 6666_\\text{eight}", "base_b_alg": "Partial Sums", "base_b_ans": "11375_\\text{eight}", "__seed__": "0002"}}, {"seed": 3, "data": {"base_ten_prob": "7586 - 5306", "base_ten_alg": "Trades First", "base_ten_ans": "2280", "base_b_prob": "2000_\\text{six} + 1533_\\text{six}", "base_b_alg": "Partial Sums", "base_b_ans": "3533_\\text{six}", "__seed__": "0003"}}, {"seed": 4, "data": {"base_ten_prob": "7587 + 1889", "base_ten_alg": "Lattice", "base_ten_ans": "9476", "base_b_prob": "5530_\\text{seven} - 1464_\\text{seven}", "base_b_alg": "Trades First", "base_b_ans": "4033_\\text{seven}", "__seed__": "0004"}}, {"seed": 5, "data": {"base_ten_prob": "9882 + 2708", "base_ten_alg": "Partial Sums", "base_ten_ans": "12590", "base_b_prob": "1415_\\text{nine} - 556_\\text{nine}", "base_b_alg": "Equal Additions", "base_b_ans": "748_\\text{nine}", "__seed__": "0005"}}, {"seed": 6, "data": {"base_ten_prob": "8665 + 6557", "base_ten_alg": "Partial Sums", "base_ten_ans": "15222", "base_b_prob": "1304_\\text{six} - 544_\\text{six}", "base_b_alg": "Subtract from the Base", "base_b_ans": "320_\\text{six}", "__seed__": "0006"}}, {"seed": 7, "data": {"base_ten_prob": "5686 + 9939", "base_ten_alg": "Lattice", "base_ten_ans": "15625", "base_b_prob": "2004_\\text{five} - 344_\\text{five}", "base_b_alg": "Subtract from the Base", "base_b_ans": "1110_\\text{five}", "__seed__": "0007"}}, {"seed": 8, "data": {"base_ten_prob": "3999 + 9574", "base_ten_alg": "Column Addition", "base_ten_ans": "13573", "base_b_prob": "1313_\\text{four} - 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1205_\\text{seven}", "base_b_alg": "Equal Additions", "base_b_ans": "105_\\text{seven}", "__seed__": "0996"}}, {"seed": 997, "data": {"base_ten_prob": "5629 - 4655", "base_ten_alg": "Subtract from the Base", "base_ten_ans": "974", "base_b_prob": "7303_\\text{nine} + 6877_\\text{nine}", "base_b_alg": "Column Addition", "base_b_ans": "15281_\\text{nine}", "__seed__": "0997"}}, {"seed": 998, "data": {"base_ten_prob": "6676 + 3976", "base_ten_alg": "Lattice", "base_ten_ans": "10652", "base_b_prob": "2502_\\text{six} - 1434_\\text{six}", "base_b_alg": "Trades First", "base_b_ans": "1024_\\text{six}", "__seed__": "0998"}}, {"seed": 999, "data": {"base_ten_prob": "9558 - 5786", "base_ten_alg": "Trades First", "base_ten_ans": "3772", "base_b_prob": "1347_\\text{eight} + 7075_\\text{eight}", "base_b_alg": "Column Addition", "base_b_ans": "10444_\\text{eight}", "__seed__": "0999"}}]}, {"title": "Properties of Addition and Multiplication", "slug": "W3", "description": "\n I can identify uses of the associative, commutative, identity, zero product, and distributive properties of addition and multiplication.\n ", "template": "\n\n \n

For each of the following equations, state the property that is being exemplified.

\n
\n \n \n

{{p1_prob}}

\n
\n \n

{{p1_ans}}

\n
\n
\n \n \n

{{p2_prob}}

\n
\n \n

{{p2_ans}}

\n
\n
\n \n \n

{{p3_prob}}

\n
\n \n

{{p3_ans}}

\n
\n
\n \n \n

{{p4_prob}}

\n
\n \n

{{p4_ans}}

\n
\n
\n \n \n

{{p5_prob}}

\n
\n \n

{{p5_ans}}

\n
\n
\n \n \n

{{p6_prob}}

\n
\n \n

{{p6_ans}}

\n
\n
\n \n \n

{{p7_prob}}

\n
\n \n

{{p7_ans}}

\n
\n
\n \n \n

{{p8_prob}}

\n
\n \n

{{p8_ans}}

\n
\n
\n \n \n

{{p9_prob}}

\n
\n \n

{{p9_ans}}

\n
\n
\n \n \n

{{p10_prob}}

\n
\n \n

{{p10_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"p1_prob": "g \\times 0 = 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "d \\times 0 = 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "n \\times (a \\times w) = (a \\times w) \\times n", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vB", "p4_prob": "p + f \\times j - f \\times m = p + f(j - m)", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "(v \\times a) \\times w = v \\times (a \\times w)", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": " (n - 0 + b) - p = (n - b) - p", "p6_ans": "Identity Property of Addition", "p6_ver": "vB", "p7_prob": "(19 \\times 6) \\times 7 = 19 \\times (6 \\times 7)", "p7_ans": "Associative Property of Multiplication", "p7_ver": "v0", "p8_prob": "(q + y) \\times p = (y + q) \\times p", "p8_ans": "Commutative Property of Addition", "p8_ver": "vA", "p9_prob": "7 \\times 0 + 6 = 0 \\times 7 + 6", "p9_ans": "Commutative Property of Multiplication", "p9_ver": "vC", "p10_prob": "19 \\times 0 \\times 15 = 19 \\times 0", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0000"}}, {"seed": 1, "data": {"p1_prob": "(19 \\times 11) \\times 3 - 2 = 19 \\times (11 \\times 3) - 2", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "7 \\times (21 - 5) = (21 - 5) \\times 7", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vB", "p3_prob": "(6 \\times 3) \\times 13 = 6 \\times (3 \\times 13)", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": "17 + 21 + 8 = 17 + 8 + 21", "p4_ans": "Commutative Property of Addition", "p4_ver": "vC", "p5_prob": "m \\times y + m \\times q + d = m(y + q) + d", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "12 \\times 1 + 18 = 12 + 18", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "k + w \\times u - x \\times u = k + (w - x) \\times u", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "g - (u - j) = g - (u - j + 0) ", "p8_ans": "Identity Property of Addition", "p8_ver": "vB", "p9_prob": "d + (g + q) = (d + g) + q", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "3 - 0 \\times 10 = 3 - 0", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0001"}}, {"seed": 2, "data": {"p1_prob": "5 + 9 = 0 + 5 + 9", "p1_ans": "Identity Property of Addition", "p1_ver": "vA", "p2_prob": "(13 + 18) + 8 = (18 + 13) + 8", "p2_ans": "Commutative Property of Addition", "p2_ver": "vA", "p3_prob": "(g + q) + j + f = g + (q + j) + f", "p3_ans": "Associative Property of Addition", "p3_ver": "v0", "p4_prob": "s \\times (p - a - b) = (p - a - b) \\times s", "p4_ans": "Commutative Property of Multiplication", "p4_ver": "vB", "p5_prob": "0 \\times n - s = 0 - s", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "u \\times c - s \\times c = (u - s) \\times c", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "t(y - w) + m = t \\times y - t \\times w + m", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "36 + 30 = 2(18 + 15)", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "t + s + w = s + t + w", "p9_ans": "Commutative Property of Addition", "p9_ver": "vC", "p10_prob": "s + (p + a) + b = (s + p) + a + b", "p10_ans": "Associative Property of Addition", "p10_ver": "v0", "__seed__": "0002"}}, {"seed": 3, "data": {"p1_prob": "20 + (5 + 8) + 3 = (20 + 5) + 8 + 3", "p1_ans": "Associative Property of Addition", "p1_ver": "v0", "p2_prob": "19 \\times 0 = 19 \\times 0 \\times 10", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "g - d \\times 0 = g - 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "p + (t + k + 0) = p + (t + k) ", "p4_ans": "Identity Property of Addition", "p4_ver": "vB", "p5_prob": "z(s + r) = z \\times s + z \\times r", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "(x + f) \\times d = d \\times (x + f)", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vB", "p7_prob": "v = v \\times 1", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vA", "p8_prob": "u + 0 = u + 0 \\times q", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "(x + p) - y = (p + x) - y", "p9_ans": "Commutative Property of Addition", "p9_ver": "vA", "p10_prob": "v \\times k - v \\times j = v(k - j)", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0003"}}, {"seed": 4, "data": {"p1_prob": "36 - 216 = (3 - 18) \\times 12", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "(z + k) + s = z + (k + s)", "p2_ans": "Associative Property of Addition", "p2_ver": "v0", "p3_prob": "y \\times b \\times m = b \\times y \\times m", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vC", "p4_prob": "16 \\times (0 \\times 19) = (16 \\times 0) \\times 19", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "91 + 39 = 13(7 + 3)", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "y + (g + c) = (g + c) + y", "p6_ans": "Commutative Property of Addition", "p6_ver": "vB", "p7_prob": "0 = 0 \\times 17", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "c - (q \\times y) = c - (y \\times q)", "p8_ans": "Commutative Property of Multiplication", "p8_ver": "vA", "p9_prob": "19 \\times (20 \\times 8) \\times 12 = 19 \\times 20 \\times (8 \\times 12)", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "r = 0 + r", "p10_ans": "Identity Property of Addition", "p10_ver": "vA", "__seed__": "0004"}}, {"seed": 5, "data": {"p1_prob": "13 + (9 + 19) = (9 + 19) + 13", "p1_ans": "Commutative Property of Addition", "p1_ver": "vB", "p2_prob": "(21 + 2) - 13 = (2 + 21) - 13", "p2_ans": "Commutative Property of Addition", "p2_ver": "vA", "p3_prob": "0 + u = 0 \\times w + u", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "(16 + 21) + 2 + 19 = 16 + (21 + 2) + 19", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "n + v = 0 + n + v", "p5_ans": "Identity Property of Addition", "p5_ver": "vA", "p6_prob": "0 \\times 7 + 4 = 7 \\times 0 + 4", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vC", "p7_prob": "13 - (2 - 11) = 13 - (2 - 11 + 0) ", "p7_ans": "Identity Property of Addition", "p7_ver": "vB", "p8_prob": "w + x(t + y) = w + x \\times t + x \\times y", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "m - u = m - u \\times 1", "p9_ans": "Identity Property of Multiplication", "p9_ver": "vA", "p10_prob": "m + r(x + k) = m + r \\times x + r \\times k", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0005"}}, {"seed": 6, "data": {"p1_prob": "j + m + a = m + j + a", "p1_ans": "Commutative Property of Addition", "p1_ver": "vC", "p2_prob": "(16 + 2) + 13 + 15 = 16 + (2 + 13) + 15", "p2_ans": "Associative Property of Addition", "p2_ver": "v0", "p3_prob": "0 \\times n + a = 0 + a", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "(6 \\times 18) \\times 1 = 6 \\times (18 \\times 1)", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "0 + q = u \\times 0 + q", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "20 + 30 = 5(4 + 6)", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "f \\times 0 + u = 0 + u", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "d(k + b) + y = d \\times k + d \\times b + y", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": " (4) - 5 = (4 \\times 1) - 5", "p9_ans": "Identity Property of Multiplication", "p9_ver": "vB", "p10_prob": "(1 + 0) + 19 + 2 = 1 + (0 + 19) + 2", "p10_ans": "Associative Property of Addition", "p10_ver": "v0", "__seed__": "0006"}}, {"seed": 7, "data": {"p1_prob": "(c + j) + x = c + (j + x)", "p1_ans": "Associative Property of Addition", "p1_ver": "v0", "p2_prob": "20 = 0 + 20", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "18 \\times 0 = 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "v \\times u + h \\times u + q = (v + h) \\times u + q", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "r \\times 0 = r \\times 0 \\times f", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "8 + 19 + 15 = 8 + 15 + 19", "p6_ans": "Commutative Property of Addition", "p6_ver": "vC", "p7_prob": "(p - f) \\times z + c = p \\times z - f \\times z + c", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "6(22 + 10) = 132 + 60", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "(17 \\times 11 \\times 13) + 12 = 12 + (17 \\times 11 \\times 13)", "p9_ans": "Commutative Property of Addition", "p9_ver": "vB", "p10_prob": "(5 \\times 7) \\times 9 = 5 \\times (7 \\times 9)", "p10_ans": "Associative Property of Multiplication", "p10_ver": "v0", "__seed__": "0007"}}, {"seed": 8, "data": {"p1_prob": "x \\times a \\times 0 = x \\times 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "7 \\times 6 - 22 = 6 \\times 7 - 22", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vC", "p3_prob": "7 + 168 + 126 = 7 + 14(12 + 9)", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "g \\times (a \\times v) - j = (g \\times a) \\times v - j", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "d + (v \\times t) \\times c = d + v \\times (t \\times c)", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "(f + v) \\times x = (v + f) \\times x", "p6_ans": "Commutative Property of Addition", "p6_ver": "vA", "p7_prob": "4 + (8 + 9) + 18 = (4 + 8) + 9 + 18", "p7_ans": "Associative Property of Addition", "p7_ver": "v0", "p8_prob": "13 + (19 \\times 20 \\times 1) = (19 \\times 20 \\times 1) + 13", "p8_ans": "Commutative Property of Addition", "p8_ver": "vB", "p9_prob": "r - s = r - s + 0", "p9_ans": "Identity Property of Addition", "p9_ver": "vA", "p10_prob": "(9 + 22) \\times 11 = 99 + 242", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0008"}}, {"seed": 9, "data": {"p1_prob": "n - (a - v) = n - (0 + a - v) ", "p1_ans": "Identity Property of Addition", "p1_ver": "vB", "p2_prob": "p(q + s) + w = p \\times q + p \\times s + w", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "z + 0 \\times y = z + 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "19 - 17 = 19 - 0 + 17", "p4_ans": "Identity Property of Addition", "p4_ver": "vA", "p5_prob": "(3 + 4) \\times 2 = (4 + 3) \\times 2", "p5_ans": "Commutative Property of Addition", "p5_ver": "vA", "p6_prob": "3 \\times 22 \\times 15 = 22 \\times 3 \\times 15", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vC", "p7_prob": "0 - b = c \\times 0 - b", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "0 + 12 = 0 \\times 2 + 12", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "22 - (21) = 22 - (1 \\times 21) ", "p9_ans": "Identity Property of Multiplication", "p9_ver": "vB", "p10_prob": "h + s + (z + n) = h + (s + z) + n", "p10_ans": "Associative Property of Addition", "p10_ver": "v0", "__seed__": "0009"}}, {"seed": 10, "data": {"p1_prob": "0 \\times g = 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "8(15 + 6) = 120 + 48", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "12 + (5 \\times 1) \\times 16 = 12 + 5 \\times (1 \\times 16)", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": "18 \\times 0 + 9 = 0 + 9", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": "q \\times r = q \\times r \\times 1", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vA", "p6_prob": "w \\times r + j \\times r + t = (w + j) \\times r + t", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "z + (s + q) = (z + s) + q", "p7_ans": "Associative Property of Addition", "p7_ver": "v0", "p8_prob": "b + (r \\times u) = (r \\times u) + b", "p8_ans": "Commutative Property of Addition", "p8_ver": "vB", "p9_prob": "63 - 18 + 4 = (7 - 2) \\times 9 + 4", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "16 \\times 18 \\times 12 = 16 \\times 12 \\times 18", "p10_ans": "Commutative Property of Multiplication", "p10_ver": "vC", "__seed__": "0010"}}, {"seed": 11, "data": {"p1_prob": "t \\times x = x \\times t", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vC", "p2_prob": "t - 0 + n = t - n", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "h \\times y \\times 0 = h \\times 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "13 \\times (2 \\times 10) = 13 \\times (1 \\times 2 \\times 10) ", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vB", "p5_prob": "9 + 6 = 9 \\times 1 + 6", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vA", "p6_prob": "0 = 0 \\times h", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "z + (p + u) + d = (z + p) + u + d", "p7_ans": "Associative Property of Addition", "p7_ver": "v0", "p8_prob": "f \\times u + f \\times s + a = f(u + s) + a", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "12 + (11 + 0 + 16) = (11 + 0 + 16) + 12", "p9_ans": "Commutative Property of Addition", "p9_ver": "vB", "p10_prob": "14 + (12 + 19) \\times 21 = 14 + 252 + 399", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0011"}}, {"seed": 12, "data": {"p1_prob": "0 - 18 = 10 \\times 0 - 18", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "(2 + 13) + 9 = 9 + (2 + 13)", "p2_ans": "Commutative Property of Addition", "p2_ver": "vB", "p3_prob": "y - h = y - h + 0", "p3_ans": "Identity Property of Addition", "p3_ver": "vA", "p4_prob": "17 \\times (3 \\times 21) = 17 \\times (3 \\times 21 \\times 1) ", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vB", "p5_prob": "(12 - 8) \\times 4 = 48 - 32", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "(r + g) \\times h = (g + r) \\times h", "p6_ans": "Commutative Property of Addition", "p6_ver": "vA", "p7_prob": "17 + 234 + 126 = 17 + (13 + 7) \\times 18", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "30 + 18 = 3(10 + 6)", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "7 + (5 + 11) + 14 = (7 + 5) + 11 + 14", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "h \\times f = f \\times h", "p10_ans": "Commutative Property of Multiplication", "p10_ver": "vC", "__seed__": "0012"}}, {"seed": 13, "data": {"p1_prob": "10 + 22(16 + 13) = 10 + 352 + 286", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "v \\times g - 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15 = 6 + (21 - 3) \\times 5", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "(n \\times y \\times a) \\times v = v \\times (n \\times y \\times a)", "p10_ans": "Commutative Property of Multiplication", "p10_ver": "vB", "__seed__": "0990"}}, {"seed": 991, "data": {"p1_prob": "(3 \\times 20) \\times (9 \\times 11 \\times 7) = (9 \\times 11 \\times 7) \\times (3 \\times 20)", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vB", "p2_prob": "(j \\times m) \\times a \\times w = j \\times (m \\times a) \\times w", "p2_ans": "Associative Property of Multiplication", "p2_ver": "v0", "p3_prob": "j(g + d) + q = j \\times g + j \\times d + q", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "11 + (17 + 4) + 13 = 11 + 17 + (4 + 13)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "c \\times (a \\times j) = c \\times (j \\times a)", "p5_ans": "Commutative Property of Multiplication", "p5_ver": "vA", "p6_prob": "12 = 0 + 12", "p6_ans": "Identity Property of Addition", "p6_ver": "vA", "p7_prob": "6 + 11 + 3 = 11 + 6 + 3", "p7_ans": "Commutative Property of Addition", "p7_ver": "vC", "p8_prob": "4 \\times (8 \\times 11) + 5 = (4 \\times 8) \\times 11 + 5", "p8_ans": "Associative Property of Multiplication", "p8_ver": "v0", "p9_prob": "0 \\times b = 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "0 = 0 \\times d", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0991"}}, {"seed": 992, "data": {"p1_prob": "t - (x - a + 0) = t - (x - a) ", "p1_ans": "Identity Property of Addition", "p1_ver": "vB", "p2_prob": "y + (w + c) \\times k = y + w \\times k + c \\times k", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "(6 \\times 4) \\times 18 = 6 \\times (4 \\times 18)", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": " (s - z) - u = (s - 0 + z) - u", "p4_ans": "Identity Property of Addition", "p4_ver": "vB", "p5_prob": "r \\times 0 \\times z = 0 \\times z", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "0 - 20 = 0 \\times 4 - 20", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "15 - 10 = 15 \\times 1 - 10", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vA", "p8_prob": "(h \\times r) \\times b = h \\times (r \\times b)", "p8_ans": "Associative Property of Multiplication", "p8_ver": "v0", "p9_prob": "t + (d \\times u \\times f) = (d \\times u \\times f) + t", "p9_ans": "Commutative Property of Addition", "p9_ver": "vB", "p10_prob": "z \\times (a \\times k) + r = (z \\times a) \\times k + r", "p10_ans": "Associative Property of Multiplication", "p10_ver": "v0", "__seed__": "0992"}}, {"seed": 993, "data": {"p1_prob": "12 + 19 + 8 = 12 + 8 + 19", "p1_ans": "Commutative Property of Addition", "p1_ver": "vC", "p2_prob": "0 = c \\times 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": " (11 - 6) - 13 = (11 - 6 \\times 1) - 13", "p3_ans": "Identity Property of Multiplication", "p3_ver": "vB", "p4_prob": "v \\times 1 = v", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vA", "p5_prob": " (5 \\times 4) \\times 6 = (5 \\times 1 \\times 4) \\times 6", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vB", "p6_prob": "20 + 7(15 - 19) = 20 + 105 - 133", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "15 - (18 \\times 13) \\times 17 = 15 - 18 \\times (13 \\times 17)", "p7_ans": "Associative Property of Multiplication", "p7_ver": "v0", "p8_prob": "176 - 120 = (22 - 15) \\times 8", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "15 + 9(17 - 20) = 15 + 153 - 180", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "0 \\times d + y = 0 + y", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0993"}}, {"seed": 994, "data": {"p1_prob": "(14 + 15) \\times 5 = 5 \\times (14 + 15)", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vB", "p2_prob": "6 + 26 + 247 = 6 + 13(2 + 19)", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "18 - (19 - 22 + 0) = 18 - (19 - 22) ", "p3_ans": "Identity Property of Addition", "p3_ver": "vB", "p4_prob": "21 + (17 + 0) + 1 = 21 + 17 + (0 + 1)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "7(18 - 17) = 126 - 119", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "22 \\times (14 + 19) = 22 \\times (19 + 14)", "p6_ans": "Commutative Property of Addition", "p6_ver": "vA", "p7_prob": "0 = 0 \\times m", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "0 \\times j = 0", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "k \\times c - h \\times c = (k - h) \\times c", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "0 \\times z = j \\times 0 \\times z", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0994"}}, {"seed": 995, "data": {"p1_prob": "0 \\times 5 \\times 2 = 0 \\times 2", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "(g \\times u) \\times w \\times v = g \\times (u \\times w) \\times v", "p2_ans": "Associative Property of Multiplication", "p2_ver": "v0", "p3_prob": "0 \\times g = h \\times 0 \\times g", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "s - (q + x) = s - (x + q)", "p4_ans": "Commutative Property of Addition", "p4_ver": "vA", "p5_prob": "t + (q + j) = (q + j) + t", "p5_ans": "Commutative Property of Addition", "p5_ver": "vB", "p6_prob": " (b + x) + p = (b + 1 \\times x) + p", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vB", "p7_prob": "5 + 105 + 133 = 5 + (15 + 19) \\times 7", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "21 - 0 = 21 - 0 \\times 16", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "8 - 4 \\times (13 \\times 1) = 8 - (4 \\times 13) \\times 1", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "h \\times (x \\times s) = (h \\times x) \\times s", "p10_ans": "Associative Property of Multiplication", "p10_ver": "v0", "__seed__": "0995"}}, {"seed": 996, "data": {"p1_prob": "(22 \\times 11) \\times 19 = 19 \\times (22 \\times 11)", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vB", "p2_prob": "h + 0 - c = h - c", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "0 - 19 = 13 \\times 0 - 19", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "w + v + (g + b) = w + (v + g) + b", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "j + 0 = j + 0 \\times p", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "t + b \\times v - n \\times v = t + (b - n) \\times v", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "(y + a) - n = (a + y) - n", "p7_ans": "Commutative Property of Addition", "p7_ver": "vA", "p8_prob": "21 \\times 13 \\times (5 \\times 19) = 21 \\times (13 \\times 5) \\times 19", "p8_ans": "Associative Property of Multiplication", "p8_ver": "v0", "p9_prob": "1 \\times (15 \\times 7) + 21 = (1 \\times 15) \\times 7 + 21", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "z + b + k = z + k + b", "p10_ans": "Commutative Property of Addition", "p10_ver": "vC", "__seed__": "0996"}}, {"seed": 997, "data": {"p1_prob": "r + h \\times 0 = r + 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "a + t = 0 + a + t", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "(a + p) \\times b = b \\times (a + p)", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vB", "p4_prob": "24 + 28 + 2 = 4(6 + 7) + 2", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "14 + 126 - 60 = 14 + 6(21 - 10)", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "0 = 14 \\times 0", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "v - m \\times w = v - w \\times m", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vC", "p8_prob": "9 \\times 0 - 22 = 0 - 22", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "20 + (14 + 9) + 12 = (20 + 14) + 9 + 12", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "(p + m) + j + z = p + (m + j) + z", "p10_ans": "Associative Property of Addition", "p10_ver": "v0", "__seed__": "0997"}}, {"seed": 998, "data": {"p1_prob": "12 + 48 + 24 = 12 + (8 + 4) \\times 6", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": " (0 + 20 + 3) + 9 = (20 + 3) + 9", "p2_ans": "Identity Property of Addition", "p2_ver": "vB", "p3_prob": "22 + (12 \\times 14) \\times 16 = 22 + 12 \\times (14 \\times 16)", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": "(8 \\times 0) \\times 14 = 8 \\times (0 \\times 14)", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "(10 - 11) \\times 8 + 5 = 80 - 88 + 5", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "18 + 12 \\times 0 = 18 + 0", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "0 \\times m = 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "d - z = d - 1 \\times z", "p8_ans": "Identity Property of Multiplication", "p8_ver": "vA", "p9_prob": "(y + z + w) \\times u = u \\times (y + z + w)", "p9_ans": "Commutative Property of Multiplication", "p9_ver": "vB", "p10_prob": "z + u + y = u + z + y", "p10_ans": "Commutative Property of Addition", "p10_ver": "vC", "__seed__": "0998"}}, {"seed": 999, "data": {"p1_prob": "17 + (18 + 12) \\times 16 = 17 + 288 + 192", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "q + (c + s) = q + (s + c)", "p2_ans": "Commutative Property of Addition", "p2_ver": "vA", "p3_prob": "n + t \\times f - x \\times f = n + (t - x) \\times f", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "b \\times s - n \\times s + w = (b - n) \\times s + w", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "a - (1 \\times h) = a - (h) ", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vB", "p6_prob": "1 \\times 3 = 3", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "(11 \\times 14) \\times 0 = 11 \\times (14 \\times 0)", "p7_ans": "Associative Property of Multiplication", "p7_ver": "v0", "p8_prob": "10 \\times 0 = 0", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "p \\times 0 = 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "h \\times 0 + x = 0 + x", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0999"}}]}, {"title": "Base-b Multiplication Algorithms", "slug": "W5", "description": "\n I can compute multiplication of multi-digit base-b whole numbers using non-standard multiplication algorithms.\n ", "template": "\n\n \n

Compute each of the following using the stated algorithm. You must show all calculations in the desired base, and not by converting between bases.

\n
\n \n \n

{{base_ten_prob}} ({{base_ten_alg}})

\n
\n \n

{{base_ten_ans}}

\n
\n
\n \n \n

{{base_b_prob}} ({{base_b_alg}})

\n
\n \n

{{base_b_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"base_ten_prob": "4556 \\times 342", "base_ten_alg": "Lattice", "base_ten_ans": "1558152", "base_b_prob": "333_\\text{four} \\times 33_\\text{four}", "base_b_alg": "Partial Sums", "base_b_ans": "32301_\\text{four}", "base_b_base": "4", "__seed__": "0000"}}, {"seed": 1, "data": {"base_ten_prob": "8728 \\times 79", "base_ten_alg": "Partial Sums", "base_ten_ans": "689512", "base_b_prob": "387_\\text{nine} \\times 35_\\text{nine}", "base_b_alg": "Lattice", "base_b_ans": "15118_\\text{nine}", "base_b_base": "9", "__seed__": "0001"}}, {"seed": 2, "data": {"base_ten_prob": "6233 \\times 884", "base_ten_alg": "Partial Sums", "base_ten_ans": "5509972", "base_b_prob": "534_\\text{seven} \\times 55_\\text{seven}", "base_b_alg": "Lattice", "base_b_ans": "43326_\\text{seven}", "base_b_base": "7", "__seed__": "0002"}}, {"seed": 3, "data": {"base_ten_prob": "7858 \\times 89", "base_ten_alg": "Partial Sums", "base_ten_ans": "699362", "base_b_prob": "222_\\text{eight} \\times 52_\\text{eight}", "base_b_alg": "Lattice", "base_b_ans": "13764_\\text{eight}", "base_b_base": "8", "__seed__": "0003"}}, {"seed": 4, "data": {"base_ten_prob": "2254 \\times 725", "base_ten_alg": "Partial Sums", "base_ten_ans": "1634150", "base_b_prob": "672_\\text{eight} \\times 74_\\text{eight}", "base_b_alg": "Lattice", "base_b_ans": "63630_\\text{eight}", "base_b_base": "8", "__seed__": "0004"}}, {"seed": 5, "data": {"base_ten_prob": "95 \\times 33", "base_ten_alg": "Partial Sums", "base_ten_ans": "3135", "base_b_prob": "2233_\\text{four} \\times 322_\\text{four}", "base_b_alg": "Lattice", "base_b_ans": "2132212_\\text{four}", "base_b_base": "4", "__seed__": "0005"}}, {"seed": 6, "data": {"base_ten_prob": "928 \\times 57", "base_ten_alg": "Lattice", "base_ten_ans": "52896", "base_b_prob": "32_\\text{six} \\times 44_\\text{six}", "base_b_alg": "Partial Sums", "base_b_ans": "2332_\\text{six}", "base_b_base": "6", "__seed__": "0006"}}, {"seed": 7, "data": {"base_ten_prob": "865 \\times 52", "base_ten_alg": "Lattice", "base_ten_ans": "44980", "base_b_prob": "64_\\text{nine} \\times 33_\\text{nine}", "base_b_alg": "Partial Sums", "base_b_ans": "2343_\\text{nine}", "base_b_base": "9", "__seed__": "0007"}}, {"seed": 8, "data": {"base_ten_prob": "3886 \\times 557", "base_ten_alg": "Partial Sums", "base_ten_ans": "2164502", "base_b_prob": "8767_\\text{nine} \\times 76_\\text{nine}", "base_b_alg": "Lattice", "base_b_ans": "748386_\\text{nine}", "base_b_base": "9", "__seed__": "0008"}}, {"seed": 9, "data": {"base_ten_prob": "954 \\times 52", "base_ten_alg": "Partial Sums", "base_ten_ans": "49608", "base_b_prob": "425_\\text{six} \\times 34_\\text{six}", "base_b_alg": "Lattice", "base_b_ans": "24222_\\text{six}", "base_b_base": "6", "__seed__": "0009"}}, {"seed": 10, "data": {"base_ten_prob": "9489 \\times 788", "base_ten_alg": "Lattice", "base_ten_ans": "7477332", "base_b_prob": "78_\\text{nine} \\times 47_\\text{nine}", "base_b_alg": "Partial Sums", "base_b_ans": "4162_\\text{nine}", "base_b_base": "9", "__seed__": "0010"}}, {"seed": 11, "data": {"base_ten_prob": "552 \\times 46", "base_ten_alg": "Lattice", "base_ten_ans": "25392", "base_b_prob": "567_\\text{nine} \\times 32_\\text{nine}", "base_b_alg": "Partial Sums", "base_b_ans": "20475_\\text{nine}", "base_b_base": "9", "__seed__": "0011"}}, {"seed": 12, "data": {"base_ten_prob": "856 \\times 89", "base_ten_alg": "Lattice", "base_ten_ans": "76184", "base_b_prob": "32_\\text{four} \\times 32_\\text{four}", "base_b_alg": "Partial Sums", "base_b_ans": "3010_\\text{four}", "base_b_base": "4", "__seed__": "0012"}}, {"seed": 13, "data": {"base_ten_prob": "459 \\times 53", "base_ten_alg": "Partial Sums", "base_ten_ans": "24327", "base_b_prob": "3422_\\text{five} \\times 43_\\text{five}", "base_b_alg": "Lattice", "base_b_ans": "324301_\\text{five}", "base_b_base": "5", "__seed__": "0013"}}, {"seed": 14, "data": {"base_ten_prob": "8629 \\times 422", "base_ten_alg": "Partial 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"base_b_prob": "523_\\text{six} \\times 54_\\text{six}", "base_b_alg": "Lattice", "base_b_ans": "50410_\\text{six}", "base_b_base": "6", "__seed__": "0997"}}, {"seed": 998, "data": {"base_ten_prob": "2324 \\times 422", "base_ten_alg": "Lattice", "base_ten_ans": "980728", "base_b_prob": "22_\\text{five} \\times 32_\\text{five}", "base_b_alg": "Partial Sums", "base_b_ans": "1304_\\text{five}", "base_b_base": "5", "__seed__": "0998"}}, {"seed": 999, "data": {"base_ten_prob": "2997 \\times 836", "base_ten_alg": "Partial Sums", "base_ten_ans": "2505492", "base_b_prob": "8346_\\text{nine} \\times 34_\\text{nine}", "base_b_alg": "Lattice", "base_b_ans": "318106_\\text{nine}", "base_b_base": "9", "__seed__": "0999"}}]}, {"title": "Long Division Algorithms", "slug": "W6", "description": "\n I can compute the quotient of two whole or decimal numbers using standard and non-standard algorithms.\n ", "template": "\n\n \n

{{directions}}

\n
\n \n \n

{{div_prob}}

\n
\n \n

{{answer}}

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\n", "exercises": [{"seed": 0, "data": {"algorithm": "Standard", "answer": "1.407", "directions": "Compute the following quotient. Give your final answer as a decimal. 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There should not be a remainder.", "div_prob": "50.99276 \\div 0.52", "__seed__": "0724"}}, {"seed": 725, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "72,658 remainder 17", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "3,560,259 \\div 49", "__seed__": "0725"}}, {"seed": 726, "data": {"algorithm": "Standard", "answer": "6,145 remainder 97", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "4,750,182 \\div 773", "__seed__": "0726"}}, {"seed": 727, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "9,772 remainder 529", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "5,619,429 \\div 575", "__seed__": "0727"}}, {"seed": 728, "data": {"algorithm": "Standard", "answer": "55.77", "directions": "Compute the following quotient. 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Give your final answer as a decimal. There should not be a remainder.", "div_prob": "26,091.6 \\div 34", "__seed__": "0976"}}, {"seed": 977, "data": {"algorithm": "Standard", "answer": "7,539", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "624,229.2 \\div 82.8", "__seed__": "0977"}}, {"seed": 978, "data": {"algorithm": "Standard", "answer": "0.12637", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "0.859316 \\div 6.8", "__seed__": "0978"}}, {"seed": 979, "data": {"algorithm": "Standard", "answer": "81.386", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "36,623.7 \\div 450", "__seed__": "0979"}}, {"seed": 980, "data": {"algorithm": "Standard", "answer": "0.24408", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "18.306 \\div 75", "__seed__": "0980"}}, {"seed": 981, "data": {"algorithm": "Standard", "answer": "8,890 remainder 0", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "160,020 \\div 18", "__seed__": "0981"}}, {"seed": 982, "data": {"algorithm": "Standard", "answer": "747.82", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "358.9536 \\div 0.48", "__seed__": "0982"}}, {"seed": 983, "data": {"algorithm": "Standard", "answer": "1,585 remainder 10", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "30,125 \\div 19", "__seed__": "0983"}}, {"seed": 984, "data": {"algorithm": "Standard", "answer": "4,537 remainder 107", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "3,797,576 \\div 837", "__seed__": "0984"}}, {"seed": 985, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "2,139 remainder 246", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "1,251,561 \\div 585", "__seed__": "0985"}}, {"seed": 986, "data": {"algorithm": "Standard", "answer": "2,563.5", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,333.02 \\div 0.52", "__seed__": "0986"}}, {"seed": 987, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "22,255 remainder 10", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "489,620 \\div 22", "__seed__": "0987"}}, {"seed": 988, "data": {"algorithm": "Standard", "answer": "55.176", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "209.6688 \\div 3.8", "__seed__": "0988"}}, {"seed": 989, "data": {"algorithm": "Standard", "answer": "3.6993", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "192.3636 \\div 52", "__seed__": "0989"}}, {"seed": 990, "data": {"algorithm": "Standard", "answer": "273.68", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,094.72 \\div 4", "__seed__": "0990"}}, {"seed": 991, "data": {"algorithm": "Scaffold or Partial Quotients", "answer": "37,280 remainder 47", "directions": "Compute the following quotient and remainder using the Scaffold or Partial Quotients algorithm.", "div_prob": "2,945,167 \\div 79", "__seed__": "0991"}}, {"seed": 992, "data": {"algorithm": "Standard", "answer": "5.574", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "33,722.7 \\div 6,050", "__seed__": "0992"}}, {"seed": 993, "data": {"algorithm": "Standard", "answer": "32,826 remainder 38", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "3,184,160 \\div 97", "__seed__": "0993"}}, {"seed": 994, "data": {"algorithm": "Standard", "answer": "0.1274", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "8.918 \\div 70", "__seed__": "0994"}}, {"seed": 995, "data": {"algorithm": "Standard", "answer": "0.2564", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "789.712 \\div 3,080", "__seed__": "0995"}}, {"seed": 996, "data": {"algorithm": "Standard", "answer": "92,442 remainder 21", "directions": "Compute the following quotient and remainder using the Standard algorithm.", "div_prob": "4,159,911 \\div 45", "__seed__": "0996"}}, {"seed": 997, "data": {"algorithm": "Standard", "answer": "1,458", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "5,103 \\div 3.5", "__seed__": "0997"}}, {"seed": 998, "data": {"algorithm": "Standard", "answer": "12.769", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "1,659.97 \\div 130", "__seed__": "0998"}}, {"seed": 999, "data": {"algorithm": "Standard", "answer": "0.1769", "directions": "Compute the following quotient. Give your final answer as a decimal. There should not be a remainder.", "div_prob": "0.72529 \\div 4.1", "__seed__": "0999"}}]}, {"title": "Divisibility Statements", "slug": "N1", "description": "\n I can identify divisibility statements as true or false.\n ", "template": "\n\n \n

Determine if each of the statements below is true or false.

\n
\n \n \n

{{p1_prob}}

\n
\n \n

{{p1_ans}}

\n
\n
\n \n \n

{{p2_prob}}

\n
\n \n

{{p2_ans}}

\n
\n
\n \n \n

{{p3_prob}}

\n
\n \n

{{p3_ans}}

\n
\n
\n \n \n

{{p4_prob}}

\n
\n \n

{{p4_ans}}

\n
\n
\n \n \n

{{p5_prob}}

\n
\n \n

{{p5_ans}}

\n
\n
\n \n \n

{{p6_prob}}

\n
\n \n

{{p6_ans}}

\n
\n
\n \n \n

{{p7_prob}}

\n
\n \n

{{p7_ans}}

\n
\n
\n \n \n

{{p8_prob}}

\n
\n \n

{{p8_ans}}

\n
\n
\n \n \n

{{p9_prob}}

\n
\n \n

{{p9_ans}}

\n
\n
\n \n \n

{{p10_prob}}

\n
\n \n

{{p10_ans}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"p1_prob": "4 \\times (21 \\times 1) + 8 = (4 \\times 21) \\times 1 + 8", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "(9 \\times 11) \\times 12 = 9 \\times (11 \\times 12)", "p2_ans": "Associative Property of Multiplication", "p2_ver": "v0", "p3_prob": "6 \\times 0 = 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "22(6 - 5) = 132 - 110", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "s \\times 0 = s \\times 0 \\times m", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "(12 + 2) + 5 = 12 + (2 + 5)", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "(10 - 22 - 0) + (9 - 7) = (9 - 7) + (10 - 22 - 0)", "p7_ans": "Commutative Property of Addition", "p7_ver": "vB", "p8_prob": "(0 + 11) - 9 = (11 + 0) - 9", "p8_ans": "Commutative Property of Addition", "p8_ver": "vA", "p9_prob": "(f - h) \\times v + z = f \\times v - h \\times v + z", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "16 = 16 \\times 1", "p10_ans": "Identity Property of Multiplication", "p10_ver": "vA", "__seed__": "0000"}}, {"seed": 1, "data": {"p1_prob": "19 + 33 - 99 = 19 + (3 - 9) \\times 11", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "21 + 6 = 21 + 1 \\times 6", "p2_ans": "Identity Property of Multiplication", "p2_ver": "vA", "p3_prob": "w + 0 \\times n = w + 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "0 \\times n = 0", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": "0 \\times 2 \\times 21 = 0 \\times 21", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "20 + (5 \\times 9) \\times 2 = 20 + 5 \\times (9 \\times 2)", "p6_ans": "Associative Property of Multiplication", "p6_ver": "v0", "p7_prob": "(b \\times a) \\times j = j \\times (b \\times a)", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vB", "p8_prob": "w \\times (a \\times m) \\times v = (w \\times a) \\times m \\times v", "p8_ans": "Associative Property of Multiplication", "p8_ver": "v0", "p9_prob": "19 + 16 + 12 = 19 + 12 + 16", "p9_ans": "Commutative Property of Addition", "p9_ver": "vC", "p10_prob": "x + (m + p) = (x + m) + p", "p10_ans": "Associative Property of Addition", "p10_ver": "v0", "__seed__": "0001"}}, {"seed": 2, "data": {"p1_prob": "4 \\times (1 \\times 19) = 4 \\times (19) ", "p1_ans": "Identity Property of Multiplication", "p1_ver": "vB", "p2_prob": "(11 - 13) \\times (0 - 5 - 22) = (0 - 5 - 22) \\times (11 - 13)", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vB", "p3_prob": "0 \\times k = a \\times 0 \\times k", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "20 - 0 \\times 3 = 20 - 0", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": " (0 + 21) + 14 = (21) + 14", "p5_ans": "Identity Property of Addition", "p5_ver": "vB", "p6_prob": "w + (y + x) + p = w + y + (x + p)", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "340 + 323 = 17(20 + 19)", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "w + b \\times z = w + z \\times b", "p8_ans": "Commutative Property of Multiplication", "p8_ver": "vC", "p9_prob": "21 + (2 \\times 0) + 20 = 21 + (0 \\times 2) + 20", "p9_ans": "Commutative Property of Multiplication", "p9_ver": "vA", "p10_prob": "m = m \\times 1", "p10_ans": "Identity Property of Multiplication", "p10_ver": "vA", "__seed__": "0002"}}, {"seed": 3, "data": {"p1_prob": "15 + 272 - 68 = 15 + 17(16 - 4)", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "s \\times 0 \\times u = 0 \\times u", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "9 + (11 \\times 21) = 9 + (21 \\times 11)", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vA", "p4_prob": "8 \\times 20 \\times 9 = 8 \\times 9 \\times 20", "p4_ans": "Commutative Property of Multiplication", "p4_ver": "vC", "p5_prob": "16 + 18(2 - 6) = 16 + 36 - 108", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "0 = 0 \\times g", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "13 \\times (22 \\times 16) \\times 20 = 13 \\times 22 \\times (16 \\times 20)", "p7_ans": "Associative Property of Multiplication", "p7_ver": "v0", "p8_prob": " (8 + 2) + 4 = (8 + 0 + 2) + 4", "p8_ans": "Identity Property of Addition", "p8_ver": "vB", "p9_prob": "(19 + 18) + 10 = 19 + (18 + 10)", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "v + 1 \\times j = v + j", "p10_ans": "Identity Property of Multiplication", "p10_ver": "vA", "__seed__": "0003"}}, {"seed": 4, "data": {"p1_prob": "k \\times 0 \\times n = 0 \\times n", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "b + d = d + b", "p2_ans": "Commutative Property of Addition", "p2_ver": "vC", "p3_prob": "75 - 330 = 15(5 - 22)", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "(3 + 1 + 15) + 5 = 5 + (3 + 1 + 15)", "p4_ans": "Commutative Property of Addition", "p4_ver": "vB", "p5_prob": "v \\times f + g \\times f = (v + g) \\times f", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "(h \\times y) \\times a = h \\times (y \\times a)", "p6_ans": "Associative Property of Multiplication", "p6_ver": "v0", "p7_prob": "v \\times 0 - t = 0 - t", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": " (a + 0 + w) + x = (a + w) + x", "p8_ans": "Identity Property of Addition", "p8_ver": "vB", "p9_prob": "19 \\times 0 = 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "(x + s) - d = (s + x) - d", "p10_ans": "Commutative Property of Addition", "p10_ver": "vA", "__seed__": "0004"}}, {"seed": 5, "data": {"p1_prob": "9 \\times 5 \\times 7 = 5 \\times 9 \\times 7", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vC", "p2_prob": "n \\times 0 \\times w = n \\times 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "9 + (8 + 4) = (9 + 8) + 4", "p3_ans": "Associative Property of Addition", "p3_ver": "v0", "p4_prob": "8 \\times (11 \\times 18) = (8 \\times 11) \\times 18", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "0 \\times 15 \\times 14 = 0 \\times 14", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "(d + p) \\times x = d \\times x + p \\times x", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "10 + (18 + 9) + 1 = 10 + 18 + (9 + 1)", "p7_ans": "Associative Property of Addition", "p7_ver": "v0", "p8_prob": "(f + g + z) \\times (d + y) = (d + y) \\times (f + g + z)", "p8_ans": "Commutative Property of Multiplication", "p8_ver": "vB", "p9_prob": "u + (k + 0) = u + (k) ", "p9_ans": "Identity Property of Addition", "p9_ver": "vB", "p10_prob": "22 - (13 + 3) = 22 - (3 + 13)", "p10_ans": "Commutative Property of Addition", "p10_ver": "vA", "__seed__": "0005"}}, {"seed": 6, "data": {"p1_prob": "w \\times (k \\times u) = (w \\times k) \\times u", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "20 \\times 0 = 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "11 + 60 + 95 = 11 + 5(12 + 19)", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "0 \\times (11 \\times 2) = (0 \\times 11) \\times 2", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "11 \\times (17 + 16) = 11 \\times (16 + 17)", "p5_ans": "Commutative Property of Addition", "p5_ver": "vA", "p6_prob": "(15 + 11) + 6 = 15 + (11 + 6)", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "98 - 140 = (14 - 20) \\times 7", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "k - b \\times 0 = k - 0", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "18 + 11 = 18 + 0 + 11", "p9_ans": "Identity Property of Addition", "p9_ver": "vA", "p10_prob": "(4 + 7 + 15) \\times 20 = 20 \\times (4 + 7 + 15)", "p10_ans": "Commutative Property of Multiplication", "p10_ver": "vB", "__seed__": "0006"}}, {"seed": 7, "data": {"p1_prob": "13 \\times 0 = 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "0 + v + r = v + r", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "y - (f - u) = y - (f - u \\times 1) ", "p3_ans": "Identity Property of Multiplication", "p3_ver": "vB", "p4_prob": "(18 \\times 10) \\times 3 = 18 \\times (10 \\times 3)", "p4_ans": "Associative Property of Multiplication", "p4_ver": "v0", "p5_prob": "v + 0 \\times q = v + 0", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "5 + (12 + 0) = (5 + 12) + 0", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "c \\times k \\times p = c \\times p \\times k", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vC", "p8_prob": "(c + h) + (x + g + k) = (x + g + k) + (c + h)", "p8_ans": "Commutative Property of Addition", "p8_ver": "vB", "p9_prob": "(a + k) - f = (k + a) - f", "p9_ans": "Commutative Property of Addition", "p9_ver": "vA", "p10_prob": "(d + q) \\times y = d \\times y + q \\times y", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0007"}}, {"seed": 8, "data": {"p1_prob": "y \\times (z \\times b) \\times d = y \\times z \\times (b \\times d)", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": " (2 + 22) + 10 = (1 \\times 2 + 22) + 10", "p2_ans": "Identity Property of Multiplication", "p2_ver": "vB", "p3_prob": "0 = 0 \\times 3", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "(g + w) + r = g + (w + r)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "b \\times 1 + g = b + g", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vA", "p6_prob": "(v + k) \\times g = v \\times g + k \\times g", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "(3 \\times 4) + 18 = 18 + (3 \\times 4)", "p7_ans": "Commutative Property of Addition", "p7_ver": "vB", "p8_prob": "(21 \\times 14) \\times 20 = 21 \\times (14 \\times 20)", "p8_ans": "Associative Property of Multiplication", "p8_ver": "v0", "p9_prob": "0 = g \\times 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "(f + u) - n = (u + f) - n", "p10_ans": "Commutative Property of Addition", "p10_ver": "vA", "__seed__": "0008"}}, {"seed": 9, "data": {"p1_prob": "m(q + b) + c = m \\times q + m \\times b + c", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "(17 \\times 11) + 19 = (11 \\times 17) + 19", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vA", "p3_prob": "v + q + (x + g) = v + (q + x) + g", "p3_ans": "Associative Property of Addition", "p3_ver": "v0", "p4_prob": "100 + 140 + 8 = 20(5 + 7) + 8", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "(4 + 22) + 1 + 10 = 4 + (22 + 1) + 10", "p5_ans": "Associative Property of Addition", "p5_ver": "v0", "p6_prob": "g + 0 + j = g + j", "p6_ans": "Identity Property of Addition", "p6_ver": "vA", "p7_prob": "m \\times f = f \\times m", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vC", "p8_prob": "128 - 72 = 8(16 - 9)", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "n + (u + m) + v = n + u + (m + v)", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "0 \\times 12 = 0", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0009"}}, {"seed": 10, "data": {"p1_prob": "a \\times p + a \\times h + q = a(p + h) + q", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "10 \\times 0 = 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "0 + (1 + 14) + 4 = (0 + 1) + 14 + 4", "p3_ans": "Associative Property of Addition", "p3_ver": "v0", "p4_prob": "a - (f - n + 0) = a - (f - n) ", "p4_ans": "Identity Property of Addition", "p4_ver": "vB", "p5_prob": "1 \\times (2 \\times 7) \\times 15 = (1 \\times 2) \\times 7 \\times 15", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "x(d - g) + m = x \\times d - x \\times g + m", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "c - (m \\times f) = c - (f \\times m)", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vA", "p8_prob": "h + (k + x) + q = (h + k) + x + q", "p8_ans": "Associative Property of Addition", "p8_ver": "v0", "p9_prob": "s \\times h \\times 1 = s \\times h", "p9_ans": "Identity Property of Multiplication", "p9_ver": "vA", "p10_prob": "k \\times c + k \\times g + m = k(c + g) + m", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0010"}}, {"seed": 11, "data": {"p1_prob": "136 - 112 = (17 - 14) \\times 8", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "z + (y + x) + j = (z + y) + x + j", "p2_ans": "Associative Property of Addition", "p2_ver": "v0", "p3_prob": "0 \\times y = g \\times 0 \\times y", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "19 + 5 + 16 = 5 + 19 + 16", "p4_ans": "Commutative Property of Addition", "p4_ver": "vC", "p5_prob": "j + (q \\times v) + d = j + (v \\times q) + d", "p5_ans": "Commutative Property of Multiplication", "p5_ver": "vA", "p6_prob": "b \\times (t \\times c) \\times s = (b \\times t) \\times c \\times s", "p6_ans": "Associative Property of Multiplication", "p6_ver": "v0", "p7_prob": "0 + (11 - 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162 + 21 = (22 - 18) \\times 9 + 21", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": " (n + 0 + b) + d = (n + b) + d", "p8_ans": "Identity Property of Addition", "p8_ver": "vB", "p9_prob": "15 \\times (2 + 20) = 15 \\times (20 + 2)", "p9_ans": "Commutative Property of Addition", "p9_ver": "vA", "p10_prob": "0 \\times j \\times s = 0 \\times s", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0986"}}, {"seed": 987, "data": {"p1_prob": "(r \\times d) \\times m = r \\times (d \\times m)", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "x - (a \\times d) = x - (d \\times a)", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vA", "p3_prob": "b + f = f + b", "p3_ans": "Commutative Property of Addition", "p3_ver": "vC", "p4_prob": "(w + v) \\times (f + k) = (f + k) \\times (w + v)", "p4_ans": "Commutative Property of Multiplication", "p4_ver": "vB", "p5_prob": "(10 + 21) + 22 = 10 + (21 + 22)", "p5_ans": "Associative Property of Addition", "p5_ver": "v0", "p6_prob": "p \\times k - p \\times j + c = p(k - j) + c", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": " (s \\times j \\times 1) \\times w = (s \\times j) \\times w", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vB", "p8_prob": "0 = u \\times 0", "p8_ans": "Zero Product Property", "p8_ver": "v0", "p9_prob": "0 \\times 21 - 15 = 0 - 15", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "0 \\times x = g \\times 0 \\times x", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0987"}}, {"seed": 988, "data": {"p1_prob": "(4 \\times 5) \\times 16 - 8 = 4 \\times (5 \\times 16) - 8", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "s - (q - u \\times 1) = s - (q - u) ", "p2_ans": "Identity Property of Multiplication", "p2_ver": "vB", "p3_prob": "j + 0 = j + 0 \\times f", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "7 \\times (1 \\times 10 \\times 18) = 7 \\times (10 \\times 18) ", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vB", "p5_prob": "h + y + c = y + h + c", "p5_ans": "Commutative Property of Addition", "p5_ver": "vC", "p6_prob": "s - z = s - z \\times 1", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "0 = 0 \\times y", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "x(c + p) = x \\times c + x \\times p", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "0 \\times v + r = 0 + r", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "132 + 72 + 18 = 12(11 + 6) + 18", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0988"}}, {"seed": 989, "data": {"p1_prob": "91 - 156 + 14 = (7 - 12) \\times 13 + 14", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "(n + j) \\times v = n \\times v + j \\times v", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "11 = 0 + 11", "p3_ans": "Identity Property of Addition", "p3_ver": "vA", "p4_prob": "252 - 357 = 21(12 - 17)", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "m - 0 = m - 0 \\times b", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": " (0 + w + z) + p = (w + z) + p", "p6_ans": "Identity Property of Addition", "p6_ver": "vB", "p7_prob": "x + (n \\times c) = (n \\times c) + x", "p7_ans": "Commutative Property of Addition", "p7_ver": "vB", "p8_prob": "0 + 21 + 6 = 21 + 0 + 6", "p8_ans": "Commutative Property of Addition", "p8_ver": "vC", "p9_prob": "5 + (13 + 1) + 16 = (5 + 13) + 1 + 16", "p9_ans": "Associative Property of Addition", "p9_ver": "v0", "p10_prob": "11 + (10 \\times 18) + 0 = 11 + (18 \\times 10) + 0", "p10_ans": "Commutative Property of Multiplication", "p10_ver": "vA", "__seed__": "0989"}}, {"seed": 990, "data": {"p1_prob": "v \\times f = f \\times v", "p1_ans": "Commutative Property of Multiplication", "p1_ver": "vC", "p2_prob": "1 \\times (22 \\times 4) \\times 0 = 1 \\times (4 \\times 22) \\times 0", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vA", "p3_prob": "2 + 7 + (19 + 18) = 2 + (7 + 19) + 18", "p3_ans": "Associative Property of Addition", "p3_ver": "v0", "p4_prob": "0 = 0 \\times g", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": "12 + 0 + (15 + 17) = 12 + (0 + 15) + 17", "p5_ans": "Associative Property of Addition", "p5_ver": "v0", "p6_prob": "16 - (15 - 21) = 16 - (15 + 0 - 21) ", "p6_ans": "Identity Property of Addition", "p6_ver": "vB", "p7_prob": "u \\times d \\times 1 = u \\times d", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vA", "p8_prob": "5 + 15(18 - 9) = 5 + 270 - 135", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "0 - 22 = 0 \\times 18 - 22", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "0 - a = 0 \\times f - a", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0990"}}, {"seed": 991, "data": {"p1_prob": "q \\times h \\times (n \\times k) = q \\times (h \\times n) \\times k", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "0 \\times 5 \\times 14 = 0 \\times 14", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "105 + 270 + 11 = 15(7 + 18) + 11", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "0 \\times q \\times r = 0 \\times r", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": "12 \\times (4 + 9) \\times 21 = 12 \\times (9 + 4) \\times 21", "p5_ans": "Commutative Property of Addition", "p5_ver": "vA", "p6_prob": "(15 + 20) + 21 + 3 = 15 + (20 + 21) + 3", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "14 - 19 \\times 1 = 14 - 19", "p7_ans": "Identity Property of Multiplication", "p7_ver": "vA", "p8_prob": "3 + 9 + 15 = 3 + 15 + 9", "p8_ans": "Commutative Property of Addition", "p8_ver": "vC", "p9_prob": "7 + 374 + 68 = 7 + (22 + 4) \\times 17", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "0 \\times 14 - 20 = 0 - 20", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0991"}}, {"seed": 992, "data": {"p1_prob": "10 + 0 \\times 12 = 10 + 0", "p1_ans": "Zero Product Property", "p1_ver": "v0", "p2_prob": "x + (g \\times f) + m = x + (f \\times g) + m", "p2_ans": "Commutative Property of Multiplication", "p2_ver": "vA", "p3_prob": "64 + 76 + 17 = (16 + 19) \\times 4 + 17", "p3_ans": "Distributive Property", "p3_ver": "v0", "p4_prob": "(m + f) + x = m + (f + x)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "5 \\times (7) = 5 \\times (1 \\times 7) ", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vB", "p6_prob": "v + w = v \\times 1 + w", "p6_ans": "Identity Property of Multiplication", "p6_ver": "vA", "p7_prob": "22 + 216 + 360 = 22 + (12 + 20) \\times 18", "p7_ans": "Distributive Property", "p7_ver": "v0", "p8_prob": "18 - 0 + 2 = 18 - 2", "p8_ans": "Identity Property of Addition", "p8_ver": "vA", "p9_prob": "0 + 6 = 0 \\times 3 + 6", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "(q - z) \\times m = q \\times m - z \\times m", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0992"}}, {"seed": 993, "data": {"p1_prob": "j + (w - y) \\times t = j + w \\times t - y \\times t", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "2 + 11 + 0 = 2 + 11", "p2_ans": "Identity Property of Addition", "p2_ver": "vA", "p3_prob": "0 = f \\times 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "14 + (21 + 2) + 16 = 14 + 21 + (2 + 16)", "p4_ans": "Associative Property of Addition", "p4_ver": "v0", "p5_prob": "c + x \\times h + t \\times h = c + (x + t) \\times h", "p5_ans": "Distributive Property", "p5_ver": "v0", "p6_prob": "g + n + (b + t) = g + (n + b) + t", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "7 - 0 \\times 14 = 7 - 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "r + a = a + r", "p8_ans": "Commutative Property of Addition", "p8_ver": "vC", "p9_prob": "c + 0 \\times u = c + 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "3(9 + 11) = 27 + 33", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0993"}}, {"seed": 994, "data": {"p1_prob": "g - h = g + 0 - h", "p1_ans": "Identity Property of Addition", "p1_ver": "vA", "p2_prob": "(15 - 18) \\times 12 + 20 = 180 - 216 + 20", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "1 \\times (11 \\times 20) - 14 = (1 \\times 11) \\times 20 - 14", "p3_ans": "Associative Property of Multiplication", "p3_ver": "v0", "p4_prob": "0 \\times 22 = 0 \\times 10 \\times 22", "p4_ans": "Zero Product Property", "p4_ver": "v0", "p5_prob": " (0 + j) - b = (j) - b", "p5_ans": "Identity Property of Addition", "p5_ver": "vB", "p6_prob": "u \\times (f + d + v) = (f + d + v) \\times u", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vB", "p7_prob": "d - u \\times 0 = d - 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "z \\times w - t \\times w = (z - t) \\times w", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "g + w \\times 0 = g + 0", "p9_ans": "Zero Product Property", "p9_ver": "v0", "p10_prob": "2(20 + 5) = 40 + 10", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0994"}}, {"seed": 995, "data": {"p1_prob": "7(3 - 13) + 17 = 21 - 91 + 17", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "0 \\times 13 = 0", "p2_ans": "Zero Product Property", "p2_ver": "v0", "p3_prob": "22 + 0 = 22 + 21 \\times 0", "p3_ans": "Zero Product Property", "p3_ver": "v0", "p4_prob": "d = 1 \\times d", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vA", "p5_prob": " (6 \\times 1 - 19) - 21 = (6 - 19) - 21", "p5_ans": "Identity Property of Multiplication", "p5_ver": "vB", "p6_prob": "v \\times s = s \\times v", "p6_ans": "Commutative Property of Multiplication", "p6_ver": "vC", "p7_prob": "(y + u) + b + s = y + (u + b) + s", "p7_ans": "Associative Property of Addition", "p7_ver": "v0", "p8_prob": "2 + 7(18 - 13) = 2 + 126 - 91", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "13 - 4 = 13 - 4 + 0", "p9_ans": "Identity Property of Addition", "p9_ver": "vA", "p10_prob": "f + g \\times a - z \\times a = f + (g - z) \\times a", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0995"}}, {"seed": 996, "data": {"p1_prob": "u \\times d \\times (p \\times y) = u \\times (d \\times p) \\times y", "p1_ans": "Associative Property of Multiplication", "p1_ver": "v0", "p2_prob": "m(z - f) + j = m \\times z - m \\times f + j", "p2_ans": "Distributive Property", "p2_ver": "v0", "p3_prob": "(11 \\times 5) \\times 3 = 3 \\times (11 \\times 5)", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vB", "p4_prob": "w + k(a - f) = w + k \\times a - k \\times f", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "y \\times (m \\times z) = (y \\times m) \\times z", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "w \\times k - w \\times y = w(k - y)", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "0 \\times 18 = 0", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "c + (w + q) = c + (w + q \\times 1) ", "p8_ans": "Identity Property of Multiplication", "p8_ver": "vB", "p9_prob": "(5 \\times 8) \\times 18 = 5 \\times (8 \\times 18)", "p9_ans": "Associative Property of Multiplication", "p9_ver": "v0", "p10_prob": "1 \\times 5 - 8 = 5 - 8", "p10_ans": "Identity Property of Multiplication", "p10_ver": "vA", "__seed__": "0996"}}, {"seed": 997, "data": {"p1_prob": "5 + (9 - 15) \\times 14 = 5 + 126 - 210", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "4 + 10 = 1 \\times 4 + 10", "p2_ans": "Identity Property of Multiplication", "p2_ver": "vA", "p3_prob": "(12 \\times 7) \\times 15 = (7 \\times 12) \\times 15", "p3_ans": "Commutative Property of Multiplication", "p3_ver": "vA", "p4_prob": "(p - z) \\times g + d = p \\times g - z \\times g + d", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "(0 \\times 19) \\times 12 - 20 = 0 \\times (19 \\times 12) - 20", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "(c + n) + r + g = c + (n + r) + g", "p6_ans": "Associative Property of Addition", "p6_ver": "v0", "p7_prob": "0 - 5 = 0 \\times 14 - 5", "p7_ans": "Zero Product Property", "p7_ver": "v0", "p8_prob": "x = x \\times 1", "p8_ans": "Identity Property of Multiplication", "p8_ver": "vA", "p9_prob": " (7 - 9) - 21 = (7 + 0 - 9) - 21", "p9_ans": "Identity Property of Addition", "p9_ver": "vB", "p10_prob": "u \\times 0 = 0", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0997"}}, {"seed": 998, "data": {"p1_prob": "210 - 120 + 20 = (14 - 8) \\times 15 + 20", "p1_ans": "Distributive Property", "p1_ver": "v0", "p2_prob": "21 - (14 \\times 13) \\times 7 = 21 - 14 \\times (13 \\times 7)", "p2_ans": "Associative Property of Multiplication", "p2_ver": "v0", "p3_prob": " (4 + 14) + 13 = (0 + 4 + 14) + 13", "p3_ans": "Identity Property of Addition", "p3_ver": "vB", "p4_prob": "11 + 221 + 39 = 11 + (17 + 3) \\times 13", "p4_ans": "Distributive Property", "p4_ver": "v0", "p5_prob": "(2 \\times 0) \\times 4 = 2 \\times (0 \\times 4)", "p5_ans": "Associative Property of Multiplication", "p5_ver": "v0", "p6_prob": "0 + 8 = 0 \\times 21 + 8", "p6_ans": "Zero Product Property", "p6_ver": "v0", "p7_prob": "(k - n) + p = p + (k - n)", "p7_ans": "Commutative Property of Addition", "p7_ver": "vB", "p8_prob": "m + (w + d) + n = (m + w) + d + n", "p8_ans": "Associative Property of Addition", "p8_ver": "v0", "p9_prob": "21(4 - 5) = 84 - 105", "p9_ans": "Distributive Property", "p9_ver": "v0", "p10_prob": "0 \\times x \\times z = 0 \\times z", "p10_ans": "Zero Product Property", "p10_ver": "v0", "__seed__": "0998"}}, {"seed": 999, "data": {"p1_prob": "g = g + 0", "p1_ans": "Identity Property of Addition", "p1_ver": "vA", "p2_prob": "c + (n + a) + b = c + n + (a + b)", "p2_ans": "Associative Property of Addition", "p2_ver": "v0", "p3_prob": "1 + (19 + 8) + 11 = 1 + (8 + 19) + 11", "p3_ans": "Commutative Property of Addition", "p3_ver": "vA", "p4_prob": "6 - (19) = 6 - (19 \\times 1) ", "p4_ans": "Identity Property of Multiplication", "p4_ver": "vB", "p5_prob": "s - 0 = s - t \\times 0", "p5_ans": "Zero Product Property", "p5_ver": "v0", "p6_prob": "(10 - 6) \\times 21 = 210 - 126", "p6_ans": "Distributive Property", "p6_ver": "v0", "p7_prob": "x \\times z + s = z \\times x + s", "p7_ans": "Commutative Property of Multiplication", "p7_ver": "vC", "p8_prob": "c(j - v) = c \\times j - c \\times v", "p8_ans": "Distributive Property", "p8_ver": "v0", "p9_prob": "(u \\times m \\times y) + w = w + (u \\times m \\times y)", "p9_ans": "Commutative Property of Addition", "p9_ver": "vB", "p10_prob": "5 + 170 + 119 = 5 + 17(10 + 7)", "p10_ans": "Distributive Property", "p10_ver": "v0", "__seed__": "0999"}}]}, {"title": "Testing for Prime or Not Prime", "slug": "N2", "description": "\n I can determine if a number is prime or composite via the prime testing method.\n ", "template": "\n\n \n

Determine if the number below is prime or composite. If it is prime, you must show all work from our prime testing method. If it is composite, you must defend your answer with the appropriate work and/or explanation.

\n
\n \n \n

{{the_number}}

\n
\n \n

{{answer}}

\n

{{quotients_and_remainders}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0000"}}, {"seed": 1, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0001"}}, {"seed": 2, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0002"}}, {"seed": 3, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0003"}}, {"seed": 4, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0004"}}, {"seed": 5, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0005"}}, {"seed": 6, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0006"}}, {"seed": 7, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0007"}}, {"seed": 8, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0008"}}, {"seed": 9, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0009"}}, {"seed": 10, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0010"}}, {"seed": 11, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0011"}}, {"seed": 12, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0012"}}, {"seed": 13, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0013"}}, {"seed": 14, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0014"}}, {"seed": 15, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0015"}}, {"seed": 16, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0016"}}, {"seed": 17, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0017"}}, {"seed": 18, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0018"}}, {"seed": 19, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0019"}}, {"seed": 20, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0020"}}, {"seed": 21, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0021"}}, {"seed": 22, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0022"}}, {"seed": 23, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0023"}}, {"seed": 24, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0024"}}, {"seed": 25, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0025"}}, {"seed": 26, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0026"}}, {"seed": 27, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0027"}}, {"seed": 28, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0028"}}, {"seed": 29, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0029"}}, {"seed": 30, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0030"}}, {"seed": 31, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0031"}}, {"seed": 32, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0032"}}, {"seed": 33, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0033"}}, {"seed": 34, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0034"}}, {"seed": 35, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0035"}}, {"seed": 36, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0036"}}, {"seed": 37, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0037"}}, {"seed": 38, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0038"}}, {"seed": 39, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0039"}}, {"seed": 40, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0040"}}, {"seed": 41, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0041"}}, {"seed": 42, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0042"}}, {"seed": 43, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0043"}}, {"seed": 44, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0044"}}, {"seed": 45, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0045"}}, {"seed": 46, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0046"}}, {"seed": 47, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0047"}}, {"seed": 48, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0048"}}, {"seed": 49, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0049"}}, {"seed": 50, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0050"}}, {"seed": 51, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0051"}}, {"seed": 52, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0052"}}, {"seed": 53, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0053"}}, {"seed": 54, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0054"}}, {"seed": 55, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0055"}}, {"seed": 56, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0056"}}, {"seed": 57, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0057"}}, {"seed": 58, "data": {"the_number": "319", "answer": "The number 319 is composite. We already know that 319 has two divisors: 1 and 319. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 18 = 29, so 11 is a factor of 319. Thus 319 has at least three divisors (1, 11, and 319), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "319 \\div 2 = 159 \\text{ remainder } 1 \\\\ 319 \\div 3 = 106 \\text{ remainder } 1 \\\\ 319 \\div 5 = 63 \\text{ remainder } 4 \\\\ 319 \\div 7 = 45 \\text{ remainder } 4 \\\\ 319 \\div 11 = 29 \\\\ 319 \\div 13 = 24 \\text{ remainder } 7 \\\\ 319 \\div 17 = 18 \\text{ remainder } 13 \\\\ ", "prime_problem": false, "__seed__": "0058"}}, {"seed": 59, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0059"}}, {"seed": 60, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0060"}}, {"seed": 61, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0061"}}, {"seed": 62, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0062"}}, {"seed": 63, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0063"}}, {"seed": 64, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0064"}}, {"seed": 65, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0065"}}, {"seed": 66, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0066"}}, {"seed": 67, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0067"}}, {"seed": 68, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0068"}}, {"seed": 69, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0069"}}, {"seed": 70, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0070"}}, {"seed": 71, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0071"}}, {"seed": 72, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0072"}}, {"seed": 73, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0073"}}, {"seed": 74, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0074"}}, {"seed": 75, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0075"}}, {"seed": 76, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0076"}}, {"seed": 77, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0077"}}, {"seed": 78, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0078"}}, {"seed": 79, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0079"}}, {"seed": 80, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0080"}}, {"seed": 81, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0081"}}, {"seed": 82, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0082"}}, {"seed": 83, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0083"}}, {"seed": 84, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0084"}}, {"seed": 85, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0085"}}, {"seed": 86, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0086"}}, {"seed": 87, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0087"}}, {"seed": 88, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0088"}}, {"seed": 89, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0089"}}, {"seed": 90, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0090"}}, {"seed": 91, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0091"}}, {"seed": 92, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0092"}}, {"seed": 93, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0093"}}, {"seed": 94, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0094"}}, {"seed": 95, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0095"}}, {"seed": 96, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0096"}}, {"seed": 97, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0097"}}, {"seed": 98, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0098"}}, {"seed": 99, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0099"}}, {"seed": 100, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0100"}}, {"seed": 101, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0101"}}, {"seed": 102, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0102"}}, {"seed": 103, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0103"}}, {"seed": 104, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0104"}}, {"seed": 105, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0105"}}, {"seed": 106, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0106"}}, {"seed": 107, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0107"}}, {"seed": 108, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0108"}}, {"seed": 109, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0109"}}, {"seed": 110, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0110"}}, {"seed": 111, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0111"}}, {"seed": 112, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0112"}}, {"seed": 113, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0113"}}, {"seed": 114, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0114"}}, {"seed": 115, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0115"}}, {"seed": 116, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0116"}}, {"seed": 117, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0117"}}, {"seed": 118, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0118"}}, {"seed": 119, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0119"}}, {"seed": 120, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0120"}}, {"seed": 121, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0121"}}, {"seed": 122, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0122"}}, {"seed": 123, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0123"}}, {"seed": 124, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0124"}}, {"seed": 125, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0125"}}, {"seed": 126, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0126"}}, {"seed": 127, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0127"}}, {"seed": 128, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0128"}}, {"seed": 129, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0129"}}, {"seed": 130, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0130"}}, {"seed": 131, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0131"}}, {"seed": 132, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0132"}}, {"seed": 133, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0133"}}, {"seed": 134, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0134"}}, {"seed": 135, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0135"}}, {"seed": 136, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0136"}}, {"seed": 137, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0137"}}, {"seed": 138, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0138"}}, {"seed": 139, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0139"}}, {"seed": 140, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0140"}}, {"seed": 141, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0141"}}, {"seed": 142, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0142"}}, {"seed": 143, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0143"}}, {"seed": 144, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0144"}}, {"seed": 145, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0145"}}, {"seed": 146, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0146"}}, {"seed": 147, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0147"}}, {"seed": 148, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0148"}}, {"seed": 149, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0149"}}, {"seed": 150, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0150"}}, {"seed": 151, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0151"}}, {"seed": 152, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0152"}}, {"seed": 153, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0153"}}, {"seed": 154, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0154"}}, {"seed": 155, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0155"}}, {"seed": 156, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0156"}}, {"seed": 157, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0157"}}, {"seed": 158, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0158"}}, {"seed": 159, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0159"}}, {"seed": 160, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0160"}}, {"seed": 161, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0161"}}, {"seed": 162, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0162"}}, {"seed": 163, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0163"}}, {"seed": 164, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0164"}}, {"seed": 165, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0165"}}, {"seed": 166, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0166"}}, {"seed": 167, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0167"}}, {"seed": 168, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0168"}}, {"seed": 169, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0169"}}, {"seed": 170, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0170"}}, {"seed": 171, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0171"}}, {"seed": 172, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0172"}}, {"seed": 173, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0173"}}, {"seed": 174, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0174"}}, {"seed": 175, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0175"}}, {"seed": 176, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0176"}}, {"seed": 177, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0177"}}, {"seed": 178, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0178"}}, {"seed": 179, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0179"}}, {"seed": 180, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0180"}}, {"seed": 181, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0181"}}, {"seed": 182, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0182"}}, {"seed": 183, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0183"}}, {"seed": 184, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0184"}}, {"seed": 185, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0185"}}, {"seed": 186, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0186"}}, {"seed": 187, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0187"}}, {"seed": 188, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0188"}}, {"seed": 189, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0189"}}, {"seed": 190, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0190"}}, {"seed": 191, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0191"}}, {"seed": 192, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0192"}}, {"seed": 193, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0193"}}, {"seed": 194, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0194"}}, {"seed": 195, "data": {"the_number": "451", "answer": "The number 451 is composite. We already know that 451 has two divisors: 1 and 451. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 23 = 41, so 11 is a factor of 451. Thus 451 has at least three divisors (1, 11, and 451), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "451 \\div 2 = 225 \\text{ remainder } 1 \\\\ 451 \\div 3 = 150 \\text{ remainder } 1 \\\\ 451 \\div 5 = 90 \\text{ remainder } 1 \\\\ 451 \\div 7 = 64 \\text{ remainder } 3 \\\\ 451 \\div 11 = 41 \\\\ 451 \\div 13 = 34 \\text{ remainder } 9 \\\\ 451 \\div 17 = 26 \\text{ remainder } 9 \\\\ 451 \\div 19 = 23 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0195"}}, {"seed": 196, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0196"}}, {"seed": 197, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0197"}}, {"seed": 198, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0198"}}, {"seed": 199, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0199"}}, {"seed": 200, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0200"}}, {"seed": 201, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0201"}}, {"seed": 202, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0202"}}, {"seed": 203, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0203"}}, {"seed": 204, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0204"}}, {"seed": 205, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0205"}}, {"seed": 206, "data": {"the_number": "319", "answer": "The number 319 is composite. We already know that 319 has two divisors: 1 and 319. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 18 = 29, so 11 is a factor of 319. Thus 319 has at least three divisors (1, 11, and 319), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "319 \\div 2 = 159 \\text{ remainder } 1 \\\\ 319 \\div 3 = 106 \\text{ remainder } 1 \\\\ 319 \\div 5 = 63 \\text{ remainder } 4 \\\\ 319 \\div 7 = 45 \\text{ remainder } 4 \\\\ 319 \\div 11 = 29 \\\\ 319 \\div 13 = 24 \\text{ remainder } 7 \\\\ 319 \\div 17 = 18 \\text{ remainder } 13 \\\\ ", "prime_problem": false, "__seed__": "0206"}}, {"seed": 207, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0207"}}, {"seed": 208, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0208"}}, {"seed": 209, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0209"}}, {"seed": 210, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0210"}}, {"seed": 211, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0211"}}, {"seed": 212, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0212"}}, {"seed": 213, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0213"}}, {"seed": 214, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0214"}}, {"seed": 215, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0215"}}, {"seed": 216, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0216"}}, {"seed": 217, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0217"}}, {"seed": 218, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0218"}}, {"seed": 219, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0219"}}, {"seed": 220, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0220"}}, {"seed": 221, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0221"}}, {"seed": 222, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0222"}}, {"seed": 223, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0223"}}, {"seed": 224, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0224"}}, {"seed": 225, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0225"}}, {"seed": 226, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0226"}}, {"seed": 227, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0227"}}, {"seed": 228, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0228"}}, {"seed": 229, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0229"}}, {"seed": 230, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0230"}}, {"seed": 231, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0231"}}, {"seed": 232, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0232"}}, {"seed": 233, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0233"}}, {"seed": 234, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0234"}}, {"seed": 235, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0235"}}, {"seed": 236, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0236"}}, {"seed": 237, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0237"}}, {"seed": 238, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0238"}}, {"seed": 239, "data": {"the_number": "319", "answer": "The number 319 is composite. We already know that 319 has two divisors: 1 and 319. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 18 = 29, so 11 is a factor of 319. Thus 319 has at least three divisors (1, 11, and 319), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "319 \\div 2 = 159 \\text{ remainder } 1 \\\\ 319 \\div 3 = 106 \\text{ remainder } 1 \\\\ 319 \\div 5 = 63 \\text{ remainder } 4 \\\\ 319 \\div 7 = 45 \\text{ remainder } 4 \\\\ 319 \\div 11 = 29 \\\\ 319 \\div 13 = 24 \\text{ remainder } 7 \\\\ 319 \\div 17 = 18 \\text{ remainder } 13 \\\\ ", "prime_problem": false, "__seed__": "0239"}}, {"seed": 240, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0240"}}, {"seed": 241, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0241"}}, {"seed": 242, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0242"}}, {"seed": 243, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0243"}}, {"seed": 244, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0244"}}, {"seed": 245, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0245"}}, {"seed": 246, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0246"}}, {"seed": 247, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0247"}}, {"seed": 248, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0248"}}, {"seed": 249, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0249"}}, {"seed": 250, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0250"}}, {"seed": 251, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0251"}}, {"seed": 252, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0252"}}, {"seed": 253, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0253"}}, {"seed": 254, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0254"}}, {"seed": 255, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0255"}}, {"seed": 256, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0256"}}, {"seed": 257, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0257"}}, {"seed": 258, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0258"}}, {"seed": 259, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0259"}}, {"seed": 260, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0260"}}, {"seed": 261, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0261"}}, {"seed": 262, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0262"}}, {"seed": 263, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0263"}}, {"seed": 264, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0264"}}, {"seed": 265, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0265"}}, {"seed": 266, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0266"}}, {"seed": 267, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0267"}}, {"seed": 268, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0268"}}, {"seed": 269, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0269"}}, {"seed": 270, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0270"}}, {"seed": 271, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0271"}}, {"seed": 272, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0272"}}, {"seed": 273, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0273"}}, {"seed": 274, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0274"}}, {"seed": 275, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0275"}}, {"seed": 276, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0276"}}, {"seed": 277, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0277"}}, {"seed": 278, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0278"}}, {"seed": 279, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0279"}}, {"seed": 280, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0280"}}, {"seed": 281, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0281"}}, {"seed": 282, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0282"}}, {"seed": 283, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0283"}}, {"seed": 284, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0284"}}, {"seed": 285, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0285"}}, {"seed": 286, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0286"}}, {"seed": 287, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0287"}}, {"seed": 288, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0288"}}, {"seed": 289, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0289"}}, {"seed": 290, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0290"}}, {"seed": 291, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0291"}}, {"seed": 292, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0292"}}, {"seed": 293, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0293"}}, {"seed": 294, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0294"}}, {"seed": 295, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0295"}}, {"seed": 296, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0296"}}, {"seed": 297, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0297"}}, {"seed": 298, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0298"}}, {"seed": 299, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0299"}}, {"seed": 300, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0300"}}, {"seed": 301, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0301"}}, {"seed": 302, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0302"}}, {"seed": 303, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0303"}}, {"seed": 304, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0304"}}, {"seed": 305, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0305"}}, {"seed": 306, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0306"}}, {"seed": 307, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0307"}}, {"seed": 308, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0308"}}, {"seed": 309, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0309"}}, {"seed": 310, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0310"}}, {"seed": 311, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0311"}}, {"seed": 312, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0312"}}, {"seed": 313, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0313"}}, {"seed": 314, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0314"}}, {"seed": 315, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0315"}}, {"seed": 316, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0316"}}, {"seed": 317, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0317"}}, {"seed": 318, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0318"}}, {"seed": 319, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0319"}}, {"seed": 320, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0320"}}, {"seed": 321, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0321"}}, {"seed": 322, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0322"}}, {"seed": 323, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0323"}}, {"seed": 324, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0324"}}, {"seed": 325, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0325"}}, {"seed": 326, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0326"}}, {"seed": 327, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0327"}}, {"seed": 328, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0328"}}, {"seed": 329, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0329"}}, {"seed": 330, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0330"}}, {"seed": 331, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0331"}}, {"seed": 332, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0332"}}, {"seed": 333, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0333"}}, {"seed": 334, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0334"}}, {"seed": 335, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0335"}}, {"seed": 336, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0336"}}, {"seed": 337, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0337"}}, {"seed": 338, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0338"}}, {"seed": 339, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0339"}}, {"seed": 340, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0340"}}, {"seed": 341, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0341"}}, {"seed": 342, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0342"}}, {"seed": 343, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0343"}}, {"seed": 344, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0344"}}, {"seed": 345, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0345"}}, {"seed": 346, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0346"}}, {"seed": 347, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0347"}}, {"seed": 348, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0348"}}, {"seed": 349, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0349"}}, {"seed": 350, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0350"}}, {"seed": 351, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0351"}}, {"seed": 352, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0352"}}, {"seed": 353, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0353"}}, {"seed": 354, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0354"}}, {"seed": 355, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0355"}}, {"seed": 356, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0356"}}, {"seed": 357, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0357"}}, {"seed": 358, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0358"}}, {"seed": 359, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0359"}}, {"seed": 360, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0360"}}, {"seed": 361, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0361"}}, {"seed": 362, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0362"}}, {"seed": 363, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0363"}}, {"seed": 364, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0364"}}, {"seed": 365, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0365"}}, {"seed": 366, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0366"}}, {"seed": 367, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0367"}}, {"seed": 368, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0368"}}, {"seed": 369, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0369"}}, {"seed": 370, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0370"}}, {"seed": 371, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0371"}}, {"seed": 372, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0372"}}, {"seed": 373, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0373"}}, {"seed": 374, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0374"}}, {"seed": 375, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0375"}}, {"seed": 376, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0376"}}, {"seed": 377, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0377"}}, {"seed": 378, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0378"}}, {"seed": 379, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0379"}}, {"seed": 380, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0380"}}, {"seed": 381, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0381"}}, {"seed": 382, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0382"}}, {"seed": 383, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0383"}}, {"seed": 384, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0384"}}, {"seed": 385, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0385"}}, {"seed": 386, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0386"}}, {"seed": 387, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0387"}}, {"seed": 388, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0388"}}, {"seed": 389, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0389"}}, {"seed": 390, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0390"}}, {"seed": 391, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0391"}}, {"seed": 392, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0392"}}, {"seed": 393, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0393"}}, {"seed": 394, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0394"}}, {"seed": 395, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0395"}}, {"seed": 396, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0396"}}, {"seed": 397, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0397"}}, {"seed": 398, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0398"}}, {"seed": 399, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0399"}}, {"seed": 400, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0400"}}, {"seed": 401, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0401"}}, {"seed": 402, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0402"}}, {"seed": 403, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0403"}}, {"seed": 404, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0404"}}, {"seed": 405, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0405"}}, {"seed": 406, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0406"}}, {"seed": 407, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0407"}}, {"seed": 408, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0408"}}, {"seed": 409, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0409"}}, {"seed": 410, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0410"}}, {"seed": 411, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0411"}}, {"seed": 412, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0412"}}, {"seed": 413, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0413"}}, {"seed": 414, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0414"}}, {"seed": 415, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0415"}}, {"seed": 416, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0416"}}, {"seed": 417, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0417"}}, {"seed": 418, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0418"}}, {"seed": 419, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0419"}}, {"seed": 420, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0420"}}, {"seed": 421, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0421"}}, {"seed": 422, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0422"}}, {"seed": 423, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0423"}}, {"seed": 424, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0424"}}, {"seed": 425, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0425"}}, {"seed": 426, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0426"}}, {"seed": 427, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0427"}}, {"seed": 428, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0428"}}, {"seed": 429, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0429"}}, {"seed": 430, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0430"}}, {"seed": 431, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0431"}}, {"seed": 432, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0432"}}, {"seed": 433, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0433"}}, {"seed": 434, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0434"}}, {"seed": 435, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0435"}}, {"seed": 436, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0436"}}, {"seed": 437, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0437"}}, {"seed": 438, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0438"}}, {"seed": 439, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0439"}}, {"seed": 440, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0440"}}, {"seed": 441, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0441"}}, {"seed": 442, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0442"}}, {"seed": 443, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0443"}}, {"seed": 444, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0444"}}, {"seed": 445, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0445"}}, {"seed": 446, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0446"}}, {"seed": 447, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0447"}}, {"seed": 448, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0448"}}, {"seed": 449, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0449"}}, {"seed": 450, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0450"}}, {"seed": 451, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0451"}}, {"seed": 452, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0452"}}, {"seed": 453, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0453"}}, {"seed": 454, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0454"}}, {"seed": 455, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0455"}}, {"seed": 456, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0456"}}, {"seed": 457, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0457"}}, {"seed": 458, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0458"}}, {"seed": 459, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0459"}}, {"seed": 460, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0460"}}, {"seed": 461, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0461"}}, {"seed": 462, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0462"}}, {"seed": 463, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0463"}}, {"seed": 464, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0464"}}, {"seed": 465, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0465"}}, {"seed": 466, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0466"}}, {"seed": 467, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0467"}}, {"seed": 468, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0468"}}, {"seed": 469, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0469"}}, {"seed": 470, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0470"}}, {"seed": 471, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0471"}}, {"seed": 472, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0472"}}, {"seed": 473, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0473"}}, {"seed": 474, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0474"}}, {"seed": 475, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0475"}}, {"seed": 476, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0476"}}, {"seed": 477, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0477"}}, {"seed": 478, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0478"}}, {"seed": 479, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0479"}}, {"seed": 480, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0480"}}, {"seed": 481, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0481"}}, {"seed": 482, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0482"}}, {"seed": 483, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0483"}}, {"seed": 484, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0484"}}, {"seed": 485, "data": {"the_number": "493", "answer": "The number 493 is composite. We already know that 493 has two divisors: 1 and 493. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 25 = 29, so 17 is a factor of 493. Thus 493 has at least three divisors (1, 17, and 493), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "493 \\div 2 = 246 \\text{ remainder } 1 \\\\ 493 \\div 3 = 164 \\text{ remainder } 1 \\\\ 493 \\div 5 = 98 \\text{ remainder } 3 \\\\ 493 \\div 7 = 70 \\text{ remainder } 3 \\\\ 493 \\div 11 = 44 \\text{ remainder } 9 \\\\ 493 \\div 13 = 37 \\text{ remainder } 12 \\\\ 493 \\div 17 = 29 \\\\ 493 \\div 19 = 25 \\text{ remainder } 18 \\\\ ", "prime_problem": false, "__seed__": "0485"}}, {"seed": 486, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0486"}}, {"seed": 487, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0487"}}, {"seed": 488, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0488"}}, {"seed": 489, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0489"}}, {"seed": 490, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0490"}}, {"seed": 491, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0491"}}, {"seed": 492, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0492"}}, {"seed": 493, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0493"}}, {"seed": 494, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0494"}}, {"seed": 495, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0495"}}, {"seed": 496, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0496"}}, {"seed": 497, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0497"}}, {"seed": 498, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0498"}}, {"seed": 499, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0499"}}, {"seed": 500, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0500"}}, {"seed": 501, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0501"}}, {"seed": 502, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0502"}}, {"seed": 503, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0503"}}, {"seed": 504, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0504"}}, {"seed": 505, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0505"}}, {"seed": 506, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0506"}}, {"seed": 507, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0507"}}, {"seed": 508, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0508"}}, {"seed": 509, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0509"}}, {"seed": 510, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0510"}}, {"seed": 511, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0511"}}, {"seed": 512, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0512"}}, {"seed": 513, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0513"}}, {"seed": 514, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0514"}}, {"seed": 515, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0515"}}, {"seed": 516, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0516"}}, {"seed": 517, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0517"}}, {"seed": 518, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0518"}}, {"seed": 519, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0519"}}, {"seed": 520, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0520"}}, {"seed": 521, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0521"}}, {"seed": 522, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0522"}}, {"seed": 523, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0523"}}, {"seed": 524, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0524"}}, {"seed": 525, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0525"}}, {"seed": 526, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0526"}}, {"seed": 527, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0527"}}, {"seed": 528, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0528"}}, {"seed": 529, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0529"}}, {"seed": 530, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0530"}}, {"seed": 531, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0531"}}, {"seed": 532, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0532"}}, {"seed": 533, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0533"}}, {"seed": 534, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0534"}}, {"seed": 535, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0535"}}, {"seed": 536, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0536"}}, {"seed": 537, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0537"}}, {"seed": 538, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0538"}}, {"seed": 539, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0539"}}, {"seed": 540, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0540"}}, {"seed": 541, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0541"}}, {"seed": 542, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0542"}}, {"seed": 543, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0543"}}, {"seed": 544, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0544"}}, {"seed": 545, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0545"}}, {"seed": 546, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0546"}}, {"seed": 547, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0547"}}, {"seed": 548, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0548"}}, {"seed": 549, "data": {"the_number": "283", "answer": "The number 283 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a283 can divide 283. Since 13\u00b2 is less than or equal to 283 and 17\u00b2 is greater than 283, \u221a283 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 283 evenly. None of them divided 283, as evidenced by the list of quotients and remainders below. Thus, 283 is prime!", "quotients_and_remainders": "283 \\div 2 = 141 \\text{ remainder } 1 \\\\ 283 \\div 3 = 94 \\text{ remainder } 1 \\\\ 283 \\div 5 = 56 \\text{ remainder } 3 \\\\ 283 \\div 7 = 40 \\text{ remainder } 3 \\\\ 283 \\div 11 = 25 \\text{ remainder } 8 \\\\ 283 \\div 13 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0549"}}, {"seed": 550, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0550"}}, {"seed": 551, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0551"}}, {"seed": 552, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0552"}}, {"seed": 553, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0553"}}, {"seed": 554, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0554"}}, {"seed": 555, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0555"}}, {"seed": 556, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0556"}}, {"seed": 557, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0557"}}, {"seed": 558, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0558"}}, {"seed": 559, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0559"}}, {"seed": 560, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0560"}}, {"seed": 561, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0561"}}, {"seed": 562, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0562"}}, {"seed": 563, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0563"}}, {"seed": 564, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0564"}}, {"seed": 565, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0565"}}, {"seed": 566, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0566"}}, {"seed": 567, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0567"}}, {"seed": 568, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0568"}}, {"seed": 569, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0569"}}, {"seed": 570, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0570"}}, {"seed": 571, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0571"}}, {"seed": 572, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0572"}}, {"seed": 573, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0573"}}, {"seed": 574, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0574"}}, {"seed": 575, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0575"}}, {"seed": 576, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0576"}}, {"seed": 577, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0577"}}, {"seed": 578, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0578"}}, {"seed": 579, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0579"}}, {"seed": 580, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0580"}}, {"seed": 581, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0581"}}, {"seed": 582, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0582"}}, {"seed": 583, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0583"}}, {"seed": 584, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0584"}}, {"seed": 585, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0585"}}, {"seed": 586, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0586"}}, {"seed": 587, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0587"}}, {"seed": 588, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0588"}}, {"seed": 589, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0589"}}, {"seed": 590, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0590"}}, {"seed": 591, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0591"}}, {"seed": 592, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0592"}}, {"seed": 593, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0593"}}, {"seed": 594, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0594"}}, {"seed": 595, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0595"}}, {"seed": 596, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0596"}}, {"seed": 597, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0597"}}, {"seed": 598, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0598"}}, {"seed": 599, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0599"}}, {"seed": 600, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0600"}}, {"seed": 601, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0601"}}, {"seed": 602, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0602"}}, {"seed": 603, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0603"}}, {"seed": 604, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0604"}}, {"seed": 605, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0605"}}, {"seed": 606, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0606"}}, {"seed": 607, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0607"}}, {"seed": 608, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0608"}}, {"seed": 609, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0609"}}, {"seed": 610, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0610"}}, {"seed": 611, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0611"}}, {"seed": 612, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0612"}}, {"seed": 613, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0613"}}, {"seed": 614, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0614"}}, {"seed": 615, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0615"}}, {"seed": 616, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0616"}}, {"seed": 617, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0617"}}, {"seed": 618, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0618"}}, {"seed": 619, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0619"}}, {"seed": 620, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0620"}}, {"seed": 621, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0621"}}, {"seed": 622, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0622"}}, {"seed": 623, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0623"}}, {"seed": 624, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0624"}}, {"seed": 625, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0625"}}, {"seed": 626, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0626"}}, {"seed": 627, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0627"}}, {"seed": 628, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0628"}}, {"seed": 629, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0629"}}, {"seed": 630, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0630"}}, {"seed": 631, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0631"}}, {"seed": 632, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0632"}}, {"seed": 633, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0633"}}, {"seed": 634, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0634"}}, {"seed": 635, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0635"}}, {"seed": 636, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0636"}}, {"seed": 637, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0637"}}, {"seed": 638, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0638"}}, {"seed": 639, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0639"}}, {"seed": 640, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0640"}}, {"seed": 641, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0641"}}, {"seed": 642, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0642"}}, {"seed": 643, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0643"}}, {"seed": 644, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0644"}}, {"seed": 645, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0645"}}, {"seed": 646, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0646"}}, {"seed": 647, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0647"}}, {"seed": 648, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0648"}}, {"seed": 649, "data": {"the_number": "199", "answer": "The number 199 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a199 can divide 199. Since 13\u00b2 is less than or equal to 199 and 17\u00b2 is greater than 199, \u221a199 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 199 evenly. None of them divided 199, as evidenced by the list of quotients and remainders below. Thus, 199 is prime!", "quotients_and_remainders": "199 \\div 2 = 99 \\text{ remainder } 1 \\\\ 199 \\div 3 = 66 \\text{ remainder } 1 \\\\ 199 \\div 5 = 39 \\text{ remainder } 4 \\\\ 199 \\div 7 = 28 \\text{ remainder } 3 \\\\ 199 \\div 11 = 18 \\text{ remainder } 1 \\\\ 199 \\div 13 = 15 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0649"}}, {"seed": 650, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0650"}}, {"seed": 651, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0651"}}, {"seed": 652, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0652"}}, {"seed": 653, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0653"}}, {"seed": 654, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0654"}}, {"seed": 655, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0655"}}, {"seed": 656, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0656"}}, {"seed": 657, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0657"}}, {"seed": 658, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0658"}}, {"seed": 659, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0659"}}, {"seed": 660, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0660"}}, {"seed": 661, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0661"}}, {"seed": 662, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0662"}}, {"seed": 663, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0663"}}, {"seed": 664, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0664"}}, {"seed": 665, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0665"}}, {"seed": 666, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0666"}}, {"seed": 667, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0667"}}, {"seed": 668, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0668"}}, {"seed": 669, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0669"}}, {"seed": 670, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0670"}}, {"seed": 671, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0671"}}, {"seed": 672, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0672"}}, {"seed": 673, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0673"}}, {"seed": 674, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0674"}}, {"seed": 675, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0675"}}, {"seed": 676, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0676"}}, {"seed": 677, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0677"}}, {"seed": 678, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0678"}}, {"seed": 679, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0679"}}, {"seed": 680, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0680"}}, {"seed": 681, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0681"}}, {"seed": 682, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0682"}}, {"seed": 683, "data": {"the_number": "187", "answer": "The number 187 is composite. We already know that 187 has two divisors: 1 and 187. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 14 = 17, so 11 is a factor of 187. Thus 187 has at least three divisors (1, 11, and 187), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "187 \\div 2 = 93 \\text{ remainder } 1 \\\\ 187 \\div 3 = 62 \\text{ remainder } 1 \\\\ 187 \\div 5 = 37 \\text{ remainder } 2 \\\\ 187 \\div 7 = 26 \\text{ remainder } 5 \\\\ 187 \\div 11 = 17 \\\\ 187 \\div 13 = 14 \\text{ remainder } 5 \\\\ ", "prime_problem": false, "__seed__": "0683"}}, {"seed": 684, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0684"}}, {"seed": 685, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0685"}}, {"seed": 686, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0686"}}, {"seed": 687, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0687"}}, {"seed": 688, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0688"}}, {"seed": 689, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0689"}}, {"seed": 690, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0690"}}, {"seed": 691, "data": {"the_number": "163", "answer": "The number 163 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a163 can divide 163. Since 11\u00b2 is less than or equal to 163 and 13\u00b2 is greater than 163, \u221a163 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 163 evenly. None of them divided 163, as evidenced by the list of quotients and remainders below. Thus, 163 is prime!", "quotients_and_remainders": "163 \\div 2 = 81 \\text{ remainder } 1 \\\\ 163 \\div 3 = 54 \\text{ remainder } 1 \\\\ 163 \\div 5 = 32 \\text{ remainder } 3 \\\\ 163 \\div 7 = 23 \\text{ remainder } 2 \\\\ 163 \\div 11 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0691"}}, {"seed": 692, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0692"}}, {"seed": 693, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0693"}}, {"seed": 694, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0694"}}, {"seed": 695, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0695"}}, {"seed": 696, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0696"}}, {"seed": 697, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0697"}}, {"seed": 698, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0698"}}, {"seed": 699, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0699"}}, {"seed": 700, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0700"}}, {"seed": 701, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0701"}}, {"seed": 702, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0702"}}, {"seed": 703, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0703"}}, {"seed": 704, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0704"}}, {"seed": 705, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0705"}}, {"seed": 706, "data": {"the_number": "347", "answer": "The number 347 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a347 can divide 347. Since 17\u00b2 is less than or equal to 347 and 19\u00b2 is greater than 347, \u221a347 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 347 evenly. None of them divided 347, as evidenced by the list of quotients and remainders below. Thus, 347 is prime!", "quotients_and_remainders": "347 \\div 2 = 173 \\text{ remainder } 1 \\\\ 347 \\div 3 = 115 \\text{ remainder } 2 \\\\ 347 \\div 5 = 69 \\text{ remainder } 2 \\\\ 347 \\div 7 = 49 \\text{ remainder } 4 \\\\ 347 \\div 11 = 31 \\text{ remainder } 6 \\\\ 347 \\div 13 = 26 \\text{ remainder } 9 \\\\ 347 \\div 17 = 20 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0706"}}, {"seed": 707, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0707"}}, {"seed": 708, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0708"}}, {"seed": 709, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0709"}}, {"seed": 710, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0710"}}, {"seed": 711, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0711"}}, {"seed": 712, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0712"}}, {"seed": 713, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0713"}}, {"seed": 714, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0714"}}, {"seed": 715, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0715"}}, {"seed": 716, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0716"}}, {"seed": 717, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0717"}}, {"seed": 718, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0718"}}, {"seed": 719, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0719"}}, {"seed": 720, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0720"}}, {"seed": 721, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0721"}}, {"seed": 722, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0722"}}, {"seed": 723, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0723"}}, {"seed": 724, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0724"}}, {"seed": 725, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0725"}}, {"seed": 726, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0726"}}, {"seed": 727, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0727"}}, {"seed": 728, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0728"}}, {"seed": 729, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0729"}}, {"seed": 730, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0730"}}, {"seed": 731, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0731"}}, {"seed": 732, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0732"}}, {"seed": 733, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0733"}}, {"seed": 734, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0734"}}, {"seed": 735, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0735"}}, {"seed": 736, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0736"}}, {"seed": 737, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0737"}}, {"seed": 738, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0738"}}, {"seed": 739, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0739"}}, {"seed": 740, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0740"}}, {"seed": 741, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0741"}}, {"seed": 742, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0742"}}, {"seed": 743, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0743"}}, {"seed": 744, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0744"}}, {"seed": 745, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0745"}}, {"seed": 746, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0746"}}, {"seed": 747, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0747"}}, {"seed": 748, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0748"}}, {"seed": 749, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0749"}}, {"seed": 750, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0750"}}, {"seed": 751, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0751"}}, {"seed": 752, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0752"}}, {"seed": 753, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0753"}}, {"seed": 754, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0754"}}, {"seed": 755, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0755"}}, {"seed": 756, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0756"}}, {"seed": 757, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0757"}}, {"seed": 758, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0758"}}, {"seed": 759, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0759"}}, {"seed": 760, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0760"}}, {"seed": 761, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0761"}}, {"seed": 762, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0762"}}, {"seed": 763, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0763"}}, {"seed": 764, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0764"}}, {"seed": 765, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0765"}}, {"seed": 766, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0766"}}, {"seed": 767, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0767"}}, {"seed": 768, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0768"}}, {"seed": 769, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0769"}}, {"seed": 770, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0770"}}, {"seed": 771, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0771"}}, {"seed": 772, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0772"}}, {"seed": 773, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0773"}}, {"seed": 774, "data": {"the_number": "359", "answer": "The number 359 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a359 can divide 359. Since 17\u00b2 is less than or equal to 359 and 19\u00b2 is greater than 359, \u221a359 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 359 evenly. None of them divided 359, as evidenced by the list of quotients and remainders below. Thus, 359 is prime!", "quotients_and_remainders": "359 \\div 2 = 179 \\text{ remainder } 1 \\\\ 359 \\div 3 = 119 \\text{ remainder } 2 \\\\ 359 \\div 5 = 71 \\text{ remainder } 4 \\\\ 359 \\div 7 = 51 \\text{ remainder } 2 \\\\ 359 \\div 11 = 32 \\text{ remainder } 7 \\\\ 359 \\div 13 = 27 \\text{ remainder } 8 \\\\ 359 \\div 17 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0774"}}, {"seed": 775, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0775"}}, {"seed": 776, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0776"}}, {"seed": 777, "data": {"the_number": "329", "answer": "The number 329 is composite. We already know that 329 has two divisors: 1 and 329. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 19 = 47, so 7 is a factor of 329. Thus 329 has at least three divisors (1, 7, and 329), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "329 \\div 2 = 164 \\text{ remainder } 1 \\\\ 329 \\div 3 = 109 \\text{ remainder } 2 \\\\ 329 \\div 5 = 65 \\text{ remainder } 4 \\\\ 329 \\div 7 = 47 \\\\ 329 \\div 11 = 29 \\text{ remainder } 10 \\\\ 329 \\div 13 = 25 \\text{ remainder } 4 \\\\ 329 \\div 17 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0777"}}, {"seed": 778, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0778"}}, {"seed": 779, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0779"}}, {"seed": 780, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0780"}}, {"seed": 781, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0781"}}, {"seed": 782, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0782"}}, {"seed": 783, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0783"}}, {"seed": 784, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0784"}}, {"seed": 785, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0785"}}, {"seed": 786, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0786"}}, {"seed": 787, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0787"}}, {"seed": 788, "data": {"the_number": "253", "answer": "The number 253 is composite. We already know that 253 has two divisors: 1 and 253. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 19 = 23, so 11 is a factor of 253. Thus 253 has at least three divisors (1, 11, and 253), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "253 \\div 2 = 126 \\text{ remainder } 1 \\\\ 253 \\div 3 = 84 \\text{ remainder } 1 \\\\ 253 \\div 5 = 50 \\text{ remainder } 3 \\\\ 253 \\div 7 = 36 \\text{ remainder } 1 \\\\ 253 \\div 11 = 23 \\\\ 253 \\div 13 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0788"}}, {"seed": 789, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0789"}}, {"seed": 790, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0790"}}, {"seed": 791, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0791"}}, {"seed": 792, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0792"}}, {"seed": 793, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0793"}}, {"seed": 794, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0794"}}, {"seed": 795, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0795"}}, {"seed": 796, "data": {"the_number": "449", "answer": "The number 449 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a449 can divide 449. Since 19\u00b2 is less than or equal to 449 and 23\u00b2 is greater than 449, \u221a449 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 449 evenly. None of them divided 449, as evidenced by the list of quotients and remainders below. Thus, 449 is prime!", "quotients_and_remainders": "449 \\div 2 = 224 \\text{ remainder } 1 \\\\ 449 \\div 3 = 149 \\text{ remainder } 2 \\\\ 449 \\div 5 = 89 \\text{ remainder } 4 \\\\ 449 \\div 7 = 64 \\text{ remainder } 1 \\\\ 449 \\div 11 = 40 \\text{ remainder } 9 \\\\ 449 \\div 13 = 34 \\text{ remainder } 7 \\\\ 449 \\div 17 = 26 \\text{ remainder } 7 \\\\ 449 \\div 19 = 23 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0796"}}, {"seed": 797, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0797"}}, {"seed": 798, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0798"}}, {"seed": 799, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0799"}}, {"seed": 800, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0800"}}, {"seed": 801, "data": {"the_number": "503", "answer": "The number 503 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a503 can divide 503. Since 19\u00b2 is less than or equal to 503 and 23\u00b2 is greater than 503, \u221a503 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 503 evenly. None of them divided 503, as evidenced by the list of quotients and remainders below. Thus, 503 is prime!", "quotients_and_remainders": "503 \\div 2 = 251 \\text{ remainder } 1 \\\\ 503 \\div 3 = 167 \\text{ remainder } 2 \\\\ 503 \\div 5 = 100 \\text{ remainder } 3 \\\\ 503 \\div 7 = 71 \\text{ remainder } 6 \\\\ 503 \\div 11 = 45 \\text{ remainder } 8 \\\\ 503 \\div 13 = 38 \\text{ remainder } 9 \\\\ 503 \\div 17 = 29 \\text{ remainder } 10 \\\\ 503 \\div 19 = 26 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0801"}}, {"seed": 802, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0802"}}, {"seed": 803, "data": {"the_number": "151", "answer": "The number 151 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a151 can divide 151. Since 11\u00b2 is less than or equal to 151 and 13\u00b2 is greater than 151, \u221a151 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 151 evenly. None of them divided 151, as evidenced by the list of quotients and remainders below. Thus, 151 is prime!", "quotients_and_remainders": "151 \\div 2 = 75 \\text{ remainder } 1 \\\\ 151 \\div 3 = 50 \\text{ remainder } 1 \\\\ 151 \\div 5 = 30 \\text{ remainder } 1 \\\\ 151 \\div 7 = 21 \\text{ remainder } 4 \\\\ 151 \\div 11 = 13 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0803"}}, {"seed": 804, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0804"}}, {"seed": 805, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0805"}}, {"seed": 806, "data": {"the_number": "307", "answer": "The number 307 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a307 can divide 307. Since 17\u00b2 is less than or equal to 307 and 19\u00b2 is greater than 307, \u221a307 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 307 evenly. None of them divided 307, as evidenced by the list of quotients and remainders below. Thus, 307 is prime!", "quotients_and_remainders": "307 \\div 2 = 153 \\text{ remainder } 1 \\\\ 307 \\div 3 = 102 \\text{ remainder } 1 \\\\ 307 \\div 5 = 61 \\text{ remainder } 2 \\\\ 307 \\div 7 = 43 \\text{ remainder } 6 \\\\ 307 \\div 11 = 27 \\text{ remainder } 10 \\\\ 307 \\div 13 = 23 \\text{ remainder } 8 \\\\ 307 \\div 17 = 18 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0806"}}, {"seed": 807, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0807"}}, {"seed": 808, "data": {"the_number": "463", "answer": "The number 463 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a463 can divide 463. Since 19\u00b2 is less than or equal to 463 and 23\u00b2 is greater than 463, \u221a463 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 463 evenly. None of them divided 463, as evidenced by the list of quotients and remainders below. Thus, 463 is prime!", "quotients_and_remainders": "463 \\div 2 = 231 \\text{ remainder } 1 \\\\ 463 \\div 3 = 154 \\text{ remainder } 1 \\\\ 463 \\div 5 = 92 \\text{ remainder } 3 \\\\ 463 \\div 7 = 66 \\text{ remainder } 1 \\\\ 463 \\div 11 = 42 \\text{ remainder } 1 \\\\ 463 \\div 13 = 35 \\text{ remainder } 8 \\\\ 463 \\div 17 = 27 \\text{ remainder } 4 \\\\ 463 \\div 19 = 24 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0808"}}, {"seed": 809, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0809"}}, {"seed": 810, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0810"}}, {"seed": 811, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0811"}}, {"seed": 812, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0812"}}, {"seed": 813, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0813"}}, {"seed": 814, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0814"}}, {"seed": 815, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0815"}}, {"seed": 816, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0816"}}, {"seed": 817, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0817"}}, {"seed": 818, "data": {"the_number": "361", "answer": "The number 361 is composite. We already know that 361 has two divisors: 1 and 361. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 19 = 19, so 19 is a factor of 361. Thus 361 has at least three divisors (1, 19, and 361), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "361 \\div 2 = 180 \\text{ remainder } 1 \\\\ 361 \\div 3 = 120 \\text{ remainder } 1 \\\\ 361 \\div 5 = 72 \\text{ remainder } 1 \\\\ 361 \\div 7 = 51 \\text{ remainder } 4 \\\\ 361 \\div 11 = 32 \\text{ remainder } 9 \\\\ 361 \\div 13 = 27 \\text{ remainder } 10 \\\\ 361 \\div 17 = 21 \\text{ remainder } 4 \\\\ 361 \\div 19 = 19 \\\\ ", "prime_problem": false, "__seed__": "0818"}}, {"seed": 819, "data": {"the_number": "323", "answer": "The number 323 is composite. We already know that 323 has two divisors: 1 and 323. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 19 = 19, so 17 is a factor of 323. Thus 323 has at least three divisors (1, 17, and 323), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "323 \\div 2 = 161 \\text{ remainder } 1 \\\\ 323 \\div 3 = 107 \\text{ remainder } 2 \\\\ 323 \\div 5 = 64 \\text{ remainder } 3 \\\\ 323 \\div 7 = 46 \\text{ remainder } 1 \\\\ 323 \\div 11 = 29 \\text{ remainder } 4 \\\\ 323 \\div 13 = 24 \\text{ remainder } 11 \\\\ 323 \\div 17 = 19 \\\\ ", "prime_problem": false, "__seed__": "0819"}}, {"seed": 820, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0820"}}, {"seed": 821, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0821"}}, {"seed": 822, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0822"}}, {"seed": 823, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0823"}}, {"seed": 824, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0824"}}, {"seed": 825, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0825"}}, {"seed": 826, "data": {"the_number": "301", "answer": "The number 301 is composite. We already know that 301 has two divisors: 1 and 301. When testing the primes from 2 to 17 (our cutoff point), we found that 7 \u00d7 17 = 43, so 7 is a factor of 301. Thus 301 has at least three divisors (1, 7, and 301), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "301 \\div 2 = 150 \\text{ remainder } 1 \\\\ 301 \\div 3 = 100 \\text{ remainder } 1 \\\\ 301 \\div 5 = 60 \\text{ remainder } 1 \\\\ 301 \\div 7 = 43 \\\\ 301 \\div 11 = 27 \\text{ remainder } 4 \\\\ 301 \\div 13 = 23 \\text{ remainder } 2 \\\\ 301 \\div 17 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0826"}}, {"seed": 827, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0827"}}, {"seed": 828, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0828"}}, {"seed": 829, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0829"}}, {"seed": 830, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0830"}}, {"seed": 831, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0831"}}, {"seed": 832, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0832"}}, {"seed": 833, "data": {"the_number": "251", "answer": "The number 251 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a251 can divide 251. Since 13\u00b2 is less than or equal to 251 and 17\u00b2 is greater than 251, \u221a251 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 251 evenly. None of them divided 251, as evidenced by the list of quotients and remainders below. Thus, 251 is prime!", "quotients_and_remainders": "251 \\div 2 = 125 \\text{ remainder } 1 \\\\ 251 \\div 3 = 83 \\text{ remainder } 2 \\\\ 251 \\div 5 = 50 \\text{ remainder } 1 \\\\ 251 \\div 7 = 35 \\text{ remainder } 6 \\\\ 251 \\div 11 = 22 \\text{ remainder } 9 \\\\ 251 \\div 13 = 19 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0833"}}, {"seed": 834, "data": {"the_number": "167", "answer": "The number 167 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a167 can divide 167. Since 11\u00b2 is less than or equal to 167 and 13\u00b2 is greater than 167, \u221a167 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 167 evenly. None of them divided 167, as evidenced by the list of quotients and remainders below. Thus, 167 is prime!", "quotients_and_remainders": "167 \\div 2 = 83 \\text{ remainder } 1 \\\\ 167 \\div 3 = 55 \\text{ remainder } 2 \\\\ 167 \\div 5 = 33 \\text{ remainder } 2 \\\\ 167 \\div 7 = 23 \\text{ remainder } 6 \\\\ 167 \\div 11 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0834"}}, {"seed": 835, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0835"}}, {"seed": 836, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0836"}}, {"seed": 837, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0837"}}, {"seed": 838, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0838"}}, {"seed": 839, "data": {"the_number": "173", "answer": "The number 173 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a173 can divide 173. Since 13\u00b2 is less than or equal to 173 and 17\u00b2 is greater than 173, \u221a173 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 173 evenly. None of them divided 173, as evidenced by the list of quotients and remainders below. Thus, 173 is prime!", "quotients_and_remainders": "173 \\div 2 = 86 \\text{ remainder } 1 \\\\ 173 \\div 3 = 57 \\text{ remainder } 2 \\\\ 173 \\div 5 = 34 \\text{ remainder } 3 \\\\ 173 \\div 7 = 24 \\text{ remainder } 5 \\\\ 173 \\div 11 = 15 \\text{ remainder } 8 \\\\ 173 \\div 13 = 13 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0839"}}, {"seed": 840, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0840"}}, {"seed": 841, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0841"}}, {"seed": 842, "data": {"the_number": "317", "answer": "The number 317 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a317 can divide 317. Since 17\u00b2 is less than or equal to 317 and 19\u00b2 is greater than 317, \u221a317 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 317 evenly. None of them divided 317, as evidenced by the list of quotients and remainders below. Thus, 317 is prime!", "quotients_and_remainders": "317 \\div 2 = 158 \\text{ remainder } 1 \\\\ 317 \\div 3 = 105 \\text{ remainder } 2 \\\\ 317 \\div 5 = 63 \\text{ remainder } 2 \\\\ 317 \\div 7 = 45 \\text{ remainder } 2 \\\\ 317 \\div 11 = 28 \\text{ remainder } 9 \\\\ 317 \\div 13 = 24 \\text{ remainder } 5 \\\\ 317 \\div 17 = 18 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0842"}}, {"seed": 843, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0843"}}, {"seed": 844, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0844"}}, {"seed": 845, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0845"}}, {"seed": 846, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0846"}}, {"seed": 847, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0847"}}, {"seed": 848, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0848"}}, {"seed": 849, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0849"}}, {"seed": 850, "data": {"the_number": "119", "answer": "The number 119 is composite. We already know that 119 has two divisors: 1 and 119. When testing the primes from 2 to 7 (our cutoff point), we found that 7 \u00d7 17 = 17, so 7 is a factor of 119. Thus 119 has at least three divisors (1, 7, and 119), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "119 \\div 2 = 59 \\text{ remainder } 1 \\\\ 119 \\div 3 = 39 \\text{ remainder } 2 \\\\ 119 \\div 5 = 23 \\text{ remainder } 4 \\\\ 119 \\div 7 = 17 \\\\ ", "prime_problem": false, "__seed__": "0850"}}, {"seed": 851, "data": {"the_number": "401", "answer": "The number 401 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a401 can divide 401. Since 19\u00b2 is less than or equal to 401 and 23\u00b2 is greater than 401, \u221a401 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 401 evenly. None of them divided 401, as evidenced by the list of quotients and remainders below. Thus, 401 is prime!", "quotients_and_remainders": "401 \\div 2 = 200 \\text{ remainder } 1 \\\\ 401 \\div 3 = 133 \\text{ remainder } 2 \\\\ 401 \\div 5 = 80 \\text{ remainder } 1 \\\\ 401 \\div 7 = 57 \\text{ remainder } 2 \\\\ 401 \\div 11 = 36 \\text{ remainder } 5 \\\\ 401 \\div 13 = 30 \\text{ remainder } 11 \\\\ 401 \\div 17 = 23 \\text{ remainder } 10 \\\\ 401 \\div 19 = 21 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0851"}}, {"seed": 852, "data": {"the_number": "517", "answer": "The number 517 is composite. We already know that 517 has two divisors: 1 and 517. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 27 = 47, so 11 is a factor of 517. Thus 517 has at least three divisors (1, 11, and 517), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "517 \\div 2 = 258 \\text{ remainder } 1 \\\\ 517 \\div 3 = 172 \\text{ remainder } 1 \\\\ 517 \\div 5 = 103 \\text{ remainder } 2 \\\\ 517 \\div 7 = 73 \\text{ remainder } 6 \\\\ 517 \\div 11 = 47 \\\\ 517 \\div 13 = 39 \\text{ remainder } 10 \\\\ 517 \\div 17 = 30 \\text{ remainder } 7 \\\\ 517 \\div 19 = 27 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0852"}}, {"seed": 853, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0853"}}, {"seed": 854, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0854"}}, {"seed": 855, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0855"}}, {"seed": 856, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0856"}}, {"seed": 857, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0857"}}, {"seed": 858, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0858"}}, {"seed": 859, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0859"}}, {"seed": 860, "data": {"the_number": "481", "answer": "The number 481 is composite. We already know that 481 has two divisors: 1 and 481. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 25 = 37, so 13 is a factor of 481. Thus 481 has at least three divisors (1, 13, and 481), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "481 \\div 2 = 240 \\text{ remainder } 1 \\\\ 481 \\div 3 = 160 \\text{ remainder } 1 \\\\ 481 \\div 5 = 96 \\text{ remainder } 1 \\\\ 481 \\div 7 = 68 \\text{ remainder } 5 \\\\ 481 \\div 11 = 43 \\text{ remainder } 8 \\\\ 481 \\div 13 = 37 \\\\ 481 \\div 17 = 28 \\text{ remainder } 5 \\\\ 481 \\div 19 = 25 \\text{ remainder } 6 \\\\ ", "prime_problem": false, "__seed__": "0860"}}, {"seed": 861, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0861"}}, {"seed": 862, "data": {"the_number": "161", "answer": "The number 161 is composite. We already know that 161 has two divisors: 1 and 161. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 14 = 23, so 7 is a factor of 161. Thus 161 has at least three divisors (1, 7, and 161), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "161 \\div 2 = 80 \\text{ remainder } 1 \\\\ 161 \\div 3 = 53 \\text{ remainder } 2 \\\\ 161 \\div 5 = 32 \\text{ remainder } 1 \\\\ 161 \\div 7 = 23 \\\\ 161 \\div 11 = 14 \\text{ remainder } 7 \\\\ ", "prime_problem": false, "__seed__": "0862"}}, {"seed": 863, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0863"}}, {"seed": 864, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0864"}}, {"seed": 865, "data": {"the_number": "509", "answer": "The number 509 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a509 can divide 509. Since 19\u00b2 is less than or equal to 509 and 23\u00b2 is greater than 509, \u221a509 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 509 evenly. None of them divided 509, as evidenced by the list of quotients and remainders below. Thus, 509 is prime!", "quotients_and_remainders": "509 \\div 2 = 254 \\text{ remainder } 1 \\\\ 509 \\div 3 = 169 \\text{ remainder } 2 \\\\ 509 \\div 5 = 101 \\text{ remainder } 4 \\\\ 509 \\div 7 = 72 \\text{ remainder } 5 \\\\ 509 \\div 11 = 46 \\text{ remainder } 3 \\\\ 509 \\div 13 = 39 \\text{ remainder } 2 \\\\ 509 \\div 17 = 29 \\text{ remainder } 16 \\\\ 509 \\div 19 = 26 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0865"}}, {"seed": 866, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0866"}}, {"seed": 867, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0867"}}, {"seed": 868, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0868"}}, {"seed": 869, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0869"}}, {"seed": 870, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0870"}}, {"seed": 871, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0871"}}, {"seed": 872, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0872"}}, {"seed": 873, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0873"}}, {"seed": 874, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0874"}}, {"seed": 875, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0875"}}, {"seed": 876, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0876"}}, {"seed": 877, "data": {"the_number": "247", "answer": "The number 247 is composite. We already know that 247 has two divisors: 1 and 247. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 19 = 19, so 13 is a factor of 247. Thus 247 has at least three divisors (1, 13, and 247), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "247 \\div 2 = 123 \\text{ remainder } 1 \\\\ 247 \\div 3 = 82 \\text{ remainder } 1 \\\\ 247 \\div 5 = 49 \\text{ remainder } 2 \\\\ 247 \\div 7 = 35 \\text{ remainder } 2 \\\\ 247 \\div 11 = 22 \\text{ remainder } 5 \\\\ 247 \\div 13 = 19 \\\\ ", "prime_problem": false, "__seed__": "0877"}}, {"seed": 878, "data": {"the_number": "433", "answer": "The number 433 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a433 can divide 433. Since 19\u00b2 is less than or equal to 433 and 23\u00b2 is greater than 433, \u221a433 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 433 evenly. None of them divided 433, as evidenced by the list of quotients and remainders below. Thus, 433 is prime!", "quotients_and_remainders": "433 \\div 2 = 216 \\text{ remainder } 1 \\\\ 433 \\div 3 = 144 \\text{ remainder } 1 \\\\ 433 \\div 5 = 86 \\text{ remainder } 3 \\\\ 433 \\div 7 = 61 \\text{ remainder } 6 \\\\ 433 \\div 11 = 39 \\text{ remainder } 4 \\\\ 433 \\div 13 = 33 \\text{ remainder } 4 \\\\ 433 \\div 17 = 25 \\text{ remainder } 8 \\\\ 433 \\div 19 = 22 \\text{ remainder } 15 \\\\ ", "prime_problem": true, "__seed__": "0878"}}, {"seed": 879, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0879"}}, {"seed": 880, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0880"}}, {"seed": 881, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0881"}}, {"seed": 882, "data": {"the_number": "523", "answer": "The number 523 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a523 can divide 523. Since 19\u00b2 is less than or equal to 523 and 23\u00b2 is greater than 523, \u221a523 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 523 evenly. None of them divided 523, as evidenced by the list of quotients and remainders below. Thus, 523 is prime!", "quotients_and_remainders": "523 \\div 2 = 261 \\text{ remainder } 1 \\\\ 523 \\div 3 = 174 \\text{ remainder } 1 \\\\ 523 \\div 5 = 104 \\text{ remainder } 3 \\\\ 523 \\div 7 = 74 \\text{ remainder } 5 \\\\ 523 \\div 11 = 47 \\text{ remainder } 6 \\\\ 523 \\div 13 = 40 \\text{ remainder } 3 \\\\ 523 \\div 17 = 30 \\text{ remainder } 13 \\\\ 523 \\div 19 = 27 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0882"}}, {"seed": 883, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0883"}}, {"seed": 884, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0884"}}, {"seed": 885, "data": {"the_number": "143", "answer": "The number 143 is composite. We already know that 143 has two divisors: 1 and 143. When testing the primes from 2 to 11 (our cutoff point), we found that 11 \u00d7 13 = 13, so 11 is a factor of 143. Thus 143 has at least three divisors (1, 11, and 143), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "143 \\div 2 = 71 \\text{ remainder } 1 \\\\ 143 \\div 3 = 47 \\text{ remainder } 2 \\\\ 143 \\div 5 = 28 \\text{ remainder } 3 \\\\ 143 \\div 7 = 20 \\text{ remainder } 3 \\\\ 143 \\div 11 = 13 \\\\ ", "prime_problem": false, "__seed__": "0885"}}, {"seed": 886, "data": {"the_number": "511", "answer": "The number 511 is composite. We already know that 511 has two divisors: 1 and 511. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 26 = 73, so 7 is a factor of 511. Thus 511 has at least three divisors (1, 7, and 511), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "511 \\div 2 = 255 \\text{ remainder } 1 \\\\ 511 \\div 3 = 170 \\text{ remainder } 1 \\\\ 511 \\div 5 = 102 \\text{ remainder } 1 \\\\ 511 \\div 7 = 73 \\\\ 511 \\div 11 = 46 \\text{ remainder } 5 \\\\ 511 \\div 13 = 39 \\text{ remainder } 4 \\\\ 511 \\div 17 = 30 \\text{ remainder } 1 \\\\ 511 \\div 19 = 26 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0886"}}, {"seed": 887, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0887"}}, {"seed": 888, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0888"}}, {"seed": 889, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0889"}}, {"seed": 890, "data": {"the_number": "413", "answer": "The number 413 is composite. We already know that 413 has two divisors: 1 and 413. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 21 = 59, so 7 is a factor of 413. Thus 413 has at least three divisors (1, 7, and 413), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "413 \\div 2 = 206 \\text{ remainder } 1 \\\\ 413 \\div 3 = 137 \\text{ remainder } 2 \\\\ 413 \\div 5 = 82 \\text{ remainder } 3 \\\\ 413 \\div 7 = 59 \\\\ 413 \\div 11 = 37 \\text{ remainder } 6 \\\\ 413 \\div 13 = 31 \\text{ remainder } 10 \\\\ 413 \\div 17 = 24 \\text{ remainder } 5 \\\\ 413 \\div 19 = 21 \\text{ remainder } 14 \\\\ ", "prime_problem": false, "__seed__": "0890"}}, {"seed": 891, "data": {"the_number": "341", "answer": "The number 341 is composite. We already know that 341 has two divisors: 1 and 341. When testing the primes from 2 to 17 (our cutoff point), we found that 11 \u00d7 20 = 31, so 11 is a factor of 341. Thus 341 has at least three divisors (1, 11, and 341), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "341 \\div 2 = 170 \\text{ remainder } 1 \\\\ 341 \\div 3 = 113 \\text{ remainder } 2 \\\\ 341 \\div 5 = 68 \\text{ remainder } 1 \\\\ 341 \\div 7 = 48 \\text{ remainder } 5 \\\\ 341 \\div 11 = 31 \\\\ 341 \\div 13 = 26 \\text{ remainder } 3 \\\\ 341 \\div 17 = 20 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0891"}}, {"seed": 892, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0892"}}, {"seed": 893, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0893"}}, {"seed": 894, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0894"}}, {"seed": 895, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0895"}}, {"seed": 896, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0896"}}, {"seed": 897, "data": {"the_number": "377", "answer": "The number 377 is composite. We already know that 377 has two divisors: 1 and 377. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 19 = 29, so 13 is a factor of 377. Thus 377 has at least three divisors (1, 13, and 377), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "377 \\div 2 = 188 \\text{ remainder } 1 \\\\ 377 \\div 3 = 125 \\text{ remainder } 2 \\\\ 377 \\div 5 = 75 \\text{ remainder } 2 \\\\ 377 \\div 7 = 53 \\text{ remainder } 6 \\\\ 377 \\div 11 = 34 \\text{ remainder } 3 \\\\ 377 \\div 13 = 29 \\\\ 377 \\div 17 = 22 \\text{ remainder } 3 \\\\ 377 \\div 19 = 19 \\text{ remainder } 16 \\\\ ", "prime_problem": false, "__seed__": "0897"}}, {"seed": 898, "data": {"the_number": "211", "answer": "The number 211 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a211 can divide 211. Since 13\u00b2 is less than or equal to 211 and 17\u00b2 is greater than 211, \u221a211 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 211 evenly. None of them divided 211, as evidenced by the list of quotients and remainders below. Thus, 211 is prime!", "quotients_and_remainders": "211 \\div 2 = 105 \\text{ remainder } 1 \\\\ 211 \\div 3 = 70 \\text{ remainder } 1 \\\\ 211 \\div 5 = 42 \\text{ remainder } 1 \\\\ 211 \\div 7 = 30 \\text{ remainder } 1 \\\\ 211 \\div 11 = 19 \\text{ remainder } 2 \\\\ 211 \\div 13 = 16 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0898"}}, {"seed": 899, "data": {"the_number": "149", "answer": "The number 149 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a149 can divide 149. Since 11\u00b2 is less than or equal to 149 and 13\u00b2 is greater than 149, \u221a149 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 149 evenly. None of them divided 149, as evidenced by the list of quotients and remainders below. Thus, 149 is prime!", "quotients_and_remainders": "149 \\div 2 = 74 \\text{ remainder } 1 \\\\ 149 \\div 3 = 49 \\text{ remainder } 2 \\\\ 149 \\div 5 = 29 \\text{ remainder } 4 \\\\ 149 \\div 7 = 21 \\text{ remainder } 2 \\\\ 149 \\div 11 = 13 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0899"}}, {"seed": 900, "data": {"the_number": "491", "answer": "The number 491 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a491 can divide 491. Since 19\u00b2 is less than or equal to 491 and 23\u00b2 is greater than 491, \u221a491 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 491 evenly. None of them divided 491, as evidenced by the list of quotients and remainders below. Thus, 491 is prime!", "quotients_and_remainders": "491 \\div 2 = 245 \\text{ remainder } 1 \\\\ 491 \\div 3 = 163 \\text{ remainder } 2 \\\\ 491 \\div 5 = 98 \\text{ remainder } 1 \\\\ 491 \\div 7 = 70 \\text{ remainder } 1 \\\\ 491 \\div 11 = 44 \\text{ remainder } 7 \\\\ 491 \\div 13 = 37 \\text{ remainder } 10 \\\\ 491 \\div 17 = 28 \\text{ remainder } 15 \\\\ 491 \\div 19 = 25 \\text{ remainder } 16 \\\\ ", "prime_problem": true, "__seed__": "0900"}}, {"seed": 901, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0901"}}, {"seed": 902, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0902"}}, {"seed": 903, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0903"}}, {"seed": 904, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0904"}}, {"seed": 905, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0905"}}, {"seed": 906, "data": {"the_number": "431", "answer": "The number 431 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a431 can divide 431. Since 19\u00b2 is less than or equal to 431 and 23\u00b2 is greater than 431, \u221a431 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 431 evenly. None of them divided 431, as evidenced by the list of quotients and remainders below. Thus, 431 is prime!", "quotients_and_remainders": "431 \\div 2 = 215 \\text{ remainder } 1 \\\\ 431 \\div 3 = 143 \\text{ remainder } 2 \\\\ 431 \\div 5 = 86 \\text{ remainder } 1 \\\\ 431 \\div 7 = 61 \\text{ remainder } 4 \\\\ 431 \\div 11 = 39 \\text{ remainder } 2 \\\\ 431 \\div 13 = 33 \\text{ remainder } 2 \\\\ 431 \\div 17 = 25 \\text{ remainder } 6 \\\\ 431 \\div 19 = 22 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0906"}}, {"seed": 907, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0907"}}, {"seed": 908, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0908"}}, {"seed": 909, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0909"}}, {"seed": 910, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0910"}}, {"seed": 911, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0911"}}, {"seed": 912, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0912"}}, {"seed": 913, "data": {"the_number": "227", "answer": "The number 227 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a227 can divide 227. Since 13\u00b2 is less than or equal to 227 and 17\u00b2 is greater than 227, \u221a227 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 227 evenly. None of them divided 227, as evidenced by the list of quotients and remainders below. Thus, 227 is prime!", "quotients_and_remainders": "227 \\div 2 = 113 \\text{ remainder } 1 \\\\ 227 \\div 3 = 75 \\text{ remainder } 2 \\\\ 227 \\div 5 = 45 \\text{ remainder } 2 \\\\ 227 \\div 7 = 32 \\text{ remainder } 3 \\\\ 227 \\div 11 = 20 \\text{ remainder } 7 \\\\ 227 \\div 13 = 17 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0913"}}, {"seed": 914, "data": {"the_number": "367", "answer": "The number 367 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a367 can divide 367. Since 19\u00b2 is less than or equal to 367 and 23\u00b2 is greater than 367, \u221a367 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 367 evenly. None of them divided 367, as evidenced by the list of quotients and remainders below. Thus, 367 is prime!", "quotients_and_remainders": "367 \\div 2 = 183 \\text{ remainder } 1 \\\\ 367 \\div 3 = 122 \\text{ remainder } 1 \\\\ 367 \\div 5 = 73 \\text{ remainder } 2 \\\\ 367 \\div 7 = 52 \\text{ remainder } 3 \\\\ 367 \\div 11 = 33 \\text{ remainder } 4 \\\\ 367 \\div 13 = 28 \\text{ remainder } 3 \\\\ 367 \\div 17 = 21 \\text{ remainder } 10 \\\\ 367 \\div 19 = 19 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0914"}}, {"seed": 915, "data": {"the_number": "221", "answer": "The number 221 is composite. We already know that 221 has two divisors: 1 and 221. When testing the primes from 2 to 13 (our cutoff point), we found that 13 \u00d7 17 = 17, so 13 is a factor of 221. Thus 221 has at least three divisors (1, 13, and 221), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "221 \\div 2 = 110 \\text{ remainder } 1 \\\\ 221 \\div 3 = 73 \\text{ remainder } 2 \\\\ 221 \\div 5 = 44 \\text{ remainder } 1 \\\\ 221 \\div 7 = 31 \\text{ remainder } 4 \\\\ 221 \\div 11 = 20 \\text{ remainder } 1 \\\\ 221 \\div 13 = 17 \\\\ ", "prime_problem": false, "__seed__": "0915"}}, {"seed": 916, "data": {"the_number": "437", "answer": "The number 437 is composite. We already know that 437 has two divisors: 1 and 437. When testing the primes from 2 to 19 (our cutoff point), we found that 19 \u00d7 23 = 23, so 19 is a factor of 437. Thus 437 has at least three divisors (1, 19, and 437), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "437 \\div 2 = 218 \\text{ remainder } 1 \\\\ 437 \\div 3 = 145 \\text{ remainder } 2 \\\\ 437 \\div 5 = 87 \\text{ remainder } 2 \\\\ 437 \\div 7 = 62 \\text{ remainder } 3 \\\\ 437 \\div 11 = 39 \\text{ remainder } 8 \\\\ 437 \\div 13 = 33 \\text{ remainder } 8 \\\\ 437 \\div 17 = 25 \\text{ remainder } 12 \\\\ 437 \\div 19 = 23 \\\\ ", "prime_problem": false, "__seed__": "0916"}}, {"seed": 917, "data": {"the_number": "337", "answer": "The number 337 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a337 can divide 337. Since 17\u00b2 is less than or equal to 337 and 19\u00b2 is greater than 337, \u221a337 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 337 evenly. None of them divided 337, as evidenced by the list of quotients and remainders below. Thus, 337 is prime!", "quotients_and_remainders": "337 \\div 2 = 168 \\text{ remainder } 1 \\\\ 337 \\div 3 = 112 \\text{ remainder } 1 \\\\ 337 \\div 5 = 67 \\text{ remainder } 2 \\\\ 337 \\div 7 = 48 \\text{ remainder } 1 \\\\ 337 \\div 11 = 30 \\text{ remainder } 7 \\\\ 337 \\div 13 = 25 \\text{ remainder } 12 \\\\ 337 \\div 17 = 19 \\text{ remainder } 14 \\\\ ", "prime_problem": true, "__seed__": "0917"}}, {"seed": 918, "data": {"the_number": "241", "answer": "The number 241 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a241 can divide 241. Since 13\u00b2 is less than or equal to 241 and 17\u00b2 is greater than 241, \u221a241 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 241 evenly. None of them divided 241, as evidenced by the list of quotients and remainders below. Thus, 241 is prime!", "quotients_and_remainders": "241 \\div 2 = 120 \\text{ remainder } 1 \\\\ 241 \\div 3 = 80 \\text{ remainder } 1 \\\\ 241 \\div 5 = 48 \\text{ remainder } 1 \\\\ 241 \\div 7 = 34 \\text{ remainder } 3 \\\\ 241 \\div 11 = 21 \\text{ remainder } 10 \\\\ 241 \\div 13 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0918"}}, {"seed": 919, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0919"}}, {"seed": 920, "data": {"the_number": "131", "answer": "The number 131 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a131 can divide 131. Since 11\u00b2 is less than or equal to 131 and 13\u00b2 is greater than 131, \u221a131 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 131 evenly. None of them divided 131, as evidenced by the list of quotients and remainders below. Thus, 131 is prime!", "quotients_and_remainders": "131 \\div 2 = 65 \\text{ remainder } 1 \\\\ 131 \\div 3 = 43 \\text{ remainder } 2 \\\\ 131 \\div 5 = 26 \\text{ remainder } 1 \\\\ 131 \\div 7 = 18 \\text{ remainder } 5 \\\\ 131 \\div 11 = 11 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0920"}}, {"seed": 921, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0921"}}, {"seed": 922, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0922"}}, {"seed": 923, "data": {"the_number": "269", "answer": "The number 269 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a269 can divide 269. Since 13\u00b2 is less than or equal to 269 and 17\u00b2 is greater than 269, \u221a269 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 269 evenly. None of them divided 269, as evidenced by the list of quotients and remainders below. Thus, 269 is prime!", "quotients_and_remainders": "269 \\div 2 = 134 \\text{ remainder } 1 \\\\ 269 \\div 3 = 89 \\text{ remainder } 2 \\\\ 269 \\div 5 = 53 \\text{ remainder } 4 \\\\ 269 \\div 7 = 38 \\text{ remainder } 3 \\\\ 269 \\div 11 = 24 \\text{ remainder } 5 \\\\ 269 \\div 13 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0923"}}, {"seed": 924, "data": {"the_number": "419", "answer": "The number 419 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a419 can divide 419. Since 19\u00b2 is less than or equal to 419 and 23\u00b2 is greater than 419, \u221a419 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 419 evenly. None of them divided 419, as evidenced by the list of quotients and remainders below. Thus, 419 is prime!", "quotients_and_remainders": "419 \\div 2 = 209 \\text{ remainder } 1 \\\\ 419 \\div 3 = 139 \\text{ remainder } 2 \\\\ 419 \\div 5 = 83 \\text{ remainder } 4 \\\\ 419 \\div 7 = 59 \\text{ remainder } 6 \\\\ 419 \\div 11 = 38 \\text{ remainder } 1 \\\\ 419 \\div 13 = 32 \\text{ remainder } 3 \\\\ 419 \\div 17 = 24 \\text{ remainder } 11 \\\\ 419 \\div 19 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0924"}}, {"seed": 925, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0925"}}, {"seed": 926, "data": {"the_number": "409", "answer": "The number 409 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a409 can divide 409. Since 19\u00b2 is less than or equal to 409 and 23\u00b2 is greater than 409, \u221a409 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 409 evenly. None of them divided 409, as evidenced by the list of quotients and remainders below. Thus, 409 is prime!", "quotients_and_remainders": "409 \\div 2 = 204 \\text{ remainder } 1 \\\\ 409 \\div 3 = 136 \\text{ remainder } 1 \\\\ 409 \\div 5 = 81 \\text{ remainder } 4 \\\\ 409 \\div 7 = 58 \\text{ remainder } 3 \\\\ 409 \\div 11 = 37 \\text{ remainder } 2 \\\\ 409 \\div 13 = 31 \\text{ remainder } 6 \\\\ 409 \\div 17 = 24 \\text{ remainder } 1 \\\\ 409 \\div 19 = 21 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0926"}}, {"seed": 927, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0927"}}, {"seed": 928, "data": {"the_number": "467", "answer": "The number 467 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a467 can divide 467. Since 19\u00b2 is less than or equal to 467 and 23\u00b2 is greater than 467, \u221a467 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 467 evenly. None of them divided 467, as evidenced by the list of quotients and remainders below. Thus, 467 is prime!", "quotients_and_remainders": "467 \\div 2 = 233 \\text{ remainder } 1 \\\\ 467 \\div 3 = 155 \\text{ remainder } 2 \\\\ 467 \\div 5 = 93 \\text{ remainder } 2 \\\\ 467 \\div 7 = 66 \\text{ remainder } 5 \\\\ 467 \\div 11 = 42 \\text{ remainder } 5 \\\\ 467 \\div 13 = 35 \\text{ remainder } 12 \\\\ 467 \\div 17 = 27 \\text{ remainder } 8 \\\\ 467 \\div 19 = 24 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0928"}}, {"seed": 929, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0929"}}, {"seed": 930, "data": {"the_number": "457", "answer": "The number 457 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a457 can divide 457. Since 19\u00b2 is less than or equal to 457 and 23\u00b2 is greater than 457, \u221a457 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 457 evenly. None of them divided 457, as evidenced by the list of quotients and remainders below. Thus, 457 is prime!", "quotients_and_remainders": "457 \\div 2 = 228 \\text{ remainder } 1 \\\\ 457 \\div 3 = 152 \\text{ remainder } 1 \\\\ 457 \\div 5 = 91 \\text{ remainder } 2 \\\\ 457 \\div 7 = 65 \\text{ remainder } 2 \\\\ 457 \\div 11 = 41 \\text{ remainder } 6 \\\\ 457 \\div 13 = 35 \\text{ remainder } 2 \\\\ 457 \\div 17 = 26 \\text{ remainder } 15 \\\\ 457 \\div 19 = 24 \\text{ remainder } 1 \\\\ ", "prime_problem": true, "__seed__": "0930"}}, {"seed": 931, "data": {"the_number": "379", "answer": "The number 379 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a379 can divide 379. Since 19\u00b2 is less than or equal to 379 and 23\u00b2 is greater than 379, \u221a379 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 379 evenly. None of them divided 379, as evidenced by the list of quotients and remainders below. Thus, 379 is prime!", "quotients_and_remainders": "379 \\div 2 = 189 \\text{ remainder } 1 \\\\ 379 \\div 3 = 126 \\text{ remainder } 1 \\\\ 379 \\div 5 = 75 \\text{ remainder } 4 \\\\ 379 \\div 7 = 54 \\text{ remainder } 1 \\\\ 379 \\div 11 = 34 \\text{ remainder } 5 \\\\ 379 \\div 13 = 29 \\text{ remainder } 2 \\\\ 379 \\div 17 = 22 \\text{ remainder } 5 \\\\ 379 \\div 19 = 19 \\text{ remainder } 18 \\\\ ", "prime_problem": true, "__seed__": "0931"}}, {"seed": 932, "data": {"the_number": "137", "answer": "The number 137 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a137 can divide 137. Since 11\u00b2 is less than or equal to 137 and 13\u00b2 is greater than 137, \u221a137 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 137 evenly. None of them divided 137, as evidenced by the list of quotients and remainders below. Thus, 137 is prime!", "quotients_and_remainders": "137 \\div 2 = 68 \\text{ remainder } 1 \\\\ 137 \\div 3 = 45 \\text{ remainder } 2 \\\\ 137 \\div 5 = 27 \\text{ remainder } 2 \\\\ 137 \\div 7 = 19 \\text{ remainder } 4 \\\\ 137 \\div 11 = 12 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0932"}}, {"seed": 933, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0933"}}, {"seed": 934, "data": {"the_number": "311", "answer": "The number 311 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a311 can divide 311. Since 17\u00b2 is less than or equal to 311 and 19\u00b2 is greater than 311, \u221a311 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 311 evenly. None of them divided 311, as evidenced by the list of quotients and remainders below. Thus, 311 is prime!", "quotients_and_remainders": "311 \\div 2 = 155 \\text{ remainder } 1 \\\\ 311 \\div 3 = 103 \\text{ remainder } 2 \\\\ 311 \\div 5 = 62 \\text{ remainder } 1 \\\\ 311 \\div 7 = 44 \\text{ remainder } 3 \\\\ 311 \\div 11 = 28 \\text{ remainder } 3 \\\\ 311 \\div 13 = 23 \\text{ remainder } 12 \\\\ 311 \\div 17 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0934"}}, {"seed": 935, "data": {"the_number": "259", "answer": "The number 259 is composite. We already know that 259 has two divisors: 1 and 259. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 19 = 37, so 7 is a factor of 259. Thus 259 has at least three divisors (1, 7, and 259), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "259 \\div 2 = 129 \\text{ remainder } 1 \\\\ 259 \\div 3 = 86 \\text{ remainder } 1 \\\\ 259 \\div 5 = 51 \\text{ remainder } 4 \\\\ 259 \\div 7 = 37 \\\\ 259 \\div 11 = 23 \\text{ remainder } 6 \\\\ 259 \\div 13 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": false, "__seed__": "0935"}}, {"seed": 936, "data": {"the_number": "421", "answer": "The number 421 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a421 can divide 421. Since 19\u00b2 is less than or equal to 421 and 23\u00b2 is greater than 421, \u221a421 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 421 evenly. None of them divided 421, as evidenced by the list of quotients and remainders below. Thus, 421 is prime!", "quotients_and_remainders": "421 \\div 2 = 210 \\text{ remainder } 1 \\\\ 421 \\div 3 = 140 \\text{ remainder } 1 \\\\ 421 \\div 5 = 84 \\text{ remainder } 1 \\\\ 421 \\div 7 = 60 \\text{ remainder } 1 \\\\ 421 \\div 11 = 38 \\text{ remainder } 3 \\\\ 421 \\div 13 = 32 \\text{ remainder } 5 \\\\ 421 \\div 17 = 24 \\text{ remainder } 13 \\\\ 421 \\div 19 = 22 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0936"}}, {"seed": 937, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0937"}}, {"seed": 938, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0938"}}, {"seed": 939, "data": {"the_number": "487", "answer": "The number 487 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a487 can divide 487. Since 19\u00b2 is less than or equal to 487 and 23\u00b2 is greater than 487, \u221a487 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 487 evenly. None of them divided 487, as evidenced by the list of quotients and remainders below. Thus, 487 is prime!", "quotients_and_remainders": "487 \\div 2 = 243 \\text{ remainder } 1 \\\\ 487 \\div 3 = 162 \\text{ remainder } 1 \\\\ 487 \\div 5 = 97 \\text{ remainder } 2 \\\\ 487 \\div 7 = 69 \\text{ remainder } 4 \\\\ 487 \\div 11 = 44 \\text{ remainder } 3 \\\\ 487 \\div 13 = 37 \\text{ remainder } 6 \\\\ 487 \\div 17 = 28 \\text{ remainder } 11 \\\\ 487 \\div 19 = 25 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0939"}}, {"seed": 940, "data": {"the_number": "179", "answer": "The number 179 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a179 can divide 179. Since 13\u00b2 is less than or equal to 179 and 17\u00b2 is greater than 179, \u221a179 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 179 evenly. None of them divided 179, as evidenced by the list of quotients and remainders below. Thus, 179 is prime!", "quotients_and_remainders": "179 \\div 2 = 89 \\text{ remainder } 1 \\\\ 179 \\div 3 = 59 \\text{ remainder } 2 \\\\ 179 \\div 5 = 35 \\text{ remainder } 4 \\\\ 179 \\div 7 = 25 \\text{ remainder } 4 \\\\ 179 \\div 11 = 16 \\text{ remainder } 3 \\\\ 179 \\div 13 = 13 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0940"}}, {"seed": 941, "data": {"the_number": "353", "answer": "The number 353 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a353 can divide 353. Since 17\u00b2 is less than or equal to 353 and 19\u00b2 is greater than 353, \u221a353 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 353 evenly. None of them divided 353, as evidenced by the list of quotients and remainders below. Thus, 353 is prime!", "quotients_and_remainders": "353 \\div 2 = 176 \\text{ remainder } 1 \\\\ 353 \\div 3 = 117 \\text{ remainder } 2 \\\\ 353 \\div 5 = 70 \\text{ remainder } 3 \\\\ 353 \\div 7 = 50 \\text{ remainder } 3 \\\\ 353 \\div 11 = 32 \\text{ remainder } 1 \\\\ 353 \\div 13 = 27 \\text{ remainder } 2 \\\\ 353 \\div 17 = 20 \\text{ remainder } 13 \\\\ ", "prime_problem": true, "__seed__": "0941"}}, {"seed": 942, "data": {"the_number": "349", "answer": "The number 349 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a349 can divide 349. Since 17\u00b2 is less than or equal to 349 and 19\u00b2 is greater than 349, \u221a349 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 349 evenly. None of them divided 349, as evidenced by the list of quotients and remainders below. Thus, 349 is prime!", "quotients_and_remainders": "349 \\div 2 = 174 \\text{ remainder } 1 \\\\ 349 \\div 3 = 116 \\text{ remainder } 1 \\\\ 349 \\div 5 = 69 \\text{ remainder } 4 \\\\ 349 \\div 7 = 49 \\text{ remainder } 6 \\\\ 349 \\div 11 = 31 \\text{ remainder } 8 \\\\ 349 \\div 13 = 26 \\text{ remainder } 11 \\\\ 349 \\div 17 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0942"}}, {"seed": 943, "data": {"the_number": "403", "answer": "The number 403 is composite. We already know that 403 has two divisors: 1 and 403. When testing the primes from 2 to 19 (our cutoff point), we found that 13 \u00d7 21 = 31, so 13 is a factor of 403. Thus 403 has at least three divisors (1, 13, and 403), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "403 \\div 2 = 201 \\text{ remainder } 1 \\\\ 403 \\div 3 = 134 \\text{ remainder } 1 \\\\ 403 \\div 5 = 80 \\text{ remainder } 3 \\\\ 403 \\div 7 = 57 \\text{ remainder } 4 \\\\ 403 \\div 11 = 36 \\text{ remainder } 7 \\\\ 403 \\div 13 = 31 \\\\ 403 \\div 17 = 23 \\text{ remainder } 12 \\\\ 403 \\div 19 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": false, "__seed__": "0943"}}, {"seed": 944, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0944"}}, {"seed": 945, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0945"}}, {"seed": 946, "data": {"the_number": "223", "answer": "The number 223 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a223 can divide 223. Since 13\u00b2 is less than or equal to 223 and 17\u00b2 is greater than 223, \u221a223 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 223 evenly. None of them divided 223, as evidenced by the list of quotients and remainders below. Thus, 223 is prime!", "quotients_and_remainders": "223 \\div 2 = 111 \\text{ remainder } 1 \\\\ 223 \\div 3 = 74 \\text{ remainder } 1 \\\\ 223 \\div 5 = 44 \\text{ remainder } 3 \\\\ 223 \\div 7 = 31 \\text{ remainder } 6 \\\\ 223 \\div 11 = 20 \\text{ remainder } 3 \\\\ 223 \\div 13 = 17 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0946"}}, {"seed": 947, "data": {"the_number": "391", "answer": "The number 391 is composite. We already know that 391 has two divisors: 1 and 391. When testing the primes from 2 to 19 (our cutoff point), we found that 17 \u00d7 20 = 23, so 17 is a factor of 391. Thus 391 has at least three divisors (1, 17, and 391), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "391 \\div 2 = 195 \\text{ remainder } 1 \\\\ 391 \\div 3 = 130 \\text{ remainder } 1 \\\\ 391 \\div 5 = 78 \\text{ remainder } 1 \\\\ 391 \\div 7 = 55 \\text{ remainder } 6 \\\\ 391 \\div 11 = 35 \\text{ remainder } 6 \\\\ 391 \\div 13 = 30 \\text{ remainder } 1 \\\\ 391 \\div 17 = 23 \\\\ 391 \\div 19 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": false, "__seed__": "0947"}}, {"seed": 948, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0948"}}, {"seed": 949, "data": {"the_number": "289", "answer": "The number 289 is composite. We already know that 289 has two divisors: 1 and 289. When testing the primes from 2 to 17 (our cutoff point), we found that 17 \u00d7 17 = 17, so 17 is a factor of 289. Thus 289 has at least three divisors (1, 17, and 289), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "289 \\div 2 = 144 \\text{ remainder } 1 \\\\ 289 \\div 3 = 96 \\text{ remainder } 1 \\\\ 289 \\div 5 = 57 \\text{ remainder } 4 \\\\ 289 \\div 7 = 41 \\text{ remainder } 2 \\\\ 289 \\div 11 = 26 \\text{ remainder } 3 \\\\ 289 \\div 13 = 22 \\text{ remainder } 3 \\\\ 289 \\div 17 = 17 \\\\ ", "prime_problem": false, "__seed__": "0949"}}, {"seed": 950, "data": {"the_number": "281", "answer": "The number 281 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a281 can divide 281. Since 13\u00b2 is less than or equal to 281 and 17\u00b2 is greater than 281, \u221a281 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 281 evenly. None of them divided 281, as evidenced by the list of quotients and remainders below. Thus, 281 is prime!", "quotients_and_remainders": "281 \\div 2 = 140 \\text{ remainder } 1 \\\\ 281 \\div 3 = 93 \\text{ remainder } 2 \\\\ 281 \\div 5 = 56 \\text{ remainder } 1 \\\\ 281 \\div 7 = 40 \\text{ remainder } 1 \\\\ 281 \\div 11 = 25 \\text{ remainder } 6 \\\\ 281 \\div 13 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0950"}}, {"seed": 951, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0951"}}, {"seed": 952, "data": {"the_number": "263", "answer": "The number 263 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a263 can divide 263. Since 13\u00b2 is less than or equal to 263 and 17\u00b2 is greater than 263, \u221a263 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 263 evenly. None of them divided 263, as evidenced by the list of quotients and remainders below. Thus, 263 is prime!", "quotients_and_remainders": "263 \\div 2 = 131 \\text{ remainder } 1 \\\\ 263 \\div 3 = 87 \\text{ remainder } 2 \\\\ 263 \\div 5 = 52 \\text{ remainder } 3 \\\\ 263 \\div 7 = 37 \\text{ remainder } 4 \\\\ 263 \\div 11 = 23 \\text{ remainder } 10 \\\\ 263 \\div 13 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0952"}}, {"seed": 953, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0953"}}, {"seed": 954, "data": {"the_number": "331", "answer": "The number 331 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a331 can divide 331. Since 17\u00b2 is less than or equal to 331 and 19\u00b2 is greater than 331, \u221a331 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 331 evenly. None of them divided 331, as evidenced by the list of quotients and remainders below. Thus, 331 is prime!", "quotients_and_remainders": "331 \\div 2 = 165 \\text{ remainder } 1 \\\\ 331 \\div 3 = 110 \\text{ remainder } 1 \\\\ 331 \\div 5 = 66 \\text{ remainder } 1 \\\\ 331 \\div 7 = 47 \\text{ remainder } 2 \\\\ 331 \\div 11 = 30 \\text{ remainder } 1 \\\\ 331 \\div 13 = 25 \\text{ remainder } 6 \\\\ 331 \\div 17 = 19 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0954"}}, {"seed": 955, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0955"}}, {"seed": 956, "data": {"the_number": "217", "answer": "The number 217 is composite. We already know that 217 has two divisors: 1 and 217. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 16 = 31, so 7 is a factor of 217. Thus 217 has at least three divisors (1, 7, and 217), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "217 \\div 2 = 108 \\text{ remainder } 1 \\\\ 217 \\div 3 = 72 \\text{ remainder } 1 \\\\ 217 \\div 5 = 43 \\text{ remainder } 2 \\\\ 217 \\div 7 = 31 \\\\ 217 \\div 11 = 19 \\text{ remainder } 8 \\\\ 217 \\div 13 = 16 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0956"}}, {"seed": 957, "data": {"the_number": "229", "answer": "The number 229 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a229 can divide 229. Since 13\u00b2 is less than or equal to 229 and 17\u00b2 is greater than 229, \u221a229 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 229 evenly. None of them divided 229, as evidenced by the list of quotients and remainders below. Thus, 229 is prime!", "quotients_and_remainders": "229 \\div 2 = 114 \\text{ remainder } 1 \\\\ 229 \\div 3 = 76 \\text{ remainder } 1 \\\\ 229 \\div 5 = 45 \\text{ remainder } 4 \\\\ 229 \\div 7 = 32 \\text{ remainder } 5 \\\\ 229 \\div 11 = 20 \\text{ remainder } 9 \\\\ 229 \\div 13 = 17 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0957"}}, {"seed": 958, "data": {"the_number": "299", "answer": "The number 299 is composite. We already know that 299 has two divisors: 1 and 299. When testing the primes from 2 to 17 (our cutoff point), we found that 13 \u00d7 17 = 23, so 13 is a factor of 299. Thus 299 has at least three divisors (1, 13, and 299), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "299 \\div 2 = 149 \\text{ remainder } 1 \\\\ 299 \\div 3 = 99 \\text{ remainder } 2 \\\\ 299 \\div 5 = 59 \\text{ remainder } 4 \\\\ 299 \\div 7 = 42 \\text{ remainder } 5 \\\\ 299 \\div 11 = 27 \\text{ remainder } 2 \\\\ 299 \\div 13 = 23 \\\\ 299 \\div 17 = 17 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0958"}}, {"seed": 959, "data": {"the_number": "371", "answer": "The number 371 is composite. We already know that 371 has two divisors: 1 and 371. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 19 = 53, so 7 is a factor of 371. Thus 371 has at least three divisors (1, 7, and 371), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "371 \\div 2 = 185 \\text{ remainder } 1 \\\\ 371 \\div 3 = 123 \\text{ remainder } 2 \\\\ 371 \\div 5 = 74 \\text{ remainder } 1 \\\\ 371 \\div 7 = 53 \\\\ 371 \\div 11 = 33 \\text{ remainder } 8 \\\\ 371 \\div 13 = 28 \\text{ remainder } 7 \\\\ 371 \\div 17 = 21 \\text{ remainder } 14 \\\\ 371 \\div 19 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": false, "__seed__": "0959"}}, {"seed": 960, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0960"}}, {"seed": 961, "data": {"the_number": "181", "answer": "The number 181 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a181 can divide 181. Since 13\u00b2 is less than or equal to 181 and 17\u00b2 is greater than 181, \u221a181 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 181 evenly. None of them divided 181, as evidenced by the list of quotients and remainders below. Thus, 181 is prime!", "quotients_and_remainders": "181 \\div 2 = 90 \\text{ remainder } 1 \\\\ 181 \\div 3 = 60 \\text{ remainder } 1 \\\\ 181 \\div 5 = 36 \\text{ remainder } 1 \\\\ 181 \\div 7 = 25 \\text{ remainder } 6 \\\\ 181 \\div 11 = 16 \\text{ remainder } 5 \\\\ 181 \\div 13 = 13 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0961"}}, {"seed": 962, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0962"}}, {"seed": 963, "data": {"the_number": "439", "answer": "The number 439 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a439 can divide 439. Since 19\u00b2 is less than or equal to 439 and 23\u00b2 is greater than 439, \u221a439 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 439 evenly. None of them divided 439, as evidenced by the list of quotients and remainders below. Thus, 439 is prime!", "quotients_and_remainders": "439 \\div 2 = 219 \\text{ remainder } 1 \\\\ 439 \\div 3 = 146 \\text{ remainder } 1 \\\\ 439 \\div 5 = 87 \\text{ remainder } 4 \\\\ 439 \\div 7 = 62 \\text{ remainder } 5 \\\\ 439 \\div 11 = 39 \\text{ remainder } 10 \\\\ 439 \\div 13 = 33 \\text{ remainder } 10 \\\\ 439 \\div 17 = 25 \\text{ remainder } 14 \\\\ 439 \\div 19 = 23 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0963"}}, {"seed": 964, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0964"}}, {"seed": 965, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0965"}}, {"seed": 966, "data": {"the_number": "383", "answer": "The number 383 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a383 can divide 383. Since 19\u00b2 is less than or equal to 383 and 23\u00b2 is greater than 383, \u221a383 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 383 evenly. None of them divided 383, as evidenced by the list of quotients and remainders below. Thus, 383 is prime!", "quotients_and_remainders": "383 \\div 2 = 191 \\text{ remainder } 1 \\\\ 383 \\div 3 = 127 \\text{ remainder } 2 \\\\ 383 \\div 5 = 76 \\text{ remainder } 3 \\\\ 383 \\div 7 = 54 \\text{ remainder } 5 \\\\ 383 \\div 11 = 34 \\text{ remainder } 9 \\\\ 383 \\div 13 = 29 \\text{ remainder } 6 \\\\ 383 \\div 17 = 22 \\text{ remainder } 9 \\\\ 383 \\div 19 = 20 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0966"}}, {"seed": 967, "data": {"the_number": "157", "answer": "The number 157 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a157 can divide 157. Since 11\u00b2 is less than or equal to 157 and 13\u00b2 is greater than 157, \u221a157 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 157 evenly. None of them divided 157, as evidenced by the list of quotients and remainders below. Thus, 157 is prime!", "quotients_and_remainders": "157 \\div 2 = 78 \\text{ remainder } 1 \\\\ 157 \\div 3 = 52 \\text{ remainder } 1 \\\\ 157 \\div 5 = 31 \\text{ remainder } 2 \\\\ 157 \\div 7 = 22 \\text{ remainder } 3 \\\\ 157 \\div 11 = 14 \\text{ remainder } 3 \\\\ ", "prime_problem": true, "__seed__": "0967"}}, {"seed": 968, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0968"}}, {"seed": 969, "data": {"the_number": "193", "answer": "The number 193 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a193 can divide 193. Since 13\u00b2 is less than or equal to 193 and 17\u00b2 is greater than 193, \u221a193 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 193 evenly. None of them divided 193, as evidenced by the list of quotients and remainders below. Thus, 193 is prime!", "quotients_and_remainders": "193 \\div 2 = 96 \\text{ remainder } 1 \\\\ 193 \\div 3 = 64 \\text{ remainder } 1 \\\\ 193 \\div 5 = 38 \\text{ remainder } 3 \\\\ 193 \\div 7 = 27 \\text{ remainder } 4 \\\\ 193 \\div 11 = 17 \\text{ remainder } 6 \\\\ 193 \\div 13 = 14 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0969"}}, {"seed": 970, "data": {"the_number": "461", "answer": "The number 461 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a461 can divide 461. Since 19\u00b2 is less than or equal to 461 and 23\u00b2 is greater than 461, \u221a461 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 461 evenly. None of them divided 461, as evidenced by the list of quotients and remainders below. Thus, 461 is prime!", "quotients_and_remainders": "461 \\div 2 = 230 \\text{ remainder } 1 \\\\ 461 \\div 3 = 153 \\text{ remainder } 2 \\\\ 461 \\div 5 = 92 \\text{ remainder } 1 \\\\ 461 \\div 7 = 65 \\text{ remainder } 6 \\\\ 461 \\div 11 = 41 \\text{ remainder } 10 \\\\ 461 \\div 13 = 35 \\text{ remainder } 6 \\\\ 461 \\div 17 = 27 \\text{ remainder } 2 \\\\ 461 \\div 19 = 24 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0970"}}, {"seed": 971, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0971"}}, {"seed": 972, "data": {"the_number": "233", "answer": "The number 233 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a233 can divide 233. Since 13\u00b2 is less than or equal to 233 and 17\u00b2 is greater than 233, \u221a233 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 233 evenly. None of them divided 233, as evidenced by the list of quotients and remainders below. Thus, 233 is prime!", "quotients_and_remainders": "233 \\div 2 = 116 \\text{ remainder } 1 \\\\ 233 \\div 3 = 77 \\text{ remainder } 2 \\\\ 233 \\div 5 = 46 \\text{ remainder } 3 \\\\ 233 \\div 7 = 33 \\text{ remainder } 2 \\\\ 233 \\div 11 = 21 \\text{ remainder } 2 \\\\ 233 \\div 13 = 17 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0972"}}, {"seed": 973, "data": {"the_number": "271", "answer": "The number 271 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a271 can divide 271. Since 13\u00b2 is less than or equal to 271 and 17\u00b2 is greater than 271, \u221a271 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 271 evenly. None of them divided 271, as evidenced by the list of quotients and remainders below. Thus, 271 is prime!", "quotients_and_remainders": "271 \\div 2 = 135 \\text{ remainder } 1 \\\\ 271 \\div 3 = 90 \\text{ remainder } 1 \\\\ 271 \\div 5 = 54 \\text{ remainder } 1 \\\\ 271 \\div 7 = 38 \\text{ remainder } 5 \\\\ 271 \\div 11 = 24 \\text{ remainder } 7 \\\\ 271 \\div 13 = 20 \\text{ remainder } 11 \\\\ ", "prime_problem": true, "__seed__": "0973"}}, {"seed": 974, "data": {"the_number": "203", "answer": "The number 203 is composite. We already know that 203 has two divisors: 1 and 203. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 15 = 29, so 7 is a factor of 203. Thus 203 has at least three divisors (1, 7, and 203), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "203 \\div 2 = 101 \\text{ remainder } 1 \\\\ 203 \\div 3 = 67 \\text{ remainder } 2 \\\\ 203 \\div 5 = 40 \\text{ remainder } 3 \\\\ 203 \\div 7 = 29 \\\\ 203 \\div 11 = 18 \\text{ remainder } 5 \\\\ 203 \\div 13 = 15 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0974"}}, {"seed": 975, "data": {"the_number": "407", "answer": "The number 407 is composite. We already know that 407 has two divisors: 1 and 407. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 21 = 37, so 11 is a factor of 407. Thus 407 has at least three divisors (1, 11, and 407), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "407 \\div 2 = 203 \\text{ remainder } 1 \\\\ 407 \\div 3 = 135 \\text{ remainder } 2 \\\\ 407 \\div 5 = 81 \\text{ remainder } 2 \\\\ 407 \\div 7 = 58 \\text{ remainder } 1 \\\\ 407 \\div 11 = 37 \\\\ 407 \\div 13 = 31 \\text{ remainder } 4 \\\\ 407 \\div 17 = 23 \\text{ remainder } 16 \\\\ 407 \\div 19 = 21 \\text{ remainder } 8 \\\\ ", "prime_problem": false, "__seed__": "0975"}}, {"seed": 976, "data": {"the_number": "313", "answer": "The number 313 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a313 can divide 313. Since 17\u00b2 is less than or equal to 313 and 19\u00b2 is greater than 313, \u221a313 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 313 evenly. None of them divided 313, as evidenced by the list of quotients and remainders below. Thus, 313 is prime!", "quotients_and_remainders": "313 \\div 2 = 156 \\text{ remainder } 1 \\\\ 313 \\div 3 = 104 \\text{ remainder } 1 \\\\ 313 \\div 5 = 62 \\text{ remainder } 3 \\\\ 313 \\div 7 = 44 \\text{ remainder } 5 \\\\ 313 \\div 11 = 28 \\text{ remainder } 5 \\\\ 313 \\div 13 = 24 \\text{ remainder } 1 \\\\ 313 \\div 17 = 18 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0976"}}, {"seed": 977, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0977"}}, {"seed": 978, "data": {"the_number": "139", "answer": "The number 139 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a139 can divide 139. Since 11\u00b2 is less than or equal to 139 and 13\u00b2 is greater than 139, \u221a139 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 139 evenly. None of them divided 139, as evidenced by the list of quotients and remainders below. Thus, 139 is prime!", "quotients_and_remainders": "139 \\div 2 = 69 \\text{ remainder } 1 \\\\ 139 \\div 3 = 46 \\text{ remainder } 1 \\\\ 139 \\div 5 = 27 \\text{ remainder } 4 \\\\ 139 \\div 7 = 19 \\text{ remainder } 6 \\\\ 139 \\div 11 = 12 \\text{ remainder } 7 \\\\ ", "prime_problem": true, "__seed__": "0978"}}, {"seed": 979, "data": {"the_number": "287", "answer": "The number 287 is composite. We already know that 287 has two divisors: 1 and 287. When testing the primes from 2 to 13 (our cutoff point), we found that 7 \u00d7 22 = 41, so 7 is a factor of 287. Thus 287 has at least three divisors (1, 7, and 287), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "287 \\div 2 = 143 \\text{ remainder } 1 \\\\ 287 \\div 3 = 95 \\text{ remainder } 2 \\\\ 287 \\div 5 = 57 \\text{ remainder } 2 \\\\ 287 \\div 7 = 41 \\\\ 287 \\div 11 = 26 \\text{ remainder } 1 \\\\ 287 \\div 13 = 22 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0979"}}, {"seed": 980, "data": {"the_number": "521", "answer": "The number 521 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a521 can divide 521. Since 19\u00b2 is less than or equal to 521 and 23\u00b2 is greater than 521, \u221a521 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 521 evenly. None of them divided 521, as evidenced by the list of quotients and remainders below. Thus, 521 is prime!", "quotients_and_remainders": "521 \\div 2 = 260 \\text{ remainder } 1 \\\\ 521 \\div 3 = 173 \\text{ remainder } 2 \\\\ 521 \\div 5 = 104 \\text{ remainder } 1 \\\\ 521 \\div 7 = 74 \\text{ remainder } 3 \\\\ 521 \\div 11 = 47 \\text{ remainder } 4 \\\\ 521 \\div 13 = 40 \\text{ remainder } 1 \\\\ 521 \\div 17 = 30 \\text{ remainder } 11 \\\\ 521 \\div 19 = 27 \\text{ remainder } 8 \\\\ ", "prime_problem": true, "__seed__": "0980"}}, {"seed": 981, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0981"}}, {"seed": 982, "data": {"the_number": "209", "answer": "The number 209 is composite. We already know that 209 has two divisors: 1 and 209. When testing the primes from 2 to 13 (our cutoff point), we found that 11 \u00d7 16 = 19, so 11 is a factor of 209. Thus 209 has at least three divisors (1, 11, and 209), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "209 \\div 2 = 104 \\text{ remainder } 1 \\\\ 209 \\div 3 = 69 \\text{ remainder } 2 \\\\ 209 \\div 5 = 41 \\text{ remainder } 4 \\\\ 209 \\div 7 = 29 \\text{ remainder } 6 \\\\ 209 \\div 11 = 19 \\\\ 209 \\div 13 = 16 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0982"}}, {"seed": 983, "data": {"the_number": "397", "answer": "The number 397 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a397 can divide 397. Since 19\u00b2 is less than or equal to 397 and 23\u00b2 is greater than 397, \u221a397 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 397 evenly. None of them divided 397, as evidenced by the list of quotients and remainders below. Thus, 397 is prime!", "quotients_and_remainders": "397 \\div 2 = 198 \\text{ remainder } 1 \\\\ 397 \\div 3 = 132 \\text{ remainder } 1 \\\\ 397 \\div 5 = 79 \\text{ remainder } 2 \\\\ 397 \\div 7 = 56 \\text{ remainder } 5 \\\\ 397 \\div 11 = 36 \\text{ remainder } 1 \\\\ 397 \\div 13 = 30 \\text{ remainder } 7 \\\\ 397 \\div 17 = 23 \\text{ remainder } 6 \\\\ 397 \\div 19 = 20 \\text{ remainder } 17 \\\\ ", "prime_problem": true, "__seed__": "0983"}}, {"seed": 984, "data": {"the_number": "479", "answer": "The number 479 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a479 can divide 479. Since 19\u00b2 is less than or equal to 479 and 23\u00b2 is greater than 479, \u221a479 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 479 evenly. None of them divided 479, as evidenced by the list of quotients and remainders below. Thus, 479 is prime!", "quotients_and_remainders": "479 \\div 2 = 239 \\text{ remainder } 1 \\\\ 479 \\div 3 = 159 \\text{ remainder } 2 \\\\ 479 \\div 5 = 95 \\text{ remainder } 4 \\\\ 479 \\div 7 = 68 \\text{ remainder } 3 \\\\ 479 \\div 11 = 43 \\text{ remainder } 6 \\\\ 479 \\div 13 = 36 \\text{ remainder } 11 \\\\ 479 \\div 17 = 28 \\text{ remainder } 3 \\\\ 479 \\div 19 = 25 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0984"}}, {"seed": 985, "data": {"the_number": "239", "answer": "The number 239 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a239 can divide 239. Since 13\u00b2 is less than or equal to 239 and 17\u00b2 is greater than 239, \u221a239 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 239 evenly. None of them divided 239, as evidenced by the list of quotients and remainders below. Thus, 239 is prime!", "quotients_and_remainders": "239 \\div 2 = 119 \\text{ remainder } 1 \\\\ 239 \\div 3 = 79 \\text{ remainder } 2 \\\\ 239 \\div 5 = 47 \\text{ remainder } 4 \\\\ 239 \\div 7 = 34 \\text{ remainder } 1 \\\\ 239 \\div 11 = 21 \\text{ remainder } 8 \\\\ 239 \\div 13 = 18 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0985"}}, {"seed": 986, "data": {"the_number": "473", "answer": "The number 473 is composite. We already know that 473 has two divisors: 1 and 473. When testing the primes from 2 to 19 (our cutoff point), we found that 11 \u00d7 24 = 43, so 11 is a factor of 473. Thus 473 has at least three divisors (1, 11, and 473), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "473 \\div 2 = 236 \\text{ remainder } 1 \\\\ 473 \\div 3 = 157 \\text{ remainder } 2 \\\\ 473 \\div 5 = 94 \\text{ remainder } 3 \\\\ 473 \\div 7 = 67 \\text{ remainder } 4 \\\\ 473 \\div 11 = 43 \\\\ 473 \\div 13 = 36 \\text{ remainder } 5 \\\\ 473 \\div 17 = 27 \\text{ remainder } 14 \\\\ 473 \\div 19 = 24 \\text{ remainder } 17 \\\\ ", "prime_problem": false, "__seed__": "0986"}}, {"seed": 987, "data": {"the_number": "133", "answer": "The number 133 is composite. We already know that 133 has two divisors: 1 and 133. When testing the primes from 2 to 11 (our cutoff point), we found that 7 \u00d7 12 = 19, so 7 is a factor of 133. Thus 133 has at least three divisors (1, 7, and 133), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "133 \\div 2 = 66 \\text{ remainder } 1 \\\\ 133 \\div 3 = 44 \\text{ remainder } 1 \\\\ 133 \\div 5 = 26 \\text{ remainder } 3 \\\\ 133 \\div 7 = 19 \\\\ 133 \\div 11 = 12 \\text{ remainder } 1 \\\\ ", "prime_problem": false, "__seed__": "0987"}}, {"seed": 988, "data": {"the_number": "277", "answer": "The number 277 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a277 can divide 277. Since 13\u00b2 is less than or equal to 277 and 17\u00b2 is greater than 277, \u221a277 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 277 evenly. None of them divided 277, as evidenced by the list of quotients and remainders below. Thus, 277 is prime!", "quotients_and_remainders": "277 \\div 2 = 138 \\text{ remainder } 1 \\\\ 277 \\div 3 = 92 \\text{ remainder } 1 \\\\ 277 \\div 5 = 55 \\text{ remainder } 2 \\\\ 277 \\div 7 = 39 \\text{ remainder } 4 \\\\ 277 \\div 11 = 25 \\text{ remainder } 2 \\\\ 277 \\div 13 = 21 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0988"}}, {"seed": 989, "data": {"the_number": "389", "answer": "The number 389 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a389 can divide 389. Since 19\u00b2 is less than or equal to 389 and 23\u00b2 is greater than 389, \u221a389 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 389 evenly. None of them divided 389, as evidenced by the list of quotients and remainders below. Thus, 389 is prime!", "quotients_and_remainders": "389 \\div 2 = 194 \\text{ remainder } 1 \\\\ 389 \\div 3 = 129 \\text{ remainder } 2 \\\\ 389 \\div 5 = 77 \\text{ remainder } 4 \\\\ 389 \\div 7 = 55 \\text{ remainder } 4 \\\\ 389 \\div 11 = 35 \\text{ remainder } 4 \\\\ 389 \\div 13 = 29 \\text{ remainder } 12 \\\\ 389 \\div 17 = 22 \\text{ remainder } 15 \\\\ 389 \\div 19 = 20 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0989"}}, {"seed": 990, "data": {"the_number": "191", "answer": "The number 191 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a191 can divide 191. Since 13\u00b2 is less than or equal to 191 and 17\u00b2 is greater than 191, \u221a191 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 191 evenly. None of them divided 191, as evidenced by the list of quotients and remainders below. Thus, 191 is prime!", "quotients_and_remainders": "191 \\div 2 = 95 \\text{ remainder } 1 \\\\ 191 \\div 3 = 63 \\text{ remainder } 2 \\\\ 191 \\div 5 = 38 \\text{ remainder } 1 \\\\ 191 \\div 7 = 27 \\text{ remainder } 2 \\\\ 191 \\div 11 = 17 \\text{ remainder } 4 \\\\ 191 \\div 13 = 14 \\text{ remainder } 9 \\\\ ", "prime_problem": true, "__seed__": "0990"}}, {"seed": 991, "data": {"the_number": "443", "answer": "The number 443 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a443 can divide 443. Since 19\u00b2 is less than or equal to 443 and 23\u00b2 is greater than 443, \u221a443 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 443 evenly. None of them divided 443, as evidenced by the list of quotients and remainders below. Thus, 443 is prime!", "quotients_and_remainders": "443 \\div 2 = 221 \\text{ remainder } 1 \\\\ 443 \\div 3 = 147 \\text{ remainder } 2 \\\\ 443 \\div 5 = 88 \\text{ remainder } 3 \\\\ 443 \\div 7 = 63 \\text{ remainder } 2 \\\\ 443 \\div 11 = 40 \\text{ remainder } 3 \\\\ 443 \\div 13 = 34 \\text{ remainder } 1 \\\\ 443 \\div 17 = 26 \\text{ remainder } 1 \\\\ 443 \\div 19 = 23 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0991"}}, {"seed": 992, "data": {"the_number": "257", "answer": "The number 257 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a257 can divide 257. Since 13\u00b2 is less than or equal to 257 and 17\u00b2 is greater than 257, \u221a257 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 257 evenly. None of them divided 257, as evidenced by the list of quotients and remainders below. Thus, 257 is prime!", "quotients_and_remainders": "257 \\div 2 = 128 \\text{ remainder } 1 \\\\ 257 \\div 3 = 85 \\text{ remainder } 2 \\\\ 257 \\div 5 = 51 \\text{ remainder } 2 \\\\ 257 \\div 7 = 36 \\text{ remainder } 5 \\\\ 257 \\div 11 = 23 \\text{ remainder } 4 \\\\ 257 \\div 13 = 19 \\text{ remainder } 10 \\\\ ", "prime_problem": true, "__seed__": "0992"}}, {"seed": 993, "data": {"the_number": "373", "answer": "The number 373 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a373 can divide 373. Since 19\u00b2 is less than or equal to 373 and 23\u00b2 is greater than 373, \u221a373 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 373 evenly. None of them divided 373, as evidenced by the list of quotients and remainders below. Thus, 373 is prime!", "quotients_and_remainders": "373 \\div 2 = 186 \\text{ remainder } 1 \\\\ 373 \\div 3 = 124 \\text{ remainder } 1 \\\\ 373 \\div 5 = 74 \\text{ remainder } 3 \\\\ 373 \\div 7 = 53 \\text{ remainder } 2 \\\\ 373 \\div 11 = 33 \\text{ remainder } 10 \\\\ 373 \\div 13 = 28 \\text{ remainder } 9 \\\\ 373 \\div 17 = 21 \\text{ remainder } 16 \\\\ 373 \\div 19 = 19 \\text{ remainder } 12 \\\\ ", "prime_problem": true, "__seed__": "0993"}}, {"seed": 994, "data": {"the_number": "499", "answer": "The number 499 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a499 can divide 499. Since 19\u00b2 is less than or equal to 499 and 23\u00b2 is greater than 499, \u221a499 must be between 19 and 23. This means we can stop testing at 19. We checked to see if any of the primes up to that point divide 499 evenly. None of them divided 499, as evidenced by the list of quotients and remainders below. Thus, 499 is prime!", "quotients_and_remainders": "499 \\div 2 = 249 \\text{ remainder } 1 \\\\ 499 \\div 3 = 166 \\text{ remainder } 1 \\\\ 499 \\div 5 = 99 \\text{ remainder } 4 \\\\ 499 \\div 7 = 71 \\text{ remainder } 2 \\\\ 499 \\div 11 = 45 \\text{ remainder } 4 \\\\ 499 \\div 13 = 38 \\text{ remainder } 5 \\\\ 499 \\div 17 = 29 \\text{ remainder } 6 \\\\ 499 \\div 19 = 26 \\text{ remainder } 5 \\\\ ", "prime_problem": true, "__seed__": "0994"}}, {"seed": 995, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0995"}}, {"seed": 996, "data": {"the_number": "427", "answer": "The number 427 is composite. We already know that 427 has two divisors: 1 and 427. When testing the primes from 2 to 19 (our cutoff point), we found that 7 \u00d7 22 = 61, so 7 is a factor of 427. Thus 427 has at least three divisors (1, 7, and 427), and must be composite! Our work for testing potential prime divisors is shown below.", "quotients_and_remainders": "427 \\div 2 = 213 \\text{ remainder } 1 \\\\ 427 \\div 3 = 142 \\text{ remainder } 1 \\\\ 427 \\div 5 = 85 \\text{ remainder } 2 \\\\ 427 \\div 7 = 61 \\\\ 427 \\div 11 = 38 \\text{ remainder } 9 \\\\ 427 \\div 13 = 32 \\text{ remainder } 11 \\\\ 427 \\div 17 = 25 \\text{ remainder } 2 \\\\ 427 \\div 19 = 22 \\text{ remainder } 9 \\\\ ", "prime_problem": false, "__seed__": "0996"}}, {"seed": 997, "data": {"the_number": "197", "answer": "The number 197 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a197 can divide 197. Since 13\u00b2 is less than or equal to 197 and 17\u00b2 is greater than 197, \u221a197 must be between 13 and 17. This means we can stop testing at 13. We checked to see if any of the primes up to that point divide 197 evenly. None of them divided 197, as evidenced by the list of quotients and remainders below. Thus, 197 is prime!", "quotients_and_remainders": "197 \\div 2 = 98 \\text{ remainder } 1 \\\\ 197 \\div 3 = 65 \\text{ remainder } 2 \\\\ 197 \\div 5 = 39 \\text{ remainder } 2 \\\\ 197 \\div 7 = 28 \\text{ remainder } 1 \\\\ 197 \\div 11 = 17 \\text{ remainder } 10 \\\\ 197 \\div 13 = 15 \\text{ remainder } 2 \\\\ ", "prime_problem": true, "__seed__": "0997"}}, {"seed": 998, "data": {"the_number": "293", "answer": "The number 293 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a293 can divide 293. Since 17\u00b2 is less than or equal to 293 and 19\u00b2 is greater than 293, \u221a293 must be between 17 and 19. This means we can stop testing at 17. We checked to see if any of the primes up to that point divide 293 evenly. None of them divided 293, as evidenced by the list of quotients and remainders below. Thus, 293 is prime!", "quotients_and_remainders": "293 \\div 2 = 146 \\text{ remainder } 1 \\\\ 293 \\div 3 = 97 \\text{ remainder } 2 \\\\ 293 \\div 5 = 58 \\text{ remainder } 3 \\\\ 293 \\div 7 = 41 \\text{ remainder } 6 \\\\ 293 \\div 11 = 26 \\text{ remainder } 7 \\\\ 293 \\div 13 = 22 \\text{ remainder } 7 \\\\ 293 \\div 17 = 17 \\text{ remainder } 4 \\\\ ", "prime_problem": true, "__seed__": "0998"}}, {"seed": 999, "data": {"the_number": "127", "answer": "The number 127 is prime according to our test from class. According to the test, we must check if any of the primes less than or equal to \u221a127 can divide 127. Since 11\u00b2 is less than or equal to 127 and 13\u00b2 is greater than 127, \u221a127 must be between 11 and 13. This means we can stop testing at 11. We checked to see if any of the primes up to that point divide 127 evenly. None of them divided 127, as evidenced by the list of quotients and remainders below. Thus, 127 is prime!", "quotients_and_remainders": "127 \\div 2 = 63 \\text{ remainder } 1 \\\\ 127 \\div 3 = 42 \\text{ remainder } 1 \\\\ 127 \\div 5 = 25 \\text{ remainder } 2 \\\\ 127 \\div 7 = 18 \\text{ remainder } 1 \\\\ 127 \\div 11 = 11 \\text{ remainder } 6 \\\\ ", "prime_problem": true, "__seed__": "0999"}}]}, {"title": "Finding the GCD", "slug": "N3", "description": "\n I can compute the greatest common divisor (GCD) of two numbers using the listing and prime factorization methods.\n ", "template": "\n\n \n \n

Find {{listing_prob}} using the listing method (sometimes called the set intersection method). You must show correct lists and a final answer.

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Divisors of {{listing_a}}: {{listing_list_a}}

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Divisors of {{listing_b}}: {{listing_list_b}}

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The largest divisor appearing in both lists simultaneously is {{listing_gcd}}, so {{listing_prob}} = {{listing_gcd}}

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Find {{factorization_prob}} using the prime factorization method. You must show your factorization(s) before giving the final answer.

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Prime factorization of {{factorization_a}}: {{factorization_mult_a}}

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Prime factorization of {{factorization_b}}: {{factorization_mult_b}}

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Multiplying together all common factors gives us {{factorization_mult_gcd}}, so {{factorization_prob}} = {{factorization_gcd}}

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\n", "exercises": [{"seed": 0, "data": {"listing_a": "30", "listing_b": "40", "listing_prob": "\\text{GCD}(30,40)", "listing_list_a": "1, 2, 3, 5, 6, 10, 15, 30", "listing_list_b": "1, 2, 4, 5, 8, 10, 20, 40", "listing_gcd": "10", "listing_gcd_type": "share composite", "factorization_a": "360", "factorization_b": "500", "factorization_prob": "\\text{GCD}(360,500)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 5 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 2 \\times 5", "factorization_gcd": "20", "factorization_type": "b not prefactored, a_b kernel 20", "__seed__": "0000"}}, {"seed": 1, "data": {"listing_a": "18", "listing_b": "30", "listing_prob": "\\text{GCD}(18,30)", "listing_list_a": "1, 2, 3, 6, 9, 18", "listing_list_b": "1, 2, 3, 5, 6, 10, 15, 30", "listing_gcd": "6", "listing_gcd_type": "share composite", "factorization_a": "210", "factorization_b": "294", "factorization_prob": "\\text{GCD}(210,294)", "factorization_mult_a": "2 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_gcd": "2 \\times 3 \\times 7", "factorization_gcd": "42", "factorization_type": "b not prefactored, a_b kernel 14", "__seed__": "0001"}}, {"seed": 2, "data": {"listing_a": "68", "listing_b": "75", "listing_prob": "\\text{GCD}(68,75)", "listing_list_a": "1, 2, 4, 17, 34, 68", "listing_list_b": "1, 3, 5, 15, 25, 75", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "125", "factorization_b": "5^4", "factorization_prob": "\\text{GCD}(125,5^4)", "factorization_mult_a": "5 \\times 5 \\times 5", "factorization_mult_b": "5 \\times 5 \\times 5 \\times 5", "factorization_mult_gcd": "5 \\times 5 \\times 5", "factorization_gcd": "125", "factorization_type": "b prefactored, a_b kernel 125", "__seed__": "0002"}}, {"seed": 3, "data": {"listing_a": "42", "listing_b": "98", "listing_prob": "\\text{GCD}(42,98)", 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"listing_gcd_type": "share prime", "factorization_a": "100", "factorization_b": "2^2 \\times 5^2 \\times 7", "factorization_prob": "\\text{GCD}(100,2^2 \\times 5^2 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 5 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 5 \\times 5", "factorization_gcd": "100", "factorization_type": "b prefactored, a_b kernel 10", "__seed__": "0978"}}, {"seed": 979, "data": {"listing_a": "66", "listing_b": "99", "listing_prob": "\\text{GCD}(66,99)", "listing_list_a": "1, 2, 3, 6, 11, 22, 33, 66", "listing_list_b": "1, 3, 9, 11, 33, 99", "listing_gcd": "33", "listing_gcd_type": "share composite", "factorization_a": "189", "factorization_b": "2 \\times 3^2 \\times 5 \\times 7", "factorization_prob": "\\text{GCD}(189,2 \\times 3^2 \\times 5 \\times 7)", "factorization_mult_a": "3 \\times 3 \\times 3 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "3 \\times 3 \\times 7", "factorization_gcd": "63", "factorization_type": "b prefactored, a_b kernel 63", "__seed__": "0979"}}, {"seed": 980, "data": {"listing_a": "30", "listing_b": "91", "listing_prob": "\\text{GCD}(30,91)", "listing_list_a": "1, 2, 3, 5, 6, 10, 15, 30", "listing_list_b": "1, 7, 13, 91", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "72", "factorization_b": "2^3 \\times 3 \\times 7", "factorization_prob": "\\text{GCD}(72,2^3 \\times 3 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 2 \\times 3", "factorization_gcd": "24", "factorization_type": "b prefactored, a_b kernel 6", "__seed__": "0980"}}, {"seed": 981, "data": {"listing_a": "42", "listing_b": "78", "listing_prob": "\\text{GCD}(42,78)", "listing_list_a": "1, 2, 3, 6, 7, 14, 21, 42", "listing_list_b": "1, 2, 3, 6, 13, 26, 39, 78", "listing_gcd": "6", "listing_gcd_type": "share composite", "factorization_a": "300", "factorization_b": "2 \\times 3^2 \\times 5^2", "factorization_prob": "\\text{GCD}(300,2 \\times 3^2 \\times 5^2)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 3 \\times 5 \\times 5", "factorization_gcd": "150", "factorization_type": "b prefactored, a_b kernel 30", "__seed__": "0981"}}, {"seed": 982, "data": {"listing_a": "76", "listing_b": "92", "listing_prob": "\\text{GCD}(76,92)", "listing_list_a": "1, 2, 4, 19, 38, 76", "listing_list_b": "1, 2, 4, 23, 46, 92", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "294", "factorization_b": "2 \\times 5 \\times 7 \\times 11", "factorization_prob": "\\text{GCD}(294,2 \\times 5 \\times 7 \\times 11)", "factorization_mult_a": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_b": "2 \\times 5 \\times 7 \\times 11", "factorization_mult_gcd": "2 \\times 7", "factorization_gcd": "14", "factorization_type": "b prefactored, a_b kernel 14", "__seed__": "0982"}}, {"seed": 983, "data": {"listing_a": "20", "listing_b": "81", "listing_prob": "\\text{GCD}(20,81)", "listing_list_a": "1, 2, 4, 5, 10, 20", "listing_list_b": "1, 3, 9, 27, 81", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "70", "factorization_b": "350", "factorization_prob": "\\text{GCD}(70,350)", "factorization_mult_a": "2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 5 \\times 7", "factorization_gcd": "70", "factorization_type": "b not prefactored, a_b kernel 70", "__seed__": "0983"}}, {"seed": 984, "data": {"listing_a": "50", "listing_b": "75", "listing_prob": "\\text{GCD}(50,75)", "listing_list_a": "1, 2, 5, 10, 25, 50", "listing_list_b": "1, 3, 5, 15, 25, 75", "listing_gcd": "25", "listing_gcd_type": "share composite", "factorization_a": "120", "factorization_b": "2^3 \\times 3 \\times 5 \\times 7", "factorization_prob": "\\text{GCD}(120,2^3 \\times 3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 2 \\times 3 \\times 5", "factorization_gcd": "120", "factorization_type": "b prefactored, a_b kernel 4", "__seed__": "0984"}}, {"seed": 985, "data": {"listing_a": "22", "listing_b": "64", "listing_prob": "\\text{GCD}(22,64)", "listing_list_a": "1, 2, 11, 22", "listing_list_b": "1, 2, 4, 8, 16, 32, 64", "listing_gcd": "2", "listing_gcd_type": "share prime", "factorization_a": "360", "factorization_b": "2 \\times 3^4", "factorization_prob": "\\text{GCD}(360,2 \\times 3^4)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 3 \\times 3", "factorization_mult_gcd": "2 \\times 3 \\times 3", "factorization_gcd": "18", "factorization_type": "b prefactored, a_b kernel 9", "__seed__": "0985"}}, {"seed": 986, "data": {"listing_a": "32", "listing_b": "91", "listing_prob": "\\text{GCD}(32,91)", "listing_list_a": "1, 2, 4, 8, 16, 32", "listing_list_b": "1, 7, 13, 91", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "126", "factorization_b": "2^3 \\times 3^2 \\times 7", "factorization_prob": "\\text{GCD}(126,2^3 \\times 3^2 \\times 7)", "factorization_mult_a": "2 \\times 3 \\times 3 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 3 \\times 3 \\times 7", "factorization_gcd": "126", "factorization_type": "b prefactored, a_b kernel 42", "__seed__": "0986"}}, {"seed": 987, "data": {"listing_a": "15", "listing_b": "45", "listing_prob": "\\text{GCD}(15,45)", "listing_list_a": "1, 3, 5, 15", "listing_list_b": "1, 3, 5, 9, 15, 45", "listing_gcd": "15", "listing_gcd_type": "multiple", "factorization_a": "140", "factorization_b": "2^3 \\times 5 \\times 7", "factorization_prob": "\\text{GCD}(140,2^3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 5 \\times 7", "factorization_gcd": "140", "factorization_type": "b prefactored, a_b kernel 20", "__seed__": "0987"}}, {"seed": 988, "data": {"listing_a": "51", "listing_b": "95", "listing_prob": "\\text{GCD}(51,95)", "listing_list_a": "1, 3, 17, 51", "listing_list_b": "1, 5, 19, 95", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "180", "factorization_b": "252", "factorization_prob": "\\text{GCD}(180,252)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 3 \\times 3", "factorization_gcd": "36", "factorization_type": "b not prefactored, a_b kernel 9", "__seed__": "0988"}}, {"seed": 989, "data": {"listing_a": "65", "listing_b": "92", "listing_prob": "\\text{GCD}(65,92)", "listing_list_a": "1, 5, 13, 65", "listing_list_b": "1, 2, 4, 23, 46, 92", "listing_gcd": "1", "listing_gcd_type": "relatively prime", "factorization_a": "315", "factorization_b": "3 \\times 5^2 \\times 7", "factorization_prob": "\\text{GCD}(315,3 \\times 5^2 \\times 7)", "factorization_mult_a": "3 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "3 \\times 5 \\times 5 \\times 7", "factorization_mult_gcd": "3 \\times 5 \\times 7", "factorization_gcd": "105", "factorization_type": "b prefactored, a_b kernel 15", "__seed__": "0989"}}, {"seed": 990, "data": {"listing_a": "45", "listing_b": "99", "listing_prob": "\\text{GCD}(45,99)", "listing_list_a": "1, 3, 5, 9, 15, 45", "listing_list_b": "1, 3, 9, 11, 33, 99", "listing_gcd": "9", "listing_gcd_type": "share composite", "factorization_a": "108", "factorization_b": "540", "factorization_prob": "\\text{GCD}(108,540)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 3 \\times 3", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 3 \\times 3 \\times 5", "factorization_mult_gcd": "2 \\times 2 \\times 3 \\times 3 \\times 3", "factorization_gcd": "108", "factorization_type": "b not prefactored, a_b kernel 9", "__seed__": "0990"}}, {"seed": 991, "data": {"listing_a": "28", "listing_b": "64", "listing_prob": "\\text{GCD}(28,64)", "listing_list_a": "1, 2, 4, 7, 14, 28", "listing_list_b": "1, 2, 4, 8, 16, 32, 64", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "126", "factorization_b": "189", "factorization_prob": "\\text{GCD}(126,189)", "factorization_mult_a": "2 \\times 3 \\times 3 \\times 7", "factorization_mult_b": "3 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "3 \\times 3 \\times 7", "factorization_gcd": "63", "factorization_type": "b not prefactored, a_b kernel 63", "__seed__": "0991"}}, {"seed": 992, "data": {"listing_a": "44", "listing_b": "76", "listing_prob": "\\text{GCD}(44,76)", "listing_list_a": "1, 2, 4, 11, 22, 44", "listing_list_b": "1, 2, 4, 19, 38, 76", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "220", "factorization_b": "420", "factorization_prob": "\\text{GCD}(220,420)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 11", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 5", "factorization_gcd": "20", "factorization_type": "b not prefactored, a_b kernel 10", "__seed__": "0992"}}, {"seed": 993, "data": {"listing_a": "12", "listing_b": "92", "listing_prob": "\\text{GCD}(12,92)", "listing_list_a": "1, 2, 3, 4, 6, 12", "listing_list_b": "1, 2, 4, 23, 46, 92", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "294", "factorization_b": "2^5 \\times 3 \\times 7", "factorization_prob": "\\text{GCD}(294,2^5 \\times 3 \\times 7)", "factorization_mult_a": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 3 \\times 7", "factorization_gcd": "42", "factorization_type": "b prefactored, a_b kernel 7", "__seed__": "0993"}}, {"seed": 994, "data": {"listing_a": "8", "listing_b": "44", "listing_prob": "\\text{GCD}(8,44)", "listing_list_a": "1, 2, 4, 8", "listing_list_b": "1, 2, 4, 11, 22, 44", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "140", "factorization_b": "450", "factorization_prob": "\\text{GCD}(140,450)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 5", "factorization_gcd": "10", "factorization_type": "b not prefactored, a_b kernel 2", "__seed__": "0994"}}, {"seed": 995, "data": {"listing_a": "88", "listing_b": "94", "listing_prob": "\\text{GCD}(88,94)", "listing_list_a": "1, 2, 4, 8, 11, 22, 44, 88", "listing_list_b": "1, 2, 47, 94", "listing_gcd": "2", "listing_gcd_type": "share prime", "factorization_a": "96", "factorization_b": "400", "factorization_prob": "\\text{GCD}(96,400)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5", "factorization_mult_gcd": "2 \\times 2 \\times 2 \\times 2", "factorization_gcd": "16", "factorization_type": "b not prefactored, a_b kernel 4", "__seed__": "0995"}}, {"seed": 996, "data": {"listing_a": "30", "listing_b": "70", "listing_prob": "\\text{GCD}(30,70)", "listing_list_a": "1, 2, 3, 5, 6, 10, 15, 30", "listing_list_b": "1, 2, 5, 7, 10, 14, 35, 70", "listing_gcd": "10", "listing_gcd_type": "share composite", "factorization_a": "315", "factorization_b": "2 \\times 3^2 \\times 5^2", "factorization_prob": "\\text{GCD}(315,2 \\times 3^2 \\times 5^2)", "factorization_mult_a": "3 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_gcd": "3 \\times 3 \\times 5", "factorization_gcd": "45", "factorization_type": "b prefactored, a_b kernel 45", "__seed__": "0996"}}, {"seed": 997, "data": {"listing_a": "8", "listing_b": "44", "listing_prob": "\\text{GCD}(8,44)", "listing_list_a": "1, 2, 4, 8", "listing_list_b": "1, 2, 4, 11, 22, 44", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "420", "factorization_b": "2^2 \\times 3^3 \\times 7", "factorization_prob": "\\text{GCD}(420,2^2 \\times 3^3 \\times 7)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 3 \\times 3 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 3 \\times 7", "factorization_gcd": "84", "factorization_type": "b prefactored, a_b kernel 4", "__seed__": "0997"}}, {"seed": 998, "data": {"listing_a": "52", "listing_b": "88", "listing_prob": "\\text{GCD}(52,88)", "listing_list_a": "1, 2, 4, 13, 26, 52", "listing_list_b": "1, 2, 4, 8, 11, 22, 44, 88", "listing_gcd": "4", "listing_gcd_type": "share composite", "factorization_a": "360", "factorization_b": "588", "factorization_prob": "\\text{GCD}(360,588)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 7 \\times 7", "factorization_mult_gcd": "2 \\times 2 \\times 3", "factorization_gcd": "12", "factorization_type": "b not prefactored, a_b kernel 6", "__seed__": "0998"}}, {"seed": 999, "data": {"listing_a": "12", "listing_b": "30", "listing_prob": "\\text{GCD}(12,30)", "listing_list_a": "1, 2, 3, 4, 6, 12", "listing_list_b": "1, 2, 3, 5, 6, 10, 15, 30", "listing_gcd": "6", "listing_gcd_type": "share composite", "factorization_a": "315", "factorization_b": "420", "factorization_prob": "\\text{GCD}(315,420)", "factorization_mult_a": "3 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_gcd": "3 \\times 5 \\times 7", "factorization_gcd": "105", "factorization_type": "b not prefactored, a_b kernel 21", "__seed__": "0999"}}]}, {"title": "Finding the LCM", "slug": "N4", "description": "\n I can compute the least common multiple (LCM) of two numbers using the listing and prime factorization methods.\n ", "template": "\n\n \n \n

Find {{listing_prob}} using the listing method (sometimes called the set intersection method). You must show correct lists and a final answer.

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\n \n

(Some) multiples of {{listing_a}}: {{listing_list_a}}

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(Some) multiples of {{listing_b}}: {{listing_list_b}}

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The smallest nonzero multiple appearing in both lists simultaneously is {{listing_lcm}}, so {{listing_prob}} = {{listing_lcm}}

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\n
\n \n \n \n

Find {{factorization_prob}} using the prime factorization method. You must show your factorizations before giving the final answer. You may leave your answer in factored form.

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\n \n

Prime factorization of {{factorization_a}}: {{factorization_mult_a}}

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Prime factorization of {{factorization_b}}: {{factorization_mult_b}}

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Multiplying together all prime factors of {{factorization_a}} and {{factorization_b}}, then removing the overlapping prime factors gives us {{factorization_mult_lcm}}, so {{factorization_prob}} = {{factorization_lcm}}

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\n
\n
\n", "exercises": [{"seed": 0, "data": {"listing_a": "21", "listing_b": "6", "listing_prob": "\\text{LCM}(21,6)", "listing_list_a": "21, 42, 63, 84, 105...", "listing_list_b": "6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90...", "listing_lcm": "42", "factorization_a": "350", "factorization_b": "375", "factorization_prob": "\\text{LCM}(350,375)", "factorization_mult_a": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_b": "3 \\times 5 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 3 \\times 5 \\times 5 \\times 5 \\times 7", "factorization_lcm": "5250", "factorization_type": "b not prefactored, a_b kernel 25", "__seed__": "0000"}}, {"seed": 1, "data": {"listing_a": "14", "listing_b": "8", "listing_prob": "\\text{LCM}(14,8)", "listing_list_a": "14, 28, 42, 56, 70, 84, 98, 112, 126...", "listing_list_b": "8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120...", "listing_lcm": "56", "factorization_a": "147", "factorization_b": "378", "factorization_prob": "\\text{LCM}(147,378)", "factorization_mult_a": "3 \\times 7 \\times 7", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 3 \\times 7", "factorization_mult_lcm": "2 \\times 3 \\times 3 \\times 3 \\times 7 \\times 7", "factorization_lcm": "2646", "factorization_type": "b not prefactored, a_b kernel 21", "__seed__": "0001"}}, {"seed": 2, "data": {"listing_a": "35", "listing_b": "30", "listing_prob": "\\text{LCM}(35,30)", "listing_list_a": "35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455...", "listing_list_b": "30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450...", "listing_lcm": "210", "factorization_a": "105", "factorization_b": "2^4 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(105,2^4 \\times 5 \\times 7)", "factorization_mult_a": "3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5 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988, "data": {"listing_a": "56", "listing_b": "35", "listing_prob": "\\text{LCM}(56,35)", "listing_list_a": "56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616...", "listing_list_b": "35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455, 490, 525, 560, 595...", "listing_lcm": "280", "factorization_a": "231", "factorization_b": "2 \\times 3 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(231,2 \\times 3 \\times 5 \\times 7)", "factorization_mult_a": "3 \\times 7 \\times 11", "factorization_mult_b": "2 \\times 3 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 3 \\times 5 \\times 7 \\times 11", "factorization_lcm": "2310", "factorization_type": "b prefactored, a_b kernel 21", "__seed__": "0988"}}, {"seed": 989, "data": {"listing_a": "70", "listing_b": "49", "listing_prob": "\\text{LCM}(70,49)", "listing_list_a": "70, 140, 210, 280, 350, 420, 490, 560, 630, 700, 770, 840, 910, 980, 1050...", "listing_list_b": "49, 98, 147, 196, 245, 294, 343, 392, 441, 490, 539, 588, 637, 686, 735, 784, 833, 882, 931, 980, 1029...", "listing_lcm": "490", "factorization_a": "84", "factorization_b": "2^2 \\times 5 \\times 7^2", "factorization_prob": "\\text{LCM}(84,2^2 \\times 5 \\times 7^2)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 5 \\times 7 \\times 7", "factorization_mult_lcm": "2 \\times 2 \\times 3 \\times 5 \\times 7 \\times 7", "factorization_lcm": "2940", "factorization_type": "b prefactored, a_b kernel 14", "__seed__": "0989"}}, {"seed": 990, "data": {"listing_a": "68", "listing_b": "17", "listing_prob": "\\text{LCM}(68,17)", "listing_list_a": "68, 136, 204...", "listing_list_b": "17, 34, 51, 68, 85, 102, 119, 136, 153...", "listing_lcm": "68", "factorization_a": "220", "factorization_b": "330", "factorization_prob": "\\text{LCM}(220,330)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 11", "factorization_mult_b": "2 \\times 3 \\times 5 \\times 11", "factorization_mult_lcm": "2 \\times 2 \\times 3 \\times 5 \\times 11", "factorization_lcm": "660", "factorization_type": "b not prefactored, a_b kernel 22", "__seed__": "0990"}}, {"seed": 991, "data": {"listing_a": "72", "listing_b": "48", "listing_prob": "\\text{LCM}(72,48)", "listing_list_a": "72, 144, 216, 288, 360...", "listing_list_b": "48, 96, 144, 192, 240, 288, 336...", "listing_lcm": "144", "factorization_a": "420", "factorization_b": "600", "factorization_prob": "\\text{LCM}(420,600)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5 \\times 7", "factorization_lcm": "4200", "factorization_type": "b not prefactored, a_b kernel 12", "__seed__": "0991"}}, {"seed": 992, "data": {"listing_a": "8", "listing_b": "6", "listing_prob": "\\text{LCM}(8,6)", "listing_list_a": "8, 16, 24, 32, 40, 48, 56...", "listing_list_b": "6, 12, 18, 24, 30, 36, 42, 48, 54...", "listing_lcm": "24", "factorization_a": "360", "factorization_b": "2^3 \\times 3^2 \\times 11", "factorization_prob": "\\text{LCM}(360,2^3 \\times 3^2 \\times 11)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 11", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 5 \\times 11", "factorization_lcm": "3960", "factorization_type": "b prefactored, a_b kernel 2", "__seed__": "0992"}}, {"seed": 993, "data": {"listing_a": "15", "listing_b": "12", "listing_prob": "\\text{LCM}(15,12)", "listing_list_a": "15, 30, 45, 60, 75, 90, 105, 120, 135...", "listing_list_b": "12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132...", "listing_lcm": "60", "factorization_a": "480", "factorization_b": "2 \\times 3 \\times 7 \\times 11", "factorization_prob": "\\text{LCM}(480,2 \\times 3 \\times 7 \\times 11)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 7 \\times 11", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 7 \\times 11", "factorization_lcm": "36960", "factorization_type": "b prefactored, a_b kernel 6", "__seed__": "0993"}}, {"seed": 994, "data": {"listing_a": "64", "listing_b": "8", "listing_prob": "\\text{LCM}(64,8)", "listing_list_a": "64, 128, 192...", "listing_list_b": "8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136...", "listing_lcm": "64", "factorization_a": "350", "factorization_b": "2^3 \\times 3 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(350,2^3 \\times 3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5 \\times 7", "factorization_lcm": "4200", "factorization_type": "b prefactored, a_b kernel 70", "__seed__": "0994"}}, {"seed": 995, "data": {"listing_a": "70", "listing_b": "10", "listing_prob": "\\text{LCM}(70,10)", "listing_list_a": "70, 140, 210...", "listing_list_b": "10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150...", "listing_lcm": "70", "factorization_a": "350", "factorization_b": "490", "factorization_prob": "\\text{LCM}(350,490)", "factorization_mult_a": "2 \\times 5 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 5 \\times 7 \\times 7", "factorization_mult_lcm": "2 \\times 5 \\times 5 \\times 7 \\times 7", "factorization_lcm": "2450", "factorization_type": "b not prefactored, a_b kernel 35", "__seed__": "0995"}}, {"seed": 996, "data": {"listing_a": "63", "listing_b": "45", "listing_prob": "\\text{LCM}(63,45)", "listing_list_a": "63, 126, 189, 252, 315, 378, 441, 504, 567, 630, 693...", "listing_list_b": "45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675...", "listing_lcm": "315", "factorization_a": "300", "factorization_b": "450", "factorization_prob": "\\text{LCM}(300,450)", "factorization_mult_a": "2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 3 \\times 3 \\times 5 \\times 5", "factorization_lcm": "900", "factorization_type": "b not prefactored, a_b kernel 50", "__seed__": "0996"}}, {"seed": 997, "data": {"listing_a": "70", "listing_b": "30", "listing_prob": "\\text{LCM}(70,30)", "listing_list_a": "70, 140, 210, 280, 350, 420, 490...", "listing_list_b": "30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450...", "listing_lcm": "210", "factorization_a": "140", "factorization_b": "400", "factorization_prob": "\\text{LCM}(140,400)", "factorization_mult_a": "2 \\times 2 \\times 5 \\times 7", "factorization_mult_b": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5 \\times 7", "factorization_lcm": "2800", "factorization_type": "b not prefactored, a_b kernel 20", "__seed__": "0997"}}, {"seed": 998, "data": {"listing_a": "70", "listing_b": "20", "listing_prob": "\\text{LCM}(70,20)", "listing_list_a": "70, 140, 210, 280, 350...", "listing_list_b": "20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300...", "listing_lcm": "140", "factorization_a": "294", "factorization_b": "3^3 \\times 5 \\times 7", "factorization_prob": "\\text{LCM}(294,3^3 \\times 5 \\times 7)", "factorization_mult_a": "2 \\times 3 \\times 7 \\times 7", "factorization_mult_b": "3 \\times 3 \\times 3 \\times 5 \\times 7", "factorization_mult_lcm": "2 \\times 3 \\times 3 \\times 3 \\times 5 \\times 7 \\times 7", "factorization_lcm": "13230", "factorization_type": "b prefactored, a_b kernel 21", "__seed__": "0998"}}, {"seed": 999, "data": {"listing_a": "56", "listing_b": "49", "listing_prob": "\\text{LCM}(56,49)", "listing_list_a": "56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784, 840...", "listing_list_b": "49, 98, 147, 196, 245, 294, 343, 392, 441, 490, 539, 588, 637, 686, 735, 784, 833...", "listing_lcm": "392", "factorization_a": "400", "factorization_b": "2^2 \\times 3 \\times 5^2", "factorization_prob": "\\text{LCM}(400,2^2 \\times 3 \\times 5^2)", "factorization_mult_a": "2 \\times 2 \\times 2 \\times 2 \\times 5 \\times 5", "factorization_mult_b": "2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_mult_lcm": "2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5", "factorization_lcm": "1200", "factorization_type": "b prefactored, a_b kernel 4", "__seed__": "0999"}}]}, {"title": "Equivalent Fractions", "slug": "F1", "description": "\n I can convert fractions to different forms (including simplest form), and determine if two fractions are equivalent.\n ", "template": "\n\n \n \n

Write {{simplify_prob}} in simplest form.

\n
\n \n

The above simplifies to {{simplify_ans}}, after pulling out {{factors_sequence}} from both the numerator and denominator.

\n
\n
\n \n \n \n

Convert {{convert_prob}} to {{convert_type}}.

\n
\n \n

{{convert_ans}}

\n
\n
\n\n \n \n

Determine if {{equiv_prob_ab}} \\text{ and } {{equiv_prob_cd}} and are equivalent fractions. You may use any method of your choosing, but you must show correct work in order to pass.

\n
\n \n

The fraction {{equiv_prob_ab}} simplifies to {{equiv_ans_ab}}.

\n

The fraction {{equiv_prob_cd}} simplifies to {{equiv_ans_cd}}.

\n

{{equiv_ans_supp_1}}

\n

Alternatively, we see that the product of one pair of diagonal entries is {{equiv_prob_a}} \\times {{equiv_prob_d}} = {{equiv_ans_axd}} while the other diagonal product is {{equiv_prob_b}} \\times {{equiv_prob_c}} = {{equiv_ans_bxc}} {{equiv_ans_supp_2}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"simplify_prob": "\\dfrac{49}{196}", "simplify_ans": "\\dfrac{1}{4}", "factors_list": ["7", "7"], "factors_sequence": "7 and 7", "convert_prob": "\\dfrac{61}{15}", "convert_type": "a mixed number", "convert_ans": "4\\frac{1}{15}", "equiv_prob_a": "18", "equiv_prob_b": "30", "equiv_prob_c": "14", "equiv_prob_d": "27", "equiv_prob_ab": "\\dfrac{18}{30}", "equiv_prob_cd": "\\dfrac{14}{27}", "equiv_ans_ab": "\\dfrac{3}{5}", "equiv_ans_cd": "\\dfrac{14}{27}", "equiv_ans_axd": "486", "equiv_ans_bxc": "420", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0000"}}, {"seed": 1, "data": {"simplify_prob": "\\dfrac{22}{330}", "simplify_ans": "\\dfrac{1}{15}", "factors_list": ["2", "11"], "factors_sequence": "2 and 11", "convert_prob": "\\dfrac{25}{11}", "convert_type": "a mixed number", "convert_ans": "2\\frac{3}{11}", "equiv_prob_a": "48", "equiv_prob_b": "60", "equiv_prob_c": "36", "equiv_prob_d": "45", "equiv_prob_ab": "\\dfrac{48}{60}", "equiv_prob_cd": "\\dfrac{36}{45}", "equiv_ans_ab": "\\dfrac{4}{5}", "equiv_ans_cd": "\\dfrac{4}{5}", "equiv_ans_axd": "2160", "equiv_ans_bxc": "2160", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0001"}}, {"seed": 2, "data": {"simplify_prob": "\\dfrac{252}{273}", "simplify_ans": "\\dfrac{12}{13}", "factors_list": ["3", "7"], "factors_sequence": "3 and 7", "convert_prob": "7\\frac{9}{13}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{100}{13}", "equiv_prob_a": "20", "equiv_prob_b": "80", "equiv_prob_c": "22", "equiv_prob_d": "83", "equiv_prob_ab": "\\dfrac{20}{80}", "equiv_prob_cd": "\\dfrac{22}{83}", "equiv_ans_ab": "\\dfrac{1}{4}", "equiv_ans_cd": "\\dfrac{22}{83}", "equiv_ans_axd": "1660", "equiv_ans_bxc": "1760", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0002"}}, {"seed": 3, "data": {"simplify_prob": "\\dfrac{24}{120}", "simplify_ans": "\\dfrac{1}{5}", "factors_list": ["2", "2", "2", "3"], "factors_sequence": "2, 2, 2, and 3", "convert_prob": "\\dfrac{81}{14}", "convert_type": "a mixed number", "convert_ans": "5\\frac{11}{14}", "equiv_prob_a": "90", "equiv_prob_b": "108", "equiv_prob_c": "110", "equiv_prob_d": "132", "equiv_prob_ab": "\\dfrac{90}{108}", "equiv_prob_cd": "\\dfrac{110}{132}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{5}{6}", "equiv_ans_axd": "11880", "equiv_ans_bxc": "11880", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0003"}}, {"seed": 4, "data": {"simplify_prob": "\\dfrac{45}{180}", "simplify_ans": "\\dfrac{1}{4}", "factors_list": ["3", "3", "5"], "factors_sequence": "3, 3, and 5", "convert_prob": "\\dfrac{11}{5}", "convert_type": "a mixed number", "convert_ans": "2\\frac{1}{5}", "equiv_prob_a": "15", "equiv_prob_b": "45", "equiv_prob_c": "21", "equiv_prob_d": "51", "equiv_prob_ab": "\\dfrac{15}{45}", "equiv_prob_cd": "\\dfrac{21}{51}", "equiv_ans_ab": "\\dfrac{1}{3}", "equiv_ans_cd": "\\dfrac{7}{17}", "equiv_ans_axd": "765", "equiv_ans_bxc": "945", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0004"}}, {"seed": 5, "data": {"simplify_prob": "\\dfrac{70}{84}", "simplify_ans": "\\dfrac{5}{6}", "factors_list": ["2", "7"], "factors_sequence": "2 and 7", "convert_prob": "2\\frac{1}{4}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{9}{4}", "equiv_prob_a": "2", "equiv_prob_b": "11", "equiv_prob_c": "3", "equiv_prob_d": "11", "equiv_prob_ab": "\\dfrac{2}{11}", "equiv_prob_cd": "\\dfrac{3}{11}", "equiv_ans_ab": "\\dfrac{2}{11}", "equiv_ans_cd": "\\dfrac{3}{11}", "equiv_ans_axd": "22", "equiv_ans_bxc": "33", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0005"}}, {"seed": 6, "data": {"simplify_prob": "\\dfrac{33}{231}", "simplify_ans": "\\dfrac{1}{7}", "factors_list": ["3", "11"], "factors_sequence": "3 and 11", "convert_prob": "8\\frac{7}{8}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{71}{8}", "equiv_prob_a": "81", "equiv_prob_b": "90", "equiv_prob_c": "77", "equiv_prob_d": "85", "equiv_prob_ab": "\\dfrac{81}{90}", "equiv_prob_cd": "\\dfrac{77}{85}", "equiv_ans_ab": "\\dfrac{9}{10}", "equiv_ans_cd": "\\dfrac{77}{85}", "equiv_ans_axd": "6885", "equiv_ans_bxc": "6930", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0006"}}, {"seed": 7, "data": {"simplify_prob": "\\dfrac{25}{375}", "simplify_ans": "\\dfrac{1}{15}", "factors_list": ["5", "5"], "factors_sequence": "5 and 5", "convert_prob": "\\dfrac{65}{11}", "convert_type": "a mixed number", "convert_ans": "5\\frac{10}{11}", "equiv_prob_a": "45", "equiv_prob_b": "60", "equiv_prob_c": "57", "equiv_prob_d": "76", "equiv_prob_ab": "\\dfrac{45}{60}", "equiv_prob_cd": "\\dfrac{57}{76}", "equiv_ans_ab": "\\dfrac{3}{4}", "equiv_ans_cd": "\\dfrac{3}{4}", "equiv_ans_axd": "3420", "equiv_ans_bxc": "3420", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0007"}}, {"seed": 8, "data": {"simplify_prob": "\\dfrac{21}{105}", "simplify_ans": "\\dfrac{1}{5}", "factors_list": ["3", "7"], "factors_sequence": "3 and 7", "convert_prob": "4\\frac{5}{7}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{33}{7}", "equiv_prob_a": "126", "equiv_prob_b": "198", "equiv_prob_c": "154", "equiv_prob_d": "242", "equiv_prob_ab": "\\dfrac{126}{198}", "equiv_prob_cd": "\\dfrac{154}{242}", "equiv_ans_ab": "\\dfrac{7}{11}", "equiv_ans_cd": "\\dfrac{7}{11}", "equiv_ans_axd": "30492", "equiv_ans_bxc": "30492", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0008"}}, {"seed": 9, "data": {"simplify_prob": "\\dfrac{99}{154}", "simplify_ans": "\\dfrac{9}{14}", "factors_list": ["11"], "factors_sequence": "11", "convert_prob": "\\dfrac{107}{14}", "convert_type": "a mixed number", "convert_ans": "7\\frac{9}{14}", "equiv_prob_a": "25", "equiv_prob_b": "70", "equiv_prob_c": "26", "equiv_prob_d": "72", "equiv_prob_ab": "\\dfrac{25}{70}", "equiv_prob_cd": "\\dfrac{26}{72}", "equiv_ans_ab": "\\dfrac{5}{14}", "equiv_ans_cd": "\\dfrac{13}{36}", "equiv_ans_axd": "1800", "equiv_ans_bxc": "1820", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0009"}}, {"seed": 10, "data": {"simplify_prob": "\\dfrac{14}{105}", "simplify_ans": "\\dfrac{2}{15}", "factors_list": ["7"], "factors_sequence": "7", "convert_prob": "\\dfrac{23}{3}", "convert_type": "a mixed number", "convert_ans": "7\\frac{2}{3}", "equiv_prob_a": "154", "equiv_prob_b": "182", "equiv_prob_c": "165", "equiv_prob_d": "195", "equiv_prob_ab": "\\dfrac{154}{182}", "equiv_prob_cd": "\\dfrac{165}{195}", "equiv_ans_ab": "\\dfrac{11}{13}", "equiv_ans_cd": "\\dfrac{11}{13}", "equiv_ans_axd": "30030", "equiv_ans_bxc": "30030", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0010"}}, {"seed": 11, "data": {"simplify_prob": "\\dfrac{54}{324}", "simplify_ans": "\\dfrac{1}{6}", "factors_list": ["2", "3", "3", "3"], "factors_sequence": "2, 3, 3, and 3", "convert_prob": "4\\frac{5}{7}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{33}{7}", "equiv_prob_a": "55", "equiv_prob_b": "66", "equiv_prob_c": "48", "equiv_prob_d": "60", "equiv_prob_ab": "\\dfrac{55}{66}", "equiv_prob_cd": "\\dfrac{48}{60}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{4}{5}", "equiv_ans_axd": "3300", "equiv_ans_bxc": "3168", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0011"}}, {"seed": 12, "data": {"simplify_prob": "\\dfrac{180}{280}", "simplify_ans": "\\dfrac{9}{14}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "\\dfrac{23}{6}", "convert_type": "a mixed number", "convert_ans": "3\\frac{5}{6}", "equiv_prob_a": "70", "equiv_prob_b": "130", "equiv_prob_c": "56", "equiv_prob_d": "104", "equiv_prob_ab": "\\dfrac{70}{130}", "equiv_prob_cd": "\\dfrac{56}{104}", "equiv_ans_ab": "\\dfrac{7}{13}", "equiv_ans_cd": "\\dfrac{7}{13}", "equiv_ans_axd": "7280", "equiv_ans_bxc": "7280", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows 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"\\dfrac{5}{55}", "equiv_prob_cd": "\\dfrac{9}{57}", "equiv_ans_ab": "\\dfrac{1}{11}", "equiv_ans_cd": "\\dfrac{3}{19}", "equiv_ans_axd": "285", "equiv_ans_bxc": "495", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0977"}}, {"seed": 978, "data": {"simplify_prob": "\\dfrac{42}{196}", "simplify_ans": "\\dfrac{3}{14}", "factors_list": ["2", "7"], "factors_sequence": "2 and 7", "convert_prob": "4\\frac{1}{9}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{37}{9}", "equiv_prob_a": "20", "equiv_prob_b": "200", "equiv_prob_c": "17", "equiv_prob_d": "170", "equiv_prob_ab": "\\dfrac{20}{200}", "equiv_prob_cd": "\\dfrac{17}{170}", "equiv_ans_ab": "\\dfrac{1}{10}", "equiv_ans_cd": "\\dfrac{1}{10}", "equiv_ans_axd": "3400", "equiv_ans_bxc": "3400", "equiv_ans_supp_1": "The fractions are equivalent, 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"\\dfrac{120}{195}", "simplify_ans": "\\dfrac{8}{13}", "factors_list": ["3", "5"], "factors_sequence": "3 and 5", "convert_prob": "\\dfrac{29}{4}", "convert_type": "a mixed number", "convert_ans": "7\\frac{1}{4}", "equiv_prob_a": "15", "equiv_prob_b": "45", "equiv_prob_c": "11", "equiv_prob_d": "33", "equiv_prob_ab": "\\dfrac{15}{45}", "equiv_prob_cd": "\\dfrac{11}{33}", "equiv_ans_ab": "\\dfrac{1}{3}", "equiv_ans_cd": "\\dfrac{1}{3}", "equiv_ans_axd": "495", "equiv_ans_bxc": "495", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0980"}}, {"seed": 981, "data": {"simplify_prob": "\\dfrac{66}{396}", "simplify_ans": "\\dfrac{1}{6}", "factors_list": ["2", "3", "11"], "factors_sequence": "2, 3, and 11", "convert_prob": "\\dfrac{26}{7}", "convert_type": "a mixed number", "convert_ans": "3\\frac{5}{7}", "equiv_prob_a": "100", "equiv_prob_b": "160", "equiv_prob_c": "115", "equiv_prob_d": "184", "equiv_prob_ab": "\\dfrac{100}{160}", "equiv_prob_cd": "\\dfrac{115}{184}", "equiv_ans_ab": "\\dfrac{5}{8}", "equiv_ans_cd": "\\dfrac{5}{8}", "equiv_ans_axd": "18400", "equiv_ans_bxc": "18400", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0981"}}, {"seed": 982, "data": {"simplify_prob": "\\dfrac{286}{330}", "simplify_ans": "\\dfrac{13}{15}", "factors_list": ["2", "11"], "factors_sequence": "2 and 11", "convert_prob": "\\dfrac{38}{9}", "convert_type": "a mixed number", "convert_ans": "4\\frac{2}{9}", "equiv_prob_a": "18", "equiv_prob_b": "33", "equiv_prob_c": "22", "equiv_prob_d": "39", "equiv_prob_ab": "\\dfrac{18}{33}", "equiv_prob_cd": "\\dfrac{22}{39}", "equiv_ans_ab": "\\dfrac{6}{11}", "equiv_ans_cd": "\\dfrac{22}{39}", "equiv_ans_axd": "702", "equiv_ans_bxc": "726", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0982"}}, {"seed": 983, "data": {"simplify_prob": "\\dfrac{36}{504}", "simplify_ans": "\\dfrac{1}{14}", "factors_list": ["2", "2", "3", "3"], "factors_sequence": "2, 2, 3, and 3", "convert_prob": "6\\frac{4}{9}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{58}{9}", "equiv_prob_a": "40", "equiv_prob_b": "48", "equiv_prob_c": "46", "equiv_prob_d": "56", "equiv_prob_ab": "\\dfrac{40}{48}", "equiv_prob_cd": "\\dfrac{46}{56}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{23}{28}", "equiv_ans_axd": "2240", "equiv_ans_bxc": "2208", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0983"}}, {"seed": 984, "data": {"simplify_prob": "\\dfrac{40}{220}", "simplify_ans": "\\dfrac{2}{11}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "6\\frac{9}{11}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{75}{11}", "equiv_prob_a": "65", "equiv_prob_b": "75", "equiv_prob_c": "39", "equiv_prob_d": "45", "equiv_prob_ab": "\\dfrac{65}{75}", "equiv_prob_cd": "\\dfrac{39}{45}", "equiv_ans_ab": "\\dfrac{13}{15}", "equiv_ans_cd": "\\dfrac{13}{15}", "equiv_ans_axd": "2925", "equiv_ans_bxc": "2925", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0984"}}, {"seed": 985, "data": {"simplify_prob": "\\dfrac{110}{264}", "simplify_ans": "\\dfrac{5}{12}", "factors_list": ["2", "11"], "factors_sequence": "2 and 11", "convert_prob": "\\dfrac{91}{15}", "convert_type": "a mixed number", "convert_ans": "6\\frac{1}{15}", "equiv_prob_a": "36", "equiv_prob_b": "42", "equiv_prob_c": "24", "equiv_prob_d": "28", "equiv_prob_ab": "\\dfrac{36}{42}", "equiv_prob_cd": "\\dfrac{24}{28}", "equiv_ans_ab": "\\dfrac{6}{7}", "equiv_ans_cd": "\\dfrac{6}{7}", "equiv_ans_axd": "1008", "equiv_ans_bxc": "1008", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0985"}}, {"seed": 986, "data": {"simplify_prob": "\\dfrac{165}{495}", "simplify_ans": "\\dfrac{1}{3}", "factors_list": ["3", "5", "11"], "factors_sequence": "3, 5, and 11", "convert_prob": "\\dfrac{23}{9}", "convert_type": "a mixed number", "convert_ans": "2\\frac{5}{9}", "equiv_prob_a": "42", "equiv_prob_b": "78", "equiv_prob_c": "56", "equiv_prob_d": "104", "equiv_prob_ab": "\\dfrac{42}{78}", "equiv_prob_cd": "\\dfrac{56}{104}", "equiv_ans_ab": "\\dfrac{7}{13}", "equiv_ans_cd": "\\dfrac{7}{13}", "equiv_ans_axd": "4368", "equiv_ans_bxc": "4368", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0986"}}, {"seed": 987, "data": {"simplify_prob": "\\dfrac{160}{300}", "simplify_ans": "\\dfrac{8}{15}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "\\dfrac{79}{10}", "convert_type": "a mixed number", "convert_ans": "7\\frac{9}{10}", "equiv_prob_a": "70", "equiv_prob_b": "105", "equiv_prob_c": "62", "equiv_prob_d": "93", "equiv_prob_ab": "\\dfrac{70}{105}", "equiv_prob_cd": "\\dfrac{62}{93}", "equiv_ans_ab": "\\dfrac{2}{3}", "equiv_ans_cd": "\\dfrac{2}{3}", "equiv_ans_axd": "6510", "equiv_ans_bxc": "6510", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0987"}}, {"seed": 988, "data": {"simplify_prob": "\\dfrac{44}{396}", "simplify_ans": "\\dfrac{1}{9}", "factors_list": ["2", "2", "11"], "factors_sequence": "2, 2, and 11", "convert_prob": "6\\frac{8}{9}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{62}{9}", "equiv_prob_a": "75", "equiv_prob_b": "200", "equiv_prob_c": "69", "equiv_prob_d": "184", "equiv_prob_ab": "\\dfrac{75}{200}", "equiv_prob_cd": "\\dfrac{69}{184}", "equiv_ans_ab": "\\dfrac{3}{8}", "equiv_ans_cd": "\\dfrac{3}{8}", "equiv_ans_axd": "13800", "equiv_ans_bxc": "13800", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0988"}}, {"seed": 989, "data": {"simplify_prob": "\\dfrac{77}{231}", "simplify_ans": "\\dfrac{1}{3}", "factors_list": ["7", "11"], "factors_sequence": "7 and 11", "convert_prob": "\\dfrac{11}{4}", "convert_type": "a mixed number", "convert_ans": "2\\frac{3}{4}", "equiv_prob_a": "40", "equiv_prob_b": "56", "equiv_prob_c": "60", "equiv_prob_d": "84", "equiv_prob_ab": "\\dfrac{40}{56}", "equiv_prob_cd": "\\dfrac{60}{84}", "equiv_ans_ab": "\\dfrac{5}{7}", "equiv_ans_cd": "\\dfrac{5}{7}", "equiv_ans_axd": "3360", "equiv_ans_bxc": "3360", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0989"}}, {"seed": 990, "data": {"simplify_prob": "\\dfrac{120}{480}", "simplify_ans": "\\dfrac{1}{4}", "factors_list": ["2", "2", "2", "3", "5"], "factors_sequence": "2, 2, 2, 3, and 5", "convert_prob": "\\dfrac{91}{11}", "convert_type": "a mixed number", "convert_ans": "8\\frac{3}{11}", "equiv_prob_a": "5", "equiv_prob_b": "45", "equiv_prob_c": "12", "equiv_prob_d": "51", "equiv_prob_ab": "\\dfrac{5}{45}", "equiv_prob_cd": "\\dfrac{12}{51}", "equiv_ans_ab": "\\dfrac{1}{9}", "equiv_ans_cd": "\\dfrac{4}{17}", "equiv_ans_axd": "255", "equiv_ans_bxc": "540", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0990"}}, {"seed": 991, "data": {"simplify_prob": "\\dfrac{231}{308}", "simplify_ans": "\\dfrac{3}{4}", "factors_list": ["7", "11"], "factors_sequence": "7 and 11", "convert_prob": "\\dfrac{23}{4}", "convert_type": "a mixed number", "convert_ans": "5\\frac{3}{4}", "equiv_prob_a": "6", "equiv_prob_b": "28", "equiv_prob_c": "1", "equiv_prob_d": "21", "equiv_prob_ab": "\\dfrac{6}{28}", "equiv_prob_cd": "\\dfrac{1}{21}", "equiv_ans_ab": "\\dfrac{3}{14}", "equiv_ans_cd": "\\dfrac{1}{21}", "equiv_ans_axd": "126", "equiv_ans_bxc": "28", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0991"}}, {"seed": 992, "data": {"simplify_prob": "\\dfrac{495}{585}", "simplify_ans": "\\dfrac{11}{13}", "factors_list": ["3", "3", "5"], "factors_sequence": "3, 3, and 5", "convert_prob": "\\dfrac{43}{12}", "convert_type": "a mixed number", "convert_ans": "3\\frac{7}{12}", "equiv_prob_a": "25", "equiv_prob_b": "75", "equiv_prob_c": "24", "equiv_prob_d": "72", "equiv_prob_ab": "\\dfrac{25}{75}", "equiv_prob_cd": "\\dfrac{24}{72}", "equiv_ans_ab": "\\dfrac{1}{3}", "equiv_ans_cd": "\\dfrac{1}{3}", "equiv_ans_axd": "1800", "equiv_ans_bxc": "1800", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0992"}}, {"seed": 993, "data": {"simplify_prob": "\\dfrac{220}{240}", "simplify_ans": "\\dfrac{11}{12}", "factors_list": ["2", "2", "5"], "factors_sequence": "2, 2, and 5", "convert_prob": "5\\frac{3}{10}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{53}{10}", "equiv_prob_a": "50", "equiv_prob_b": "65", "equiv_prob_c": "47", "equiv_prob_d": "60", "equiv_prob_ab": "\\dfrac{50}{65}", "equiv_prob_cd": "\\dfrac{47}{60}", "equiv_ans_ab": "\\dfrac{10}{13}", "equiv_ans_cd": "\\dfrac{47}{60}", "equiv_ans_axd": "3000", "equiv_ans_bxc": "3055", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0993"}}, {"seed": 994, "data": {"simplify_prob": "\\dfrac{216}{288}", "simplify_ans": "\\dfrac{3}{4}", "factors_list": ["2", "2", "2", "3", "3"], "factors_sequence": "2, 2, 2, 3, and 3", "convert_prob": "\\dfrac{88}{13}", "convert_type": "a mixed number", "convert_ans": "6\\frac{10}{13}", "equiv_prob_a": "75", "equiv_prob_b": "200", "equiv_prob_c": "78", "equiv_prob_d": "208", "equiv_prob_ab": "\\dfrac{75}{200}", "equiv_prob_cd": "\\dfrac{78}{208}", "equiv_ans_ab": "\\dfrac{3}{8}", "equiv_ans_cd": "\\dfrac{3}{8}", "equiv_ans_axd": "15600", "equiv_ans_bxc": "15600", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0994"}}, {"seed": 995, "data": {"simplify_prob": "\\dfrac{231}{315}", "simplify_ans": "\\dfrac{11}{15}", "factors_list": ["3", "7"], "factors_sequence": "3 and 7", "convert_prob": "7\\frac{5}{6}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{47}{6}", "equiv_prob_a": "21", "equiv_prob_b": "49", "equiv_prob_c": "12", "equiv_prob_d": "28", "equiv_prob_ab": "\\dfrac{21}{49}", "equiv_prob_cd": "\\dfrac{12}{28}", "equiv_ans_ab": "\\dfrac{3}{7}", "equiv_ans_cd": "\\dfrac{3}{7}", "equiv_ans_axd": "588", "equiv_ans_bxc": "588", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0995"}}, {"seed": 996, "data": {"simplify_prob": "\\dfrac{378}{546}", "simplify_ans": "\\dfrac{9}{13}", "factors_list": ["2", "3", "7"], "factors_sequence": "2, 3, and 7", "convert_prob": "\\dfrac{33}{13}", "convert_type": "a mixed number", "convert_ans": "2\\frac{7}{13}", "equiv_prob_a": "4", "equiv_prob_b": "36", "equiv_prob_c": "8", "equiv_prob_d": "38", "equiv_prob_ab": "\\dfrac{4}{36}", "equiv_prob_cd": "\\dfrac{8}{38}", "equiv_ans_ab": "\\dfrac{1}{9}", "equiv_ans_cd": "\\dfrac{4}{19}", "equiv_ans_axd": "152", "equiv_ans_bxc": "288", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0996"}}, {"seed": 997, "data": {"simplify_prob": "\\dfrac{44}{528}", "simplify_ans": "\\dfrac{1}{12}", "factors_list": ["2", "2", "11"], "factors_sequence": "2, 2, and 11", "convert_prob": "5\\frac{1}{3}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{16}{3}", "equiv_prob_a": "100", "equiv_prob_b": "120", "equiv_prob_c": "90", "equiv_prob_d": "108", "equiv_prob_ab": "\\dfrac{100}{120}", "equiv_prob_cd": "\\dfrac{90}{108}", "equiv_ans_ab": "\\dfrac{5}{6}", "equiv_ans_cd": "\\dfrac{5}{6}", "equiv_ans_axd": "10800", "equiv_ans_bxc": "10800", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0997"}}, {"seed": 998, "data": {"simplify_prob": "\\dfrac{352}{572}", "simplify_ans": "\\dfrac{8}{13}", "factors_list": ["2", "2", "11"], "factors_sequence": "2, 2, and 11", "convert_prob": "5\\frac{2}{5}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{27}{5}", "equiv_prob_a": "45", "equiv_prob_b": "50", "equiv_prob_c": "46", "equiv_prob_d": "53", "equiv_prob_ab": "\\dfrac{45}{50}", "equiv_prob_cd": "\\dfrac{46}{53}", "equiv_ans_ab": "\\dfrac{9}{10}", "equiv_ans_cd": "\\dfrac{46}{53}", "equiv_ans_axd": "2385", "equiv_ans_bxc": "2300", "equiv_ans_supp_1": "The fractions are NOT equivalent, since they have different simplest forms.", "equiv_ans_supp_2": "which also shows the fractions are NOT equivalent by the cross product test for equivalence.", "__seed__": "0998"}}, {"seed": 999, "data": {"simplify_prob": "\\dfrac{150}{500}", "simplify_ans": "\\dfrac{3}{10}", "factors_list": ["2", "5", "5"], "factors_sequence": "2, 5, and 5", "convert_prob": "5\\frac{1}{4}", "convert_type": "an improper fraction", "convert_ans": "\\dfrac{21}{4}", "equiv_prob_a": "64", "equiv_prob_b": "176", "equiv_prob_c": "76", "equiv_prob_d": "209", "equiv_prob_ab": "\\dfrac{64}{176}", "equiv_prob_cd": "\\dfrac{76}{209}", "equiv_ans_ab": "\\dfrac{4}{11}", "equiv_ans_cd": "\\dfrac{4}{11}", "equiv_ans_axd": "13376", "equiv_ans_bxc": "13376", "equiv_ans_supp_1": "The fractions are equivalent, since they have the exact same simplest form.", "equiv_ans_supp_2": "which also shows the fractions are equivalent by the cross product test for equivalence.", "__seed__": "0999"}}]}, {"title": "Modeling Fractions", "slug": "F2", "description": "\n I can construct both number line and area models for fractions.\n ", "template": "\n\n \n \n

\\begin{CD} A @>a>> B \\\\ @VbVV @AAcA \\\\ C @= D \\end{CD}

\n
\n \n

This is a test.

\n
\n
\n \n
\n", "exercises": [{"seed": 0, "data": {"__seed__": "0000"}}, {"seed": 1, "data": {"__seed__": "0001"}}, {"seed": 2, "data": {"__seed__": "0002"}}, {"seed": 3, "data": {"__seed__": "0003"}}, {"seed": 4, "data": {"__seed__": "0004"}}, {"seed": 5, "data": {"__seed__": "0005"}}, {"seed": 6, "data": {"__seed__": "0006"}}, {"seed": 7, "data": {"__seed__": "0007"}}, {"seed": 8, "data": {"__seed__": "0008"}}, {"seed": 9, "data": {"__seed__": "0009"}}, {"seed": 10, "data": {"__seed__": "0010"}}, {"seed": 11, "data": {"__seed__": "0011"}}, {"seed": 12, "data": {"__seed__": "0012"}}, {"seed": 13, "data": {"__seed__": "0013"}}, {"seed": 14, "data": {"__seed__": "0014"}}, {"seed": 15, "data": {"__seed__": "0015"}}, {"seed": 16, "data": {"__seed__": "0016"}}, {"seed": 17, "data": {"__seed__": "0017"}}, {"seed": 18, "data": {"__seed__": "0018"}}, {"seed": 19, "data": {"__seed__": "0019"}}, {"seed": 20, "data": {"__seed__": "0020"}}, {"seed": 21, "data": {"__seed__": "0021"}}, {"seed": 22, "data": {"__seed__": "0022"}}, {"seed": 23, "data": {"__seed__": "0023"}}, {"seed": 24, "data": {"__seed__": "0024"}}, {"seed": 25, "data": {"__seed__": "0025"}}, {"seed": 26, "data": {"__seed__": "0026"}}, {"seed": 27, "data": {"__seed__": "0027"}}, {"seed": 28, "data": {"__seed__": "0028"}}, {"seed": 29, "data": {"__seed__": "0029"}}, {"seed": 30, "data": {"__seed__": "0030"}}, {"seed": 31, "data": {"__seed__": "0031"}}, {"seed": 32, "data": {"__seed__": "0032"}}, {"seed": 33, "data": {"__seed__": "0033"}}, {"seed": 34, "data": {"__seed__": "0034"}}, {"seed": 35, "data": {"__seed__": "0035"}}, {"seed": 36, "data": {"__seed__": "0036"}}, {"seed": 37, "data": {"__seed__": "0037"}}, {"seed": 38, "data": {"__seed__": "0038"}}, {"seed": 39, "data": {"__seed__": "0039"}}, {"seed": 40, "data": {"__seed__": "0040"}}, {"seed": 41, "data": {"__seed__": "0041"}}, {"seed": 42, "data": {"__seed__": "0042"}}, {"seed": 43, "data": {"__seed__": "0043"}}, {"seed": 44, "data": {"__seed__": "0044"}}, {"seed": 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{"__seed__": "0861"}}, {"seed": 862, "data": {"__seed__": "0862"}}, {"seed": 863, "data": {"__seed__": "0863"}}, {"seed": 864, "data": {"__seed__": "0864"}}, {"seed": 865, "data": {"__seed__": "0865"}}, {"seed": 866, "data": {"__seed__": "0866"}}, {"seed": 867, "data": {"__seed__": "0867"}}, {"seed": 868, "data": {"__seed__": "0868"}}, {"seed": 869, "data": {"__seed__": "0869"}}, {"seed": 870, "data": {"__seed__": "0870"}}, {"seed": 871, "data": {"__seed__": "0871"}}, {"seed": 872, "data": {"__seed__": "0872"}}, {"seed": 873, "data": {"__seed__": "0873"}}, {"seed": 874, "data": {"__seed__": "0874"}}, {"seed": 875, "data": {"__seed__": "0875"}}, {"seed": 876, "data": {"__seed__": "0876"}}, {"seed": 877, "data": {"__seed__": "0877"}}, {"seed": 878, "data": {"__seed__": "0878"}}, {"seed": 879, "data": {"__seed__": "0879"}}, {"seed": 880, "data": {"__seed__": "0880"}}, {"seed": 881, "data": {"__seed__": "0881"}}, {"seed": 882, "data": {"__seed__": "0882"}}, {"seed": 883, "data": {"__seed__": "0883"}}, {"seed": 884, "data": {"__seed__": "0884"}}, {"seed": 885, "data": {"__seed__": "0885"}}, {"seed": 886, "data": {"__seed__": "0886"}}, {"seed": 887, "data": {"__seed__": "0887"}}, {"seed": 888, "data": {"__seed__": "0888"}}, {"seed": 889, "data": {"__seed__": "0889"}}, {"seed": 890, "data": {"__seed__": "0890"}}, {"seed": 891, "data": {"__seed__": "0891"}}, {"seed": 892, "data": {"__seed__": "0892"}}, {"seed": 893, "data": {"__seed__": "0893"}}, {"seed": 894, "data": {"__seed__": "0894"}}, {"seed": 895, "data": {"__seed__": "0895"}}, {"seed": 896, "data": {"__seed__": "0896"}}, {"seed": 897, "data": {"__seed__": "0897"}}, {"seed": 898, "data": {"__seed__": "0898"}}, {"seed": 899, "data": {"__seed__": "0899"}}, {"seed": 900, "data": {"__seed__": "0900"}}, {"seed": 901, "data": {"__seed__": "0901"}}, {"seed": 902, "data": {"__seed__": "0902"}}, {"seed": 903, "data": {"__seed__": "0903"}}, {"seed": 904, "data": {"__seed__": "0904"}}, {"seed": 905, "data": {"__seed__": "0905"}}, {"seed": 906, "data": {"__seed__": "0906"}}, {"seed": 907, "data": {"__seed__": "0907"}}, {"seed": 908, "data": {"__seed__": "0908"}}, {"seed": 909, "data": {"__seed__": "0909"}}, {"seed": 910, "data": {"__seed__": "0910"}}, {"seed": 911, "data": {"__seed__": "0911"}}, {"seed": 912, "data": {"__seed__": "0912"}}, {"seed": 913, "data": {"__seed__": "0913"}}, {"seed": 914, "data": {"__seed__": "0914"}}, {"seed": 915, "data": {"__seed__": "0915"}}, {"seed": 916, "data": {"__seed__": "0916"}}, {"seed": 917, "data": {"__seed__": "0917"}}, {"seed": 918, "data": {"__seed__": "0918"}}, {"seed": 919, "data": {"__seed__": "0919"}}, {"seed": 920, "data": {"__seed__": "0920"}}, {"seed": 921, "data": {"__seed__": "0921"}}, {"seed": 922, "data": {"__seed__": "0922"}}, {"seed": 923, "data": {"__seed__": "0923"}}, {"seed": 924, "data": {"__seed__": "0924"}}, {"seed": 925, "data": {"__seed__": "0925"}}, {"seed": 926, "data": {"__seed__": "0926"}}, {"seed": 927, "data": {"__seed__": "0927"}}, {"seed": 928, "data": {"__seed__": "0928"}}, {"seed": 929, "data": {"__seed__": "0929"}}, {"seed": 930, "data": {"__seed__": "0930"}}, {"seed": 931, "data": {"__seed__": "0931"}}, {"seed": 932, "data": {"__seed__": "0932"}}, {"seed": 933, "data": {"__seed__": "0933"}}, {"seed": 934, "data": {"__seed__": "0934"}}, {"seed": 935, "data": {"__seed__": "0935"}}, {"seed": 936, "data": {"__seed__": "0936"}}, {"seed": 937, "data": {"__seed__": "0937"}}, {"seed": 938, "data": {"__seed__": "0938"}}, {"seed": 939, "data": {"__seed__": "0939"}}, {"seed": 940, "data": {"__seed__": "0940"}}, {"seed": 941, "data": {"__seed__": "0941"}}, {"seed": 942, "data": {"__seed__": "0942"}}, {"seed": 943, "data": {"__seed__": "0943"}}, {"seed": 944, "data": {"__seed__": "0944"}}, {"seed": 945, "data": {"__seed__": "0945"}}, {"seed": 946, "data": {"__seed__": "0946"}}, {"seed": 947, "data": {"__seed__": "0947"}}, {"seed": 948, "data": {"__seed__": "0948"}}, {"seed": 949, "data": {"__seed__": "0949"}}, {"seed": 950, "data": {"__seed__": "0950"}}, {"seed": 951, "data": {"__seed__": "0951"}}, {"seed": 952, "data": {"__seed__": "0952"}}, {"seed": 953, "data": {"__seed__": "0953"}}, {"seed": 954, "data": {"__seed__": "0954"}}, {"seed": 955, "data": {"__seed__": "0955"}}, {"seed": 956, "data": {"__seed__": "0956"}}, {"seed": 957, "data": {"__seed__": "0957"}}, {"seed": 958, "data": {"__seed__": "0958"}}, {"seed": 959, "data": {"__seed__": "0959"}}, {"seed": 960, "data": {"__seed__": "0960"}}, {"seed": 961, "data": {"__seed__": "0961"}}, {"seed": 962, "data": {"__seed__": "0962"}}, {"seed": 963, "data": {"__seed__": "0963"}}, {"seed": 964, "data": {"__seed__": "0964"}}, {"seed": 965, "data": {"__seed__": "0965"}}, {"seed": 966, "data": {"__seed__": "0966"}}, {"seed": 967, "data": {"__seed__": "0967"}}, {"seed": 968, "data": {"__seed__": "0968"}}, {"seed": 969, "data": {"__seed__": "0969"}}, {"seed": 970, "data": {"__seed__": "0970"}}, {"seed": 971, "data": {"__seed__": "0971"}}, {"seed": 972, "data": {"__seed__": "0972"}}, {"seed": 973, "data": {"__seed__": "0973"}}, {"seed": 974, "data": {"__seed__": "0974"}}, {"seed": 975, "data": {"__seed__": "0975"}}, {"seed": 976, "data": {"__seed__": "0976"}}, {"seed": 977, "data": {"__seed__": "0977"}}, {"seed": 978, "data": {"__seed__": "0978"}}, {"seed": 979, "data": {"__seed__": "0979"}}, {"seed": 980, "data": {"__seed__": "0980"}}, {"seed": 981, "data": {"__seed__": "0981"}}, {"seed": 982, "data": {"__seed__": "0982"}}, {"seed": 983, "data": {"__seed__": "0983"}}, {"seed": 984, "data": {"__seed__": "0984"}}, {"seed": 985, "data": {"__seed__": "0985"}}, {"seed": 986, "data": {"__seed__": "0986"}}, {"seed": 987, "data": {"__seed__": "0987"}}, {"seed": 988, "data": {"__seed__": "0988"}}, {"seed": 989, "data": {"__seed__": "0989"}}, {"seed": 990, "data": {"__seed__": "0990"}}, {"seed": 991, "data": {"__seed__": "0991"}}, {"seed": 992, "data": {"__seed__": "0992"}}, {"seed": 993, "data": {"__seed__": "0993"}}, {"seed": 994, "data": {"__seed__": "0994"}}, {"seed": 995, "data": {"__seed__": "0995"}}, {"seed": 996, "data": {"__seed__": "0996"}}, {"seed": 997, "data": {"__seed__": "0997"}}, {"seed": 998, "data": {"__seed__": "0998"}}, {"seed": 999, "data": {"__seed__": "0999"}}]}, {"title": "Exemplifying the Denseness Property", "slug": "F3", "description": "\n I can, given two rational numbers, find any number of rational numbers between them and, in the case of decimals, place these numbers accurately on a number line.\n ", "template": "\n\n \n \n

Find {{p1_how_many}} rational numbers between {{p1_a}} and {{p1_b}}. {{num_line_directions}}

\n
\n \n \n \n
\n\n \n \n

Find {{p2_how_many}} rational numbers between {{p2_a}} and {{p2_b}}.

\n
\n \n

{{p2_numbers}}

\n
\n
\n \n
\n", "exercises": [{"seed": 0, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.6005, 5.601, 5.602, 5.603, 5.604, 5.605, 5.606, 5.607, 5.608, and 5.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.601", "5.601999999999999", "5.603", "5.603999999999999", "5.6049999999999995", "5.606", "5.606999999999999", "5.608", "5.609"], "p1_2_xs": ["5.600499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{151}{350}, \\dfrac{156}{350}, \\dfrac{159}{350}, \\dfrac{160}{350}, \\dfrac{166}{350}, \\dfrac{171}{350}, \\dfrac{175}{350}, \\dfrac{183}{350}, \\text{ and } \\dfrac{196}{350}", "__seed__": "0000"}}, {"seed": 1, "data": {"p1_how_many": "10", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.5005, 9.501, 9.502, 9.503, 9.504, 9.505, 9.506, 9.507, 9.508, and 9.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.501", "9.502", "9.503", "9.504", "9.505", "9.506", "9.507", "9.508", "9.509"], "p1_2_xs": ["9.5005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}130}{56{,}000}, \\dfrac{16{,}244}{56{,}000}, \\dfrac{16{,}484}{56{,}000}, \\dfrac{16{,}771}{56{,}000}, \\dfrac{17{,}517}{56{,}000}, \\dfrac{17{,}842}{56{,}000}, \\dfrac{18{,}722}{56{,}000}, \\dfrac{19{,}539}{56{,}000}, \\dfrac{20{,}042}{56{,}000}, \\dfrac{20{,}117}{56{,}000}, \\text{ and } \\dfrac{20{,}878}{56{,}000}", "__seed__": "0001"}}, {"seed": 2, "data": {"p1_how_many": "12", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.2005, 9.201, 9.2015, 9.202, 9.2025, 9.203, 9.204, 9.205, 9.206, 9.207, 9.208, and 9.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.200999999999999", "9.202", "9.203", "9.203999999999999", "9.205", "9.206", "9.206999999999999", "9.207999999999998", "9.209"], "p1_2_xs": ["9.2005", "9.2015", "9.2025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{601}{4{,}200}, \\dfrac{612}{4{,}200}, \\dfrac{622}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{654}{4{,}200}, \\dfrac{657}{4{,}200}, \\dfrac{662}{4{,}200}, \\dfrac{666}{4{,}200}, \\dfrac{675}{4{,}200}, \\dfrac{679}{4{,}200}, \\text{ and } \\dfrac{683}{4{,}200}", "__seed__": "0002"}}, {"seed": 3, "data": {"p1_how_many": "12", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0003"}}, {"seed": 4, "data": {"p1_how_many": "11", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{508}{1{,}500}, \\dfrac{523}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{544}{1{,}500}, \\dfrac{563}{1{,}500}, \\dfrac{564}{1{,}500}, \\text{ and } \\dfrac{571}{1{,}500}", "__seed__": "0004"}}, {"seed": 5, "data": {"p1_how_many": "12", "p1_a": "7.01", "p1_b": "7.02", "p1_numbers": "7.0105, 7.011, 7.0115, 7.012, 7.0125, 7.013, 7.014, 7.015, 7.016, 7.017, 7.018, and 7.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.011", "7.012", "7.013", "7.013999999999999", "7.015", "7.016", "7.0169999999999995", "7.018", "7.019"], "p1_2_xs": ["7.0104999999999995", "7.0115", "7.012499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}412}{35{,}000}, \\dfrac{21{,}074}{35{,}000}, \\dfrac{21{,}811}{35{,}000}, \\dfrac{23{,}332}{35{,}000}, \\dfrac{24{,}310}{35{,}000}, \\dfrac{24{,}819}{35{,}000}, \\dfrac{25{,}142}{35{,}000}, \\dfrac{25{,}819}{35{,}000}, \\dfrac{26{,}255}{35{,}000}, \\dfrac{27{,}779}{35{,}000}, \\text{ and } \\dfrac{27{,}860}{35{,}000}", "__seed__": "0005"}}, {"seed": 6, "data": {"p1_how_many": "13", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}132}{5{,}600}, \\dfrac{2{,}133}{5{,}600}, \\dfrac{2{,}151}{5{,}600}, \\dfrac{2{,}152}{5{,}600}, \\dfrac{2{,}203}{5{,}600}, \\dfrac{2{,}235}{5{,}600}, \\dfrac{2{,}256}{5{,}600}, \\dfrac{2{,}307}{5{,}600}, \\dfrac{2{,}330}{5{,}600}, \\dfrac{2{,}340}{5{,}600}, \\dfrac{2{,}368}{5{,}600}, \\text{ and } \\dfrac{2{,}384}{5{,}600}", "__seed__": "0006"}}, {"seed": 7, "data": {"p1_how_many": "14", "p1_a": "6.63", "p1_b": "6.64", "p1_numbers": "6.6305, 6.631, 6.6315, 6.632, 6.6325, 6.633, 6.6335, 6.634, 6.6345, 6.635, 6.636, 6.637, 6.638, and 6.639", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.631", "6.632", "6.633", "6.6339999999999995", "6.635", "6.636", "6.637", "6.638", "6.639"], "p1_2_xs": ["6.6305", "6.6315", "6.632499999999999", "6.6335", "6.634499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0007"}}, {"seed": 8, "data": {"p1_how_many": "14", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.235, 8.24, 8.245, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225", "8.235", "8.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{310}{1{,}200}, \\dfrac{318}{1{,}200}, \\dfrac{323}{1{,}200}, \\dfrac{335}{1{,}200}, \\dfrac{365}{1{,}200}, \\dfrac{387}{1{,}200}, \\dfrac{391}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0008"}}, {"seed": 9, "data": {"p1_how_many": "12", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.725, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999", "1.7249999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}280}{63{,}000}, \\dfrac{28{,}666}{63{,}000}, \\dfrac{29{,}987}{63{,}000}, \\dfrac{31{,}758}{63{,}000}, \\dfrac{32{,}086}{63{,}000}, \\dfrac{33{,}361}{63{,}000}, \\dfrac{33{,}400}{63{,}000}, \\dfrac{34{,}314}{63{,}000}, \\dfrac{34{,}409}{63{,}000}, \\dfrac{35{,}562}{63{,}000}, \\dfrac{35{,}764}{63{,}000}, \\text{ and } \\dfrac{35{,}819}{63{,}000}", "__seed__": "0009"}}, {"seed": 10, "data": {"p1_how_many": "14", "p1_a": "1.32", "p1_b": "1.33", "p1_numbers": "1.3205, 1.321, 1.3215, 1.322, 1.3225, 1.323, 1.3235, 1.324, 1.3245, 1.325, 1.326, 1.327, 1.328, and 1.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.321", "1.322", "1.323", "1.324", "1.325", "1.326", "1.327", "1.328", "1.329"], "p1_2_xs": ["1.3205", "1.3215", "1.3225", "1.3235", "1.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0010"}}, {"seed": 11, "data": {"p1_how_many": "13", "p1_a": "4.01", "p1_b": "4.02", "p1_numbers": "4.0105, 4.011, 4.0115, 4.012, 4.0125, 4.013, 4.0135, 4.014, 4.015, 4.016, 4.017, 4.018, and 4.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.011", "4.012", "4.013", "4.013999999999999", "4.015", "4.016", "4.0169999999999995", "4.018", "4.019"], "p1_2_xs": ["4.0104999999999995", "4.0115", "4.012499999999999", "4.0135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{94}{630}, \\dfrac{95}{630}, \\dfrac{98}{630}, \\dfrac{100}{630}, \\dfrac{103}{630}, \\dfrac{110}{630}, \\dfrac{122}{630}, \\text{ and } \\dfrac{126}{630}", "__seed__": "0011"}}, {"seed": 12, "data": {"p1_how_many": "11", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.215, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998", "1.2149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}085}{20{,}000}, \\dfrac{4{,}204}{20{,}000}, \\dfrac{4{,}209}{20{,}000}, \\dfrac{4{,}325}{20{,}000}, \\dfrac{4{,}327}{20{,}000}, \\dfrac{4{,}333}{20{,}000}, \\dfrac{4{,}637}{20{,}000}, \\dfrac{4{,}656}{20{,}000}, \\dfrac{4{,}738}{20{,}000}, \\dfrac{4{,}794}{20{,}000}, \\dfrac{4{,}831}{20{,}000}, \\text{ and } \\dfrac{4{,}906}{20{,}000}", "__seed__": "0012"}}, {"seed": 13, "data": {"p1_how_many": "10", "p1_a": "9.04", "p1_b": "9.05", "p1_numbers": "9.0405, 9.041, 9.042, 9.043, 9.044, 9.045, 9.046, 9.047, 9.048, and 9.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.040999999999999", "9.042", "9.043", "9.043999999999999", "9.045", "9.046", "9.046999999999999", "9.047999999999998", "9.049"], "p1_2_xs": ["9.0405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{662}{1{,}500}, \\dfrac{688}{1{,}500}, \\dfrac{704}{1{,}500}, \\dfrac{772}{1{,}500}, \\dfrac{791}{1{,}500}, \\dfrac{839}{1{,}500}, \\dfrac{847}{1{,}500}, \\dfrac{853}{1{,}500}, \\dfrac{929}{1{,}500}, \\text{ and } \\dfrac{999}{1{,}500}", "__seed__": "0013"}}, {"seed": 14, "data": {"p1_how_many": "14", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.335, 7.34, 7.345, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999", "7.335", "7.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}265}{12{,}000}, \\dfrac{8{,}267}{12{,}000}, \\dfrac{8{,}276}{12{,}000}, \\dfrac{8{,}441}{12{,}000}, \\dfrac{8{,}755}{12{,}000}, \\dfrac{8{,}806}{12{,}000}, \\dfrac{8{,}933}{12{,}000}, \\text{ and } \\dfrac{8{,}996}{12{,}000}", "__seed__": "0014"}}, {"seed": 15, "data": {"p1_how_many": "14", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.645, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635", "1.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}032}{3{,}500}, \\dfrac{1{,}070}{3{,}500}, \\dfrac{1{,}077}{3{,}500}, \\dfrac{1{,}087}{3{,}500}, \\dfrac{1{,}165}{3{,}500}, \\dfrac{1{,}167}{3{,}500}, \\dfrac{1{,}249}{3{,}500}, \\dfrac{1{,}265}{3{,}500}, \\dfrac{1{,}321}{3{,}500}, \\dfrac{1{,}363}{3{,}500}, \\dfrac{1{,}387}{3{,}500}, \\text{ and } \\dfrac{1{,}399}{3{,}500}", "__seed__": "0015"}}, {"seed": 16, "data": {"p1_how_many": "13", "p1_a": "2.13", "p1_b": "2.14", "p1_numbers": "2.1305, 2.131, 2.1315, 2.132, 2.1325, 2.133, 2.1335, 2.134, 2.135, 2.136, 2.137, 2.138, and 2.139", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.131", "2.1319999999999997", "2.133", "2.134", "2.135", "2.1359999999999997", "2.137", "2.138", "2.139"], "p1_2_xs": ["2.1305", "2.1315", "2.1325", "2.1335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{812}{1{,}200}, \\dfrac{825}{1{,}200}, \\dfrac{843}{1{,}200}, \\dfrac{846}{1{,}200}, \\dfrac{847}{1{,}200}, \\dfrac{854}{1{,}200}, \\text{ and } \\dfrac{868}{1{,}200}", "__seed__": "0016"}}, {"seed": 17, "data": {"p1_how_many": "10", "p1_a": "9.46", "p1_b": "9.47", "p1_numbers": "9.4605, 9.461, 9.462, 9.463, 9.464, 9.465, 9.466, 9.467, 9.468, and 9.469", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.461", "9.462000000000002", "9.463000000000001", "9.464", "9.465000000000002", "9.466000000000001", "9.467", "9.468", "9.469000000000001"], "p1_2_xs": ["9.460500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}072}{3{,}500}, \\dfrac{2{,}130}{3{,}500}, \\dfrac{2{,}135}{3{,}500}, \\dfrac{2{,}257}{3{,}500}, \\dfrac{2{,}260}{3{,}500}, \\dfrac{2{,}371}{3{,}500}, \\dfrac{2{,}379}{3{,}500}, \\dfrac{2{,}636}{3{,}500}, \\dfrac{2{,}763}{3{,}500}, \\dfrac{2{,}778}{3{,}500}, \\text{ and } \\dfrac{2{,}786}{3{,}500}", "__seed__": "0017"}}, {"seed": 18, "data": {"p1_how_many": "11", "p1_a": "9.63", "p1_b": "9.64", "p1_numbers": "9.6305, 9.631, 9.6315, 9.632, 9.633, 9.634, 9.635, 9.636, 9.637, 9.638, and 9.639", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.631", "9.632000000000001", "9.633000000000001", "9.634", "9.635000000000002", "9.636000000000001", "9.637", "9.638", "9.639000000000001"], "p1_2_xs": ["9.630500000000001", "9.6315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}097}{12{,}000}, \\dfrac{8{,}252}{12{,}000}, \\dfrac{8{,}327}{12{,}000}, \\dfrac{8{,}525}{12{,}000}, \\dfrac{8{,}645}{12{,}000}, \\dfrac{8{,}760}{12{,}000}, \\dfrac{8{,}772}{12{,}000}, \\text{ and } \\dfrac{8{,}815}{12{,}000}", "__seed__": "0018"}}, {"seed": 19, "data": {"p1_how_many": "12", "p1_a": "9.34", "p1_b": "9.35", "p1_numbers": "9.3405, 9.341, 9.3415, 9.342, 9.3425, 9.343, 9.344, 9.345, 9.346, 9.347, 9.348, and 9.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.341", "9.342", "9.343", "9.344", "9.345", "9.346", "9.347", "9.347999999999999", "9.349"], "p1_2_xs": ["9.3405", "9.3415", "9.342500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{7{,}002}{56{,}000}, \\dfrac{7{,}021}{56{,}000}, \\dfrac{7{,}096}{56{,}000}, \\dfrac{7{,}159}{56{,}000}, \\dfrac{7{,}220}{56{,}000}, \\dfrac{7{,}321}{56{,}000}, \\dfrac{7{,}407}{56{,}000}, \\dfrac{7{,}408}{56{,}000}, \\dfrac{7{,}512}{56{,}000}, \\dfrac{7{,}689}{56{,}000}, \\dfrac{7{,}702}{56{,}000}, \\text{ and } \\dfrac{7{,}883}{56{,}000}", "__seed__": "0019"}}, {"seed": 20, "data": {"p1_how_many": "13", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{86}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0020"}}, {"seed": 21, "data": {"p1_how_many": "13", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.635, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999", "6.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}397}{20{,}000}, \\dfrac{12{,}749}{20{,}000}, \\dfrac{12{,}842}{20{,}000}, \\dfrac{12{,}851}{20{,}000}, \\dfrac{12{,}910}{20{,}000}, \\dfrac{12{,}936}{20{,}000}, \\dfrac{13{,}440}{20{,}000}, \\dfrac{13{,}549}{20{,}000}, \\dfrac{13{,}897}{20{,}000}, \\dfrac{13{,}941}{20{,}000}, \\dfrac{14{,}010}{20{,}000}, \\text{ and } \\dfrac{14{,}812}{20{,}000}", "__seed__": "0021"}}, {"seed": 22, "data": {"p1_how_many": "10", "p1_a": "9.61", "p1_b": "9.62", "p1_numbers": "9.6105, 9.611, 9.612, 9.613, 9.614, 9.615, 9.616, 9.617, 9.618, and 9.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.610999999999999", "9.612", "9.613", "9.613999999999999", "9.615", "9.616", "9.616999999999999", "9.617999999999999", "9.619"], "p1_2_xs": ["9.6105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}524}{42{,}000}, \\dfrac{30{,}556}{42{,}000}, \\dfrac{31{,}791}{42{,}000}, \\dfrac{32{,}491}{42{,}000}, \\dfrac{32{,}574}{42{,}000}, \\dfrac{33{,}445}{42{,}000}, \\dfrac{33{,}516}{42{,}000}, \\dfrac{33{,}549}{42{,}000}, \\dfrac{33{,}558}{42{,}000}, \\dfrac{34{,}268}{42{,}000}, \\text{ and } \\dfrac{34{,}794}{42{,}000}", "__seed__": "0022"}}, {"seed": 23, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}160}{35{,}000}, \\dfrac{7{,}670}{35{,}000}, \\dfrac{8{,}044}{35{,}000}, \\dfrac{8{,}205}{35{,}000}, \\dfrac{8{,}310}{35{,}000}, \\dfrac{8{,}410}{35{,}000}, \\dfrac{8{,}872}{35{,}000}, \\dfrac{9{,}095}{35{,}000}, \\text{ and } \\dfrac{9{,}911}{35{,}000}", "__seed__": "0023"}}, {"seed": 24, "data": {"p1_how_many": "10", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.52, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{92}{630}, \\dfrac{95}{630}, \\dfrac{108}{630}, \\dfrac{113}{630}, \\dfrac{118}{630}, \\dfrac{130}{630}, \\text{ and } \\dfrac{134}{630}", "__seed__": "0024"}}, {"seed": 25, "data": {"p1_how_many": "12", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}362}{20{,}000}, \\dfrac{4{,}521}{20{,}000}, \\dfrac{4{,}546}{20{,}000}, \\dfrac{4{,}628}{20{,}000}, \\dfrac{4{,}767}{20{,}000}, \\dfrac{4{,}889}{20{,}000}, \\text{ and } \\dfrac{4{,}927}{20{,}000}", "__seed__": "0025"}}, {"seed": 26, "data": {"p1_how_many": "12", "p1_a": "6.83", "p1_b": "6.84", "p1_numbers": "6.8305, 6.831, 6.8315, 6.832, 6.8325, 6.833, 6.834, 6.835, 6.836, 6.837, 6.838, and 6.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.831", "6.832", "6.833", "6.834", "6.835", "6.836", "6.837", "6.838", "6.839"], "p1_2_xs": ["6.8305", "6.8315", "6.8325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0026"}}, {"seed": 27, "data": {"p1_how_many": "12", "p1_a": "2.74", "p1_b": "2.75", "p1_numbers": "2.7405, 2.741, 2.7415, 2.742, 2.7425, 2.743, 2.744, 2.745, 2.746, 2.747, 2.748, and 2.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.741", "2.742", "2.7430000000000003", "2.744", "2.745", "2.746", "2.7470000000000003", "2.748", "2.749"], "p1_2_xs": ["2.7405000000000004", "2.7415000000000003", "2.7425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{501}{2{,}000}, \\dfrac{506}{2{,}000}, \\dfrac{527}{2{,}000}, \\dfrac{592}{2{,}000}, \\dfrac{605}{2{,}000}, \\dfrac{613}{2{,}000}, \\dfrac{671}{2{,}000}, \\dfrac{686}{2{,}000}, \\text{ and } \\dfrac{743}{2{,}000}", "__seed__": "0027"}}, {"seed": 28, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", 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"9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}098}{42{,}000}, \\dfrac{35{,}154}{42{,}000}, \\dfrac{35{,}216}{42{,}000}, \\dfrac{35{,}289}{42{,}000}, \\dfrac{35{,}374}{42{,}000}, \\dfrac{35{,}414}{42{,}000}, \\dfrac{35{,}728}{42{,}000}, \\dfrac{35{,}779}{42{,}000}, \\text{ and } \\dfrac{35{,}852}{42{,}000}", "__seed__": "0029"}}, {"seed": 30, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.5005, 7.501, 7.502, 7.503, 7.504, 7.505, 7.506, 7.507, 7.508, and 7.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.501", "7.502", "7.503", "7.504", "7.505", "7.506", "7.507", "7.508", "7.509"], "p1_2_xs": ["7.5005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}100}{30{,}000}, \\dfrac{5{,}412}{30{,}000}, \\dfrac{5{,}422}{30{,}000}, \\dfrac{5{,}455}{30{,}000}, \\dfrac{5{,}505}{30{,}000}, \\dfrac{5{,}602}{30{,}000}, \\dfrac{5{,}655}{30{,}000}, \\dfrac{5{,}842}{30{,}000}, \\text{ and } \\dfrac{5{,}858}{30{,}000}", "__seed__": "0030"}}, {"seed": 31, "data": {"p1_how_many": "12", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.0005, 7.001, 7.0015, 7.002, 7.0025, 7.003, 7.004, 7.005, 7.006, 7.007, 7.008, and 7.009", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.001", "7.002", "7.003", "7.004", "7.005", "7.006", "7.007", "7.008", "7.009"], "p1_2_xs": ["7.0005", "7.0015", "7.0024999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\dfrac{48}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0031"}}, {"seed": 32, "data": {"p1_how_many": "13", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.135, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125", "8.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}404}{15{,}000}, \\dfrac{7{,}976}{15{,}000}, \\dfrac{8{,}803}{15{,}000}, \\dfrac{9{,}397}{15{,}000}, \\dfrac{9{,}425}{15{,}000}, \\dfrac{9{,}637}{15{,}000}, \\dfrac{9{,}680}{15{,}000}, \\dfrac{9{,}685}{15{,}000}, \\text{ and } \\dfrac{9{,}786}{15{,}000}", "__seed__": "0032"}}, {"seed": 33, "data": {"p1_how_many": "11", "p1_a": "1.23", "p1_b": "1.24", "p1_numbers": "1.2305, 1.231, 1.2315, 1.232, 1.233, 1.234, 1.235, 1.236, 1.237, 1.238, and 1.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.2309999999999999", "1.232", "1.2329999999999999", "1.234", "1.2349999999999999", "1.236", "1.2369999999999999", "1.238", "1.2389999999999999"], "p1_2_xs": ["1.2305", "1.2314999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}016}{56{,}000}, \\dfrac{48{,}038}{56{,}000}, \\dfrac{48{,}193}{56{,}000}, \\dfrac{48{,}332}{56{,}000}, \\dfrac{48{,}431}{56{,}000}, \\dfrac{48{,}644}{56{,}000}, \\dfrac{48{,}711}{56{,}000}, \\dfrac{48{,}752}{56{,}000}, \\text{ and } \\dfrac{48{,}813}{56{,}000}", "__seed__": "0033"}}, {"seed": 34, "data": {"p1_how_many": "11", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0034"}}, {"seed": 35, "data": {"p1_how_many": "12", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.025, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015", "6.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{62}{150}, \\dfrac{68}{150}, \\dfrac{75}{150}, \\dfrac{76}{150}, \\dfrac{89}{150}, \\dfrac{94}{150}, \\text{ and } \\dfrac{96}{150}", "__seed__": "0035"}}, {"seed": 36, "data": {"p1_how_many": "11", "p1_a": "9.87", "p1_b": "9.88", "p1_numbers": "9.8705, 9.871, 9.8715, 9.872, 9.873, 9.874, 9.875, 9.876, 9.877, 9.878, and 9.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.870999999999999", "9.872", "9.873", "9.873999999999999", "9.875", "9.876", "9.876999999999999", "9.877999999999998", "9.879"], "p1_2_xs": ["9.8705", "9.8715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}046}{42{,}000}, \\dfrac{35{,}130}{42{,}000}, \\dfrac{35{,}275}{42{,}000}, \\dfrac{35{,}322}{42{,}000}, \\dfrac{35{,}331}{42{,}000}, \\dfrac{35{,}406}{42{,}000}, \\dfrac{35{,}471}{42{,}000}, \\dfrac{35{,}574}{42{,}000}, \\dfrac{35{,}845}{42{,}000}, \\dfrac{35{,}896}{42{,}000}, \\dfrac{35{,}917}{42{,}000}, \\text{ and } \\dfrac{35{,}969}{42{,}000}", "__seed__": "0036"}}, {"seed": 37, "data": {"p1_how_many": "10", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.12, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}725}{5{,}600}, \\dfrac{1{,}757}{5{,}600}, \\dfrac{1{,}811}{5{,}600}, \\dfrac{1{,}844}{5{,}600}, \\dfrac{1{,}901}{5{,}600}, \\dfrac{1{,}936}{5{,}600}, \\dfrac{1{,}945}{5{,}600}, \\dfrac{2{,}044}{5{,}600}, \\dfrac{2{,}075}{5{,}600}, \\text{ and } \\dfrac{2{,}091}{5{,}600}", "__seed__": "0037"}}, {"seed": 38, "data": {"p1_how_many": "14", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.535, 1.54, 1.545, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525", "1.535", "1.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{163}{350}, \\dfrac{173}{350}, \\dfrac{189}{350}, \\dfrac{193}{350}, \\dfrac{195}{350}, \\dfrac{198}{350}, \\dfrac{202}{350}, \\text{ and } \\dfrac{208}{350}", "__seed__": "0038"}}, {"seed": 39, "data": {"p1_how_many": "11", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{402}{2{,}000}, \\dfrac{412}{2{,}000}, \\dfrac{416}{2{,}000}, \\dfrac{429}{2{,}000}, \\dfrac{436}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{467}{2{,}000}, \\dfrac{473}{2{,}000}, \\dfrac{490}{2{,}000}, \\dfrac{491}{2{,}000}, \\text{ and } \\dfrac{492}{2{,}000}", "__seed__": "0039"}}, {"seed": 40, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}002}{42{,}000}, \\dfrac{6{,}142}{42{,}000}, \\dfrac{6{,}165}{42{,}000}, \\dfrac{6{,}275}{42{,}000}, \\dfrac{6{,}397}{42{,}000}, \\dfrac{6{,}408}{42{,}000}, \\dfrac{6{,}532}{42{,}000}, \\dfrac{6{,}971}{42{,}000}, \\text{ and } \\dfrac{6{,}989}{42{,}000}", "__seed__": "0040"}}, {"seed": 41, "data": {"p1_how_many": "12", "p1_a": "5.45", "p1_b": "5.46", "p1_numbers": "5.4505, 5.451, 5.4515, 5.452, 5.4525, 5.453, 5.454, 5.455, 5.456, 5.457, 5.458, and 5.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.4510000000000005", "5.452", "5.453", "5.454", "5.455", "5.456", "5.457", "5.458", "5.4590000000000005"], "p1_2_xs": ["5.4505", "5.4515", "5.4525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}016}{35{,}000}, \\dfrac{20{,}316}{35{,}000}, \\dfrac{20{,}375}{35{,}000}, \\dfrac{20{,}429}{35{,}000}, \\dfrac{20{,}494}{35{,}000}, \\dfrac{20{,}507}{35{,}000}, \\dfrac{20{,}544}{35{,}000}, \\dfrac{20{,}580}{35{,}000}, \\dfrac{20{,}601}{35{,}000}, \\dfrac{20{,}637}{35{,}000}, \\dfrac{20{,}651}{35{,}000}, \\text{ and } \\dfrac{20{,}830}{35{,}000}", "__seed__": "0041"}}, {"seed": 42, "data": {"p1_how_many": "14", "p1_a": "3.07", "p1_b": "3.08", "p1_numbers": 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"\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725", "3.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}230}{2{,}000}, \\dfrac{1{,}237}{2{,}000}, \\dfrac{1{,}299}{2{,}000}, \\dfrac{1{,}354}{2{,}000}, \\dfrac{1{,}362}{2{,}000}, \\dfrac{1{,}371}{2{,}000}, \\dfrac{1{,}388}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\text{ and } \\dfrac{1{,}443}{2{,}000}", "__seed__": "0043"}}, {"seed": 44, "data": {"p1_how_many": "13", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", 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"num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{67}{150}, \\dfrac{70}{150}, \\dfrac{71}{150}, \\dfrac{72}{150}, \\dfrac{74}{150}, \\dfrac{80}{150}, \\dfrac{82}{150}, \\dfrac{83}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0045"}}, {"seed": 46, "data": {"p1_how_many": "12", "p1_a": "6.4", "p1_b": "6.5", "p1_numbers": "6.405, 6.41, 6.415, 6.42, 6.425, 6.43, 6.44, 6.45, 6.46, 6.47, 6.48, and 6.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.41", "6.42", "6.430000000000001", "6.44", "6.45", "6.46", "6.470000000000001", "6.48", "6.49"], "p1_2_xs": ["6.405", "6.415", "6.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}362}{2{,}000}, 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{"seed": 48, "data": {"p1_how_many": "13", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.125, 9.13, 9.135, 9.14, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125", "9.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{99}{630}, \\dfrac{102}{630}, \\dfrac{112}{630}, \\dfrac{116}{630}, \\dfrac{122}{630}, \\dfrac{127}{630}, \\dfrac{130}{630}, \\dfrac{135}{630}, \\text{ and } \\dfrac{139}{630}", "__seed__": "0048"}}, {"seed": 49, "data": {"p1_how_many": "11", "p1_a": "2.14", "p1_b": "2.15", "p1_numbers": "2.1405, 2.141, 2.1415, 2.142, 2.143, 2.144, 2.145, 2.146, 2.147, 2.148, and 2.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.141", "2.142", "2.1430000000000002", "2.144", "2.145", "2.146", "2.1470000000000002", "2.148", "2.149"], "p1_2_xs": ["2.1405000000000003", "2.1415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}012}{15{,}000}, \\dfrac{5{,}026}{15{,}000}, \\dfrac{5{,}159}{15{,}000}, \\dfrac{5{,}212}{15{,}000}, \\dfrac{5{,}441}{15{,}000}, \\dfrac{5{,}513}{15{,}000}, \\dfrac{5{,}543}{15{,}000}, \\dfrac{5{,}769}{15{,}000}, \\dfrac{5{,}854}{15{,}000}, \\dfrac{5{,}953}{15{,}000}, \\dfrac{5{,}979}{15{,}000}, \\text{ and } \\dfrac{5{,}995}{15{,}000}", "__seed__": "0049"}}, {"seed": 50, "data": {"p1_how_many": "10", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}227}{2{,}000}, \\dfrac{1{,}283}{2{,}000}, \\dfrac{1{,}332}{2{,}000}, \\dfrac{1{,}369}{2{,}000}, \\dfrac{1{,}398}{2{,}000}, \\dfrac{1{,}412}{2{,}000}, \\dfrac{1{,}458}{2{,}000}, \\dfrac{1{,}482}{2{,}000}, \\text{ and } \\dfrac{1{,}487}{2{,}000}", "__seed__": "0050"}}, {"seed": 51, "data": {"p1_how_many": "13", "p1_a": "7.75", "p1_b": "7.76", "p1_numbers": "7.7505, 7.751, 7.7515, 7.752, 7.7525, 7.753, 7.7535, 7.754, 7.755, 7.756, 7.757, 7.758, and 7.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.751", "7.752", "7.753", "7.754", "7.755", "7.756", "7.757", "7.758", "7.759"], "p1_2_xs": ["7.7505", "7.7515", "7.7524999999999995", "7.7535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}002}{42{,}000}, \\dfrac{6{,}085}{42{,}000}, \\dfrac{6{,}107}{42{,}000}, \\dfrac{6{,}202}{42{,}000}, \\dfrac{6{,}246}{42{,}000}, \\dfrac{6{,}258}{42{,}000}, \\dfrac{6{,}313}{42{,}000}, \\dfrac{6{,}317}{42{,}000}, \\dfrac{6{,}487}{42{,}000}, \\dfrac{6{,}639}{42{,}000}, \\dfrac{6{,}726}{42{,}000}, \\text{ and } \\dfrac{6{,}831}{42{,}000}", "__seed__": "0051"}}, {"seed": 52, "data": {"p1_how_many": "10", "p1_a": "2.9", "p1_b": "2.1", "p1_numbers": "2.9005, 2.901, 2.902, 2.903, 2.904, 2.905, 2.906, 2.907, 2.908, and 2.909", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.901", "2.9019999999999997", "2.903", "2.904", "2.905", "2.9059999999999997", "2.907", "2.908", "2.909"], "p1_2_xs": ["2.9005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}514}{42{,}000}, \\dfrac{30{,}914}{42{,}000}, \\dfrac{31{,}270}{42{,}000}, \\dfrac{31{,}534}{42{,}000}, \\dfrac{31{,}891}{42{,}000}, \\dfrac{32{,}684}{42{,}000}, \\dfrac{32{,}988}{42{,}000}, \\dfrac{33{,}024}{42{,}000}, \\dfrac{33{,}103}{42{,}000}, \\dfrac{34{,}500}{42{,}000}, \\dfrac{34{,}832}{42{,}000}, \\text{ and } \\dfrac{34{,}929}{42{,}000}", "__seed__": "0052"}}, {"seed": 53, "data": {"p1_how_many": "12", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.625, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998", "2.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}644}{3{,}500}, \\dfrac{1{,}651}{3{,}500}, \\dfrac{1{,}693}{3{,}500}, \\dfrac{1{,}835}{3{,}500}, \\dfrac{2{,}002}{3{,}500}, \\dfrac{2{,}014}{3{,}500}, \\text{ and } \\dfrac{2{,}083}{3{,}500}", "__seed__": "0053"}}, {"seed": 54, "data": {"p1_how_many": "13", "p1_a": "5.83", "p1_b": "5.84", "p1_numbers": "5.8305, 5.831, 5.8315, 5.832, 5.8325, 5.833, 5.8335, 5.834, 5.835, 5.836, 5.837, 5.838, and 5.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.831", "5.832", "5.833", "5.834", "5.835", "5.836", "5.837", "5.838", "5.839"], "p1_2_xs": ["5.8305", "5.8315", "5.8325", "5.8335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}724}{6{,}300}, \\dfrac{2{,}731}{6{,}300}, \\dfrac{2{,}735}{6{,}300}, \\dfrac{2{,}760}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}790}{6{,}300}, \\text{ and } \\dfrac{2{,}793}{6{,}300}", "__seed__": "0054"}}, {"seed": 55, "data": {"p1_how_many": "11", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.63, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}202}{5{,}600}, \\dfrac{3{,}207}{5{,}600}, \\dfrac{3{,}264}{5{,}600}, \\dfrac{3{,}287}{5{,}600}, \\dfrac{3{,}338}{5{,}600}, \\dfrac{3{,}346}{5{,}600}, \\dfrac{3{,}422}{5{,}600}, \\dfrac{3{,}442}{5{,}600}, \\text{ and } \\dfrac{3{,}479}{5{,}600}", "__seed__": "0055"}}, {"seed": 56, "data": {"p1_how_many": "14", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.745, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735", "2.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}096}{12{,}000}, \\dfrac{3{,}121}{12{,}000}, \\dfrac{3{,}129}{12{,}000}, \\dfrac{3{,}182}{12{,}000}, \\dfrac{3{,}185}{12{,}000}, \\dfrac{3{,}299}{12{,}000}, \\dfrac{3{,}377}{12{,}000}, \\dfrac{3{,}440}{12{,}000}, \\dfrac{3{,}514}{12{,}000}, \\dfrac{3{,}697}{12{,}000}, \\dfrac{3{,}989}{12{,}000}, \\text{ and } \\dfrac{3{,}991}{12{,}000}", "__seed__": "0056"}}, {"seed": 57, "data": {"p1_how_many": "14", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.445, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435", "9.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}010}{63{,}000}, \\dfrac{27{,}035}{63{,}000}, \\dfrac{27{,}081}{63{,}000}, \\dfrac{27{,}371}{63{,}000}, \\dfrac{27{,}396}{63{,}000}, \\dfrac{27{,}611}{63{,}000}, \\dfrac{27{,}677}{63{,}000}, \\dfrac{27{,}785}{63{,}000}, \\text{ and } \\dfrac{27{,}888}{63{,}000}", "__seed__": "0057"}}, {"seed": 58, "data": {"p1_how_many": "11", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}139}{15{,}000}, \\dfrac{6{,}251}{15{,}000}, \\dfrac{7{,}090}{15{,}000}, \\dfrac{7{,}387}{15{,}000}, \\dfrac{8{,}199}{15{,}000}, \\dfrac{8{,}257}{15{,}000}, \\dfrac{8{,}737}{15{,}000}, \\dfrac{8{,}972}{15{,}000}, \\dfrac{9{,}488}{15{,}000}, \\dfrac{9{,}505}{15{,}000}, \\dfrac{9{,}609}{15{,}000}, \\text{ and } \\dfrac{9{,}781}{15{,}000}", "__seed__": "0058"}}, {"seed": 59, "data": {"p1_how_many": "12", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.625, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 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"6.46", "6.470000000000001", "6.48", "6.49"], "p1_2_xs": ["6.405", "6.415", "6.425", "6.4350000000000005", "6.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}742}{3{,}500}, \\dfrac{1{,}780}{3{,}500}, \\dfrac{1{,}821}{3{,}500}, \\dfrac{1{,}849}{3{,}500}, \\dfrac{1{,}854}{3{,}500}, \\dfrac{1{,}865}{3{,}500}, \\dfrac{1{,}967}{3{,}500}, \\text{ and } \\dfrac{2{,}019}{3{,}500}", "__seed__": "0060"}}, {"seed": 61, "data": {"p1_how_many": "10", "p1_a": "7.2", "p1_b": "7.3", "p1_numbers": "7.205, 7.21, 7.22, 7.23, 7.24, 7.25, 7.26, 7.27, 7.28, and 7.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.21", "7.22", "7.23", "7.24", "7.25", "7.26", "7.2700000000000005", "7.28", "7.29"], "p1_2_xs": ["7.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number 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"\\dfrac{320}{1{,}200}, \\dfrac{326}{1{,}200}, \\dfrac{335}{1{,}200}, \\dfrac{337}{1{,}200}, \\dfrac{339}{1{,}200}, \\dfrac{347}{1{,}200}, \\text{ and } \\dfrac{368}{1{,}200}", "__seed__": "0062"}}, {"seed": 63, "data": {"p1_how_many": "12", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}502}{2{,}000}, \\dfrac{1{,}516}{2{,}000}, \\dfrac{1{,}527}{2{,}000}, \\dfrac{1{,}529}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}551}{2{,}000}, \\dfrac{1{,}554}{2{,}000}, \\dfrac{1{,}569}{2{,}000}, \\text{ and } \\dfrac{1{,}586}{2{,}000}", "__seed__": "0063"}}, {"seed": 64, "data": {"p1_how_many": "14", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.645, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635", "1.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}170}{35{,}000}, \\dfrac{21{,}438}{35{,}000}, \\dfrac{22{,}800}{35{,}000}, \\dfrac{22{,}932}{35{,}000}, \\dfrac{23{,}416}{35{,}000}, \\dfrac{24{,}133}{35{,}000}, \\dfrac{25{,}067}{35{,}000}, \\dfrac{25{,}967}{35{,}000}, \\dfrac{26{,}570}{35{,}000}, \\text{ and } \\dfrac{26{,}586}{35{,}000}", "__seed__": "0064"}}, {"seed": 65, "data": {"p1_how_many": "11", "p1_a": "5.25", "p1_b": "5.26", "p1_numbers": "5.2505, 5.251, 5.2515, 5.252, 5.253, 5.254, 5.255, 5.256, 5.257, 5.258, and 5.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.251", "5.252", "5.253", "5.254", "5.255", "5.256", "5.257", "5.258", "5.259"], "p1_2_xs": ["5.2505", "5.2515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}509}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}524}{4{,}200}, \\dfrac{3{,}526}{4{,}200}, \\dfrac{3{,}534}{4{,}200}, \\dfrac{3{,}540}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\dfrac{3{,}588}{4{,}200}, \\text{ and } \\dfrac{3{,}599}{4{,}200}", "__seed__": "0065"}}, {"seed": 66, "data": {"p1_how_many": "12", "p1_a": "4.44", "p1_b": "4.45", "p1_numbers": "4.4405, 4.441, 4.4415, 4.442, 4.4425, 4.443, 4.444, 4.445, 4.446, 4.447, 4.448, and 4.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.441000000000001", "4.442", "4.4430000000000005", "4.444", "4.445", "4.446000000000001", "4.447", "4.448", "4.449000000000001"], "p1_2_xs": ["4.4405", "4.4415000000000004", "4.4425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{604}{1{,}500}, \\dfrac{662}{1{,}500}, \\dfrac{669}{1{,}500}, \\dfrac{771}{1{,}500}, \\dfrac{794}{1{,}500}, \\dfrac{807}{1{,}500}, \\dfrac{860}{1{,}500}, \\dfrac{875}{1{,}500}, \\dfrac{927}{1{,}500}, \\text{ and } \\dfrac{991}{1{,}500}", "__seed__": "0066"}}, {"seed": 67, "data": {"p1_how_many": "11", "p1_a": "4.02", "p1_b": "4.03", "p1_numbers": "4.0205, 4.021, 4.0215, 4.022, 4.023, 4.024, 4.025, 4.026, 4.027, 4.028, and 4.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.021", "4.021999999999999", "4.023", "4.023999999999999", "4.0249999999999995", "4.026", "4.026999999999999", "4.028", "4.029"], "p1_2_xs": ["4.020499999999999", "4.0215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}531}{5{,}600}, \\dfrac{3{,}604}{5{,}600}, \\dfrac{3{,}626}{5{,}600}, \\dfrac{3{,}708}{5{,}600}, \\dfrac{3{,}763}{5{,}600}, \\dfrac{3{,}815}{5{,}600}, \\dfrac{3{,}829}{5{,}600}, \\dfrac{3{,}868}{5{,}600}, \\dfrac{3{,}874}{5{,}600}, \\dfrac{3{,}884}{5{,}600}, \\text{ and } \\dfrac{3{,}951}{5{,}600}", "__seed__": "0067"}}, {"seed": 68, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}096}{30{,}000}, \\dfrac{24{,}225}{30{,}000}, \\dfrac{24{,}249}{30{,}000}, \\dfrac{24{,}451}{30{,}000}, \\dfrac{24{,}458}{30{,}000}, \\dfrac{24{,}464}{30{,}000}, \\dfrac{24{,}497}{30{,}000}, \\dfrac{24{,}535}{30{,}000}, \\dfrac{24{,}629}{30{,}000}, \\dfrac{24{,}735}{30{,}000}, \\text{ and } \\dfrac{24{,}998}{30{,}000}", "__seed__": "0068"}}, {"seed": 69, "data": {"p1_how_many": "10", "p1_a": "9.72", "p1_b": "9.73", "p1_numbers": "9.7205, 9.721, 9.722, 9.723, 9.724, 9.725, 9.726, 9.727, 9.728, and 9.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.721", "9.722000000000001", "9.723", "9.724", "9.725000000000001", "9.726", "9.727", "9.728", "9.729000000000001"], "p1_2_xs": ["9.720500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}219}{2{,}000}, \\dfrac{1{,}244}{2{,}000}, \\dfrac{1{,}291}{2{,}000}, \\dfrac{1{,}303}{2{,}000}, \\dfrac{1{,}368}{2{,}000}, \\dfrac{1{,}393}{2{,}000}, \\dfrac{1{,}425}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\dfrac{1{,}453}{2{,}000}, \\text{ and } \\dfrac{1{,}496}{2{,}000}", "__seed__": "0069"}}, {"seed": 70, "data": {"p1_how_many": "13", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}501}{4{,}200}, \\dfrac{3{,}505}{4{,}200}, \\dfrac{3{,}512}{4{,}200}, \\dfrac{3{,}532}{4{,}200}, \\dfrac{3{,}544}{4{,}200}, \\dfrac{3{,}546}{4{,}200}, \\text{ and } \\dfrac{3{,}593}{4{,}200}", "__seed__": "0070"}}, {"seed": 71, "data": {"p1_how_many": "14", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.545, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535", "7.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}005}{30{,}000}, \\dfrac{5{,}014}{30{,}000}, \\dfrac{5{,}075}{30{,}000}, \\dfrac{5{,}109}{30{,}000}, \\dfrac{5{,}231}{30{,}000}, \\dfrac{5{,}295}{30{,}000}, \\dfrac{5{,}352}{30{,}000}, \\dfrac{5{,}408}{30{,}000}, \\dfrac{5{,}589}{30{,}000}, \\dfrac{5{,}809}{30{,}000}, \\dfrac{5{,}908}{30{,}000}, \\text{ and } \\dfrac{5{,}966}{30{,}000}", "__seed__": "0071"}}, {"seed": 72, "data": {"p1_how_many": "10", "p1_a": "3.33", "p1_b": "3.34", "p1_numbers": "3.3305, 3.331, 3.332, 3.333, 3.334, 3.335, 3.336, 3.337, 3.338, and 3.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.331", "3.332", "3.333", "3.334", "3.335", "3.336", "3.337", "3.338", "3.339"], "p1_2_xs": ["3.3305000000000002"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}154}{20{,}000}, \\dfrac{4{,}171}{20{,}000}, \\dfrac{4{,}205}{20{,}000}, \\dfrac{4{,}251}{20{,}000}, \\dfrac{4{,}341}{20{,}000}, \\dfrac{4{,}693}{20{,}000}, \\dfrac{4{,}717}{20{,}000}, \\dfrac{4{,}802}{20{,}000}, \\text{ and } \\dfrac{4{,}962}{20{,}000}", "__seed__": "0072"}}, {"seed": 73, "data": {"p1_how_many": "10", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}381}{56{,}000}, \\dfrac{17{,}260}{56{,}000}, \\dfrac{17{,}752}{56{,}000}, \\dfrac{19{,}208}{56{,}000}, \\dfrac{20{,}611}{56{,}000}, \\dfrac{20{,}659}{56{,}000}, 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{"p1_how_many": "11", "p1_a": "6.03", "p1_b": "6.04", "p1_numbers": "6.0305, 6.031, 6.0315, 6.032, 6.033, 6.034, 6.035, 6.036, 6.037, 6.038, and 6.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.031000000000001", "6.032", "6.033", "6.034", "6.035", "6.0360000000000005", "6.037", "6.038", "6.039000000000001"], "p1_2_xs": ["6.0305", "6.0315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}400}{56{,}000}, \\dfrac{35{,}794}{56{,}000}, \\dfrac{36{,}842}{56{,}000}, \\dfrac{36{,}969}{56{,}000}, \\dfrac{37{,}025}{56{,}000}, \\dfrac{37{,}171}{56{,}000}, \\dfrac{38{,}336}{56{,}000}, \\dfrac{38{,}610}{56{,}000}, \\dfrac{38{,}915}{56{,}000}, \\dfrac{39{,}451}{56{,}000}, \\dfrac{39{,}631}{56{,}000}, \\text{ and } \\dfrac{39{,}775}{56{,}000}", "__seed__": "0075"}}, {"seed": 76, "data": {"p1_how_many": "12", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}094}{42{,}000}, \\dfrac{30{,}326}{42{,}000}, \\dfrac{30{,}504}{42{,}000}, \\dfrac{31{,}340}{42{,}000}, \\dfrac{31{,}374}{42{,}000}, \\dfrac{31{,}765}{42{,}000}, \\dfrac{32{,}079}{42{,}000}, \\dfrac{32{,}206}{42{,}000}, \\dfrac{32{,}417}{42{,}000}, \\dfrac{32{,}733}{42{,}000}, \\dfrac{33{,}990}{42{,}000}, \\text{ and } \\dfrac{34{,}154}{42{,}000}", "__seed__": "0076"}}, {"seed": 77, "data": {"p1_how_many": "11", "p1_a": "9.33", "p1_b": "9.34", "p1_numbers": "9.3305, 9.331, 9.3315, 9.332, 9.333, 9.334, 9.335, 9.336, 9.337, 9.338, and 9.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.331", "9.332", "9.333", "9.334", "9.335", "9.336", "9.337", "9.338", "9.339"], "p1_2_xs": ["9.3305", "9.3315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}001}{42{,}000}, \\dfrac{35{,}087}{42{,}000}, \\dfrac{35{,}099}{42{,}000}, \\dfrac{35{,}105}{42{,}000}, \\dfrac{35{,}185}{42{,}000}, \\dfrac{35{,}211}{42{,}000}, \\dfrac{35{,}658}{42{,}000}, \\dfrac{35{,}698}{42{,}000}, \\dfrac{35{,}769}{42{,}000}, \\dfrac{35{,}838}{42{,}000}, \\dfrac{35{,}896}{42{,}000}, \\text{ and } \\dfrac{35{,}988}{42{,}000}", "__seed__": "0077"}}, {"seed": 78, "data": {"p1_how_many": "14", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.345, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335", "5.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}645}{42{,}000}, \\dfrac{8{,}108}{42{,}000}, \\dfrac{8{,}231}{42{,}000}, \\dfrac{10{,}099}{42{,}000}, \\dfrac{10{,}474}{42{,}000}, \\dfrac{11{,}030}{42{,}000}, \\dfrac{11{,}118}{42{,}000}, \\dfrac{11{,}320}{42{,}000}, \\dfrac{11{,}354}{42{,}000}, \\dfrac{11{,}373}{42{,}000}, \\dfrac{11{,}631}{42{,}000}, \\text{ and } \\dfrac{11{,}680}{42{,}000}", "__seed__": "0078"}}, {"seed": 79, "data": {"p1_how_many": "14", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.735, 3.74, 3.745, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725", "3.735", "3.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}056}{12{,}000}, \\dfrac{3{,}068}{12{,}000}, \\dfrac{3{,}205}{12{,}000}, \\dfrac{3{,}260}{12{,}000}, \\dfrac{3{,}401}{12{,}000}, \\dfrac{3{,}479}{12{,}000}, \\dfrac{3{,}525}{12{,}000}, \\dfrac{3{,}606}{12{,}000}, \\dfrac{3{,}626}{12{,}000}, \\dfrac{3{,}816}{12{,}000}, \\dfrac{3{,}829}{12{,}000}, \\text{ and } \\dfrac{3{,}927}{12{,}000}", "__seed__": "0079"}}, {"seed": 80, "data": {"p1_how_many": "14", "p1_a": "8.56", "p1_b": "8.57", "p1_numbers": "8.5605, 8.561, 8.5615, 8.562, 8.5625, 8.563, 8.5635, 8.564, 8.5645, 8.565, 8.566, 8.567, 8.568, and 8.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.561", "8.562000000000001", "8.563", "8.564", "8.565000000000001", "8.566", "8.567", "8.568", "8.569"], "p1_2_xs": ["8.560500000000001", "8.5615", "8.562500000000002", "8.563500000000001", "8.5645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}600}{63{,}000}, \\dfrac{14{,}690}{63{,}000}, \\dfrac{14{,}767}{63{,}000}, \\dfrac{14{,}896}{63{,}000}, \\dfrac{15{,}153}{63{,}000}, \\dfrac{15{,}208}{63{,}000}, \\dfrac{15{,}435}{63{,}000}, \\dfrac{15{,}443}{63{,}000}, \\dfrac{15{,}480}{63{,}000}, \\dfrac{16{,}665}{63{,}000}, \\text{ and } \\dfrac{17{,}677}{63{,}000}", "__seed__": "0080"}}, {"seed": 81, "data": {"p1_how_many": "12", "p1_a": "6.25", "p1_b": "6.26", "p1_numbers": "6.2505, 6.251, 6.2515, 6.252, 6.2525, 6.253, 6.254, 6.255, 6.256, 6.257, 6.258, and 6.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.251", "6.252", "6.253", "6.254", "6.255", "6.256", "6.257", "6.258", "6.259"], "p1_2_xs": ["6.2505", "6.2515", "6.2524999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}209}{2{,}000}, \\dfrac{1{,}238}{2{,}000}, \\dfrac{1{,}305}{2{,}000}, \\dfrac{1{,}326}{2{,}000}, \\dfrac{1{,}328}{2{,}000}, \\dfrac{1{,}338}{2{,}000}, \\dfrac{1{,}426}{2{,}000}, \\dfrac{1{,}469}{2{,}000}, \\dfrac{1{,}489}{2{,}000}, \\text{ and } \\dfrac{1{,}493}{2{,}000}", "__seed__": "0081"}}, {"seed": 82, "data": {"p1_how_many": "12", "p1_a": "3.82", "p1_b": "3.83", "p1_numbers": "3.8205, 3.821, 3.8215, 3.822, 3.8225, 3.823, 3.824, 3.825, 3.826, 3.827, 3.828, and 3.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.8209999999999997", "3.8219999999999996", "3.823", "3.824", "3.8249999999999997", "3.8259999999999996", "3.827", "3.828", "3.8289999999999997"], "p1_2_xs": ["3.8205", "3.8215", "3.8225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{32{,}442}{42{,}000}, \\dfrac{32{,}593}{42{,}000}, \\dfrac{33{,}170}{42{,}000}, \\dfrac{33{,}298}{42{,}000}, \\dfrac{33{,}949}{42{,}000}, \\dfrac{34{,}283}{42{,}000}, \\text{ and } \\dfrac{34{,}909}{42{,}000}", "__seed__": "0082"}}, {"seed": 83, "data": {"p1_how_many": "12", "p1_a": "8.61", "p1_b": "8.62", "p1_numbers": "8.6105, 8.611, 8.6115, 8.612, 8.6125, 8.613, 8.614, 8.615, 8.616, 8.617, 8.618, and 8.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.610999999999999", "8.612", "8.613", "8.613999999999999", "8.615", "8.616", "8.616999999999999", "8.617999999999999", "8.619"], "p1_2_xs": ["8.6105", "8.6115", "8.6125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}268}{63{,}000}, \\dfrac{9{,}663}{63{,}000}, \\dfrac{10{,}499}{63{,}000}, \\dfrac{10{,}866}{63{,}000}, \\dfrac{11{,}114}{63{,}000}, \\dfrac{11{,}794}{63{,}000}, \\dfrac{11{,}983}{63{,}000}, \\dfrac{12{,}514}{63{,}000}, \\dfrac{12{,}650}{63{,}000}, \\dfrac{13{,}152}{63{,}000}, \\text{ and } \\dfrac{13{,}611}{63{,}000}", "__seed__": "0083"}}, {"seed": 84, "data": {"p1_how_many": "11", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}403}{42{,}000}, \\dfrac{8{,}219}{42{,}000}, \\dfrac{8{,}828}{42{,}000}, \\dfrac{9{,}621}{42{,}000}, \\dfrac{10{,}638}{42{,}000}, \\dfrac{10{,}897}{42{,}000}, \\dfrac{11{,}323}{42{,}000}, \\text{ and } \\dfrac{11{,}674}{42{,}000}", "__seed__": "0084"}}, {"seed": 85, "data": {"p1_how_many": "13", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.435, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425", "4.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}018}{3{,}500}, \\dfrac{1{,}049}{3{,}500}, \\dfrac{1{,}201}{3{,}500}, \\dfrac{1{,}208}{3{,}500}, \\dfrac{1{,}251}{3{,}500}, \\dfrac{1{,}281}{3{,}500}, \\dfrac{1{,}328}{3{,}500}, \\text{ and } \\dfrac{1{,}363}{3{,}500}", "__seed__": "0085"}}, {"seed": 86, "data": {"p1_how_many": "10", "p1_a": "5.03", "p1_b": "5.04", "p1_numbers": "5.0305, 5.031, 5.032, 5.033, 5.034, 5.035, 5.036, 5.037, 5.038, and 5.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.031000000000001", "5.032", "5.033", "5.034", "5.035", "5.0360000000000005", "5.037", "5.038", "5.039000000000001"], "p1_2_xs": ["5.0305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}464}{6{,}300}, \\dfrac{1{,}505}{6{,}300}, \\dfrac{1{,}530}{6{,}300}, \\dfrac{1{,}599}{6{,}300}, \\dfrac{1{,}717}{6{,}300}, \\dfrac{1{,}735}{6{,}300}, \\dfrac{1{,}740}{6{,}300}, \\dfrac{1{,}764}{6{,}300}, \\text{ and } \\dfrac{1{,}793}{6{,}300}", "__seed__": "0086"}}, {"seed": 87, "data": {"p1_how_many": "13", "p1_a": "4.25", "p1_b": "4.26", "p1_numbers": "4.2505, 4.251, 4.2515, 4.252, 4.2525, 4.253, 4.2535, 4.254, 4.255, 4.256, 4.257, 4.258, and 4.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.251", "4.252", "4.253", "4.254", "4.255", "4.256", "4.257", "4.258", "4.259"], "p1_2_xs": ["4.2505", "4.2515", "4.2524999999999995", "4.2535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}007}{56{,}000}, \\dfrac{32{,}332}{56{,}000}, \\dfrac{32{,}705}{56{,}000}, \\dfrac{33{,}022}{56{,}000}, \\dfrac{33{,}156}{56{,}000}, \\dfrac{33{,}494}{56{,}000}, \\dfrac{34{,}694}{56{,}000}, \\dfrac{34{,}881}{56{,}000}, \\text{ and } \\dfrac{34{,}909}{56{,}000}", "__seed__": "0087"}}, {"seed": 88, "data": {"p1_how_many": "14", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.635, 6.64, 6.645, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999", "6.635", "6.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}143}{20{,}000}, \\dfrac{4{,}244}{20{,}000}, \\dfrac{4{,}272}{20{,}000}, \\dfrac{4{,}370}{20{,}000}, \\dfrac{4{,}386}{20{,}000}, \\dfrac{4{,}483}{20{,}000}, \\text{ and } \\dfrac{4{,}903}{20{,}000}", "__seed__": "0088"}}, {"seed": 89, "data": {"p1_how_many": "14", "p1_a": "8.32", "p1_b": "8.33", "p1_numbers": "8.3205, 8.321, 8.3215, 8.322, 8.3225, 8.323, 8.3235, 8.324, 8.3245, 8.325, 8.326, 8.327, 8.328, and 8.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.321", "8.322000000000001", "8.323", "8.324", "8.325000000000001", "8.326", "8.327", "8.328", "8.329"], "p1_2_xs": ["8.320500000000001", "8.3215", "8.322500000000002", "8.323500000000001", "8.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{165}{350}, \\dfrac{167}{350}, \\dfrac{170}{350}, \\dfrac{174}{350}, \\dfrac{189}{350}, \\dfrac{191}{350}, \\text{ and } \\dfrac{193}{350}", "__seed__": "0089"}}, {"seed": 90, "data": {"p1_how_many": "13", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.435, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425", "4.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{61}{150}, \\dfrac{68}{150}, \\dfrac{72}{150}, \\dfrac{80}{150}, \\dfrac{85}{150}, \\dfrac{86}{150}, \\dfrac{94}{150}, \\dfrac{97}{150}, \\text{ and } \\dfrac{99}{150}", "__seed__": "0090"}}, {"seed": 91, "data": {"p1_how_many": "13", "p1_a": "7.04", "p1_b": "7.05", "p1_numbers": "7.0405, 7.041, 7.0415, 7.042, 7.0425, 7.043, 7.0435, 7.044, 7.045, 7.046, 7.047, 7.048, and 7.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.041", "7.042", "7.043", "7.044", "7.045", "7.046", "7.047", "7.048", "7.049"], "p1_2_xs": ["7.0405", "7.0415", "7.0424999999999995", "7.0435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0091"}}, {"seed": 92, "data": {"p1_how_many": "13", "p1_a": "8.15", "p1_b": "8.16", "p1_numbers": "8.1505, 8.151, 8.1515, 8.152, 8.1525, 8.153, 8.1535, 8.154, 8.155, 8.156, 8.157, 8.158, and 8.159", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.151", "8.152000000000001", "8.153", "8.154", "8.155000000000001", "8.156", "8.157", "8.158", "8.159"], "p1_2_xs": ["8.150500000000001", "8.1515", "8.152500000000002", "8.153500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}603}{5{,}600}, \\dfrac{3{,}700}{5{,}600}, \\dfrac{3{,}737}{5{,}600}, \\dfrac{3{,}825}{5{,}600}, \\dfrac{3{,}830}{5{,}600}, \\dfrac{3{,}902}{5{,}600}, \\dfrac{3{,}919}{5{,}600}, \\dfrac{3{,}921}{5{,}600}, \\text{ and } \\dfrac{3{,}978}{5{,}600}", "__seed__": "0092"}}, {"seed": 93, "data": {"p1_how_many": "10", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.52, 8.53, 8.54, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{704}{4{,}200}, \\dfrac{712}{4{,}200}, \\dfrac{727}{4{,}200}, \\dfrac{831}{4{,}200}, \\dfrac{857}{4{,}200}, \\dfrac{860}{4{,}200}, \\dfrac{960}{4{,}200}, \\text{ and } \\dfrac{1{,}086}{4{,}200}", "__seed__": "0093"}}, {"seed": 94, "data": {"p1_how_many": "12", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.6005, 1.601, 1.6015, 1.602, 1.6025, 1.603, 1.604, 1.605, 1.606, 1.607, 1.608, and 1.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.601", "1.602", "1.603", "1.604", "1.605", "1.606", "1.607", "1.608", "1.609"], "p1_2_xs": ["1.6005", "1.6015", "1.6025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}115}{12{,}000}, \\dfrac{3{,}171}{12{,}000}, \\dfrac{3{,}301}{12{,}000}, \\dfrac{3{,}364}{12{,}000}, \\dfrac{3{,}438}{12{,}000}, \\dfrac{3{,}471}{12{,}000}, \\dfrac{3{,}506}{12{,}000}, \\dfrac{3{,}546}{12{,}000}, \\dfrac{3{,}660}{12{,}000}, \\dfrac{3{,}914}{12{,}000}, \\text{ and } \\dfrac{3{,}942}{12{,}000}", "__seed__": "0094"}}, {"seed": 95, "data": {"p1_how_many": "14", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.735, 9.74, 9.745, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725", "9.735", "9.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{208}{350}, \\dfrac{244}{350}, \\dfrac{245}{350}, \\dfrac{249}{350}, \\dfrac{250}{350}, \\dfrac{252}{350}, \\dfrac{263}{350}, \\text{ and } \\dfrac{268}{350}", "__seed__": "0095"}}, {"seed": 96, "data": {"p1_how_many": "14", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.7005, 1.701, 1.7015, 1.702, 1.7025, 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7.838, and 7.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.831", "7.832", "7.833", "7.834", "7.835", "7.836", "7.837", "7.838", "7.839"], "p1_2_xs": ["7.8305", "7.8315", "7.8325", "7.8335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{56}{200}, \\dfrac{61}{200}, \\dfrac{64}{200}, \\dfrac{67}{200}, \\dfrac{70}{200}, \\dfrac{76}{200}, \\text{ and } \\dfrac{78}{200}", "__seed__": "0097"}}, {"seed": 98, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}164}{15{,}000}, \\dfrac{5{,}313}{15{,}000}, \\dfrac{5{,}356}{15{,}000}, \\dfrac{5{,}388}{15{,}000}, \\dfrac{5{,}403}{15{,}000}, \\dfrac{5{,}528}{15{,}000}, \\dfrac{5{,}748}{15{,}000}, \\dfrac{5{,}802}{15{,}000}, \\dfrac{5{,}838}{15{,}000}, \\text{ and } \\dfrac{5{,}941}{15{,}000}", "__seed__": "0098"}}, {"seed": 99, "data": {"p1_how_many": "14", "p1_a": "8.45", "p1_b": "8.46", "p1_numbers": "8.4505, 8.451, 8.4515, 8.452, 8.4525, 8.453, 8.4535, 8.454, 8.4545, 8.455, 8.456, 8.457, 8.458, and 8.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.450999999999999", "8.452", "8.453", "8.453999999999999", "8.455", "8.456", "8.456999999999999", "8.457999999999998", "8.459"], "p1_2_xs": ["8.4505", "8.4515", "8.4525", "8.4535", "8.4545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}203}{15{,}000}, \\dfrac{5{,}235}{15{,}000}, \\dfrac{5{,}241}{15{,}000}, \\dfrac{5{,}450}{15{,}000}, \\dfrac{5{,}520}{15{,}000}, \\dfrac{5{,}659}{15{,}000}, \\dfrac{5{,}692}{15{,}000}, \\dfrac{5{,}832}{15{,}000}, \\dfrac{5{,}878}{15{,}000}, \\dfrac{5{,}883}{15{,}000}, \\text{ and } \\dfrac{5{,}894}{15{,}000}", "__seed__": "0099"}}, {"seed": 100, "data": {"p1_how_many": "14", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.635, 8.64, 8.645, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625", "8.635", "8.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}146}{35{,}000}, \\dfrac{21{,}115}{35{,}000}, \\dfrac{22{,}226}{35{,}000}, \\dfrac{24{,}946}{35{,}000}, \\dfrac{26{,}221}{35{,}000}, \\dfrac{26{,}916}{35{,}000}, \\text{ and } \\dfrac{27{,}392}{35{,}000}", "__seed__": "0100"}}, {"seed": 101, "data": {"p1_how_many": "10", "p1_a": "4.06", "p1_b": "4.07", "p1_numbers": "4.0605, 4.061, 4.062, 4.063, 4.064, 4.065, 4.066, 4.067, 4.068, and 4.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.061", "4.061999999999999", "4.063", "4.063999999999999", "4.0649999999999995", "4.066", "4.066999999999999", "4.068", "4.069"], "p1_2_xs": ["4.060499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}082}{30{,}000}, \\dfrac{5{,}122}{30{,}000}, \\dfrac{5{,}226}{30{,}000}, \\dfrac{5{,}340}{30{,}000}, \\dfrac{5{,}426}{30{,}000}, \\dfrac{5{,}632}{30{,}000}, \\text{ and } \\dfrac{5{,}719}{30{,}000}", "__seed__": "0101"}}, {"seed": 102, "data": {"p1_how_many": "13", "p1_a": "3.87", "p1_b": "3.88", "p1_numbers": "3.8705, 3.871, 3.8715, 3.872, 3.8725, 3.873, 3.8735, 3.874, 3.875, 3.876, 3.877, 3.878, and 3.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.871", "3.872", "3.873", "3.874", "3.875", "3.876", "3.8770000000000002", "3.878", "3.879"], "p1_2_xs": ["3.8705000000000003", "3.8715", "3.8725", "3.8735000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}443}{42{,}000}, \\dfrac{7{,}823}{42{,}000}, \\dfrac{8{,}453}{42{,}000}, \\dfrac{8{,}720}{42{,}000}, \\dfrac{9{,}435}{42{,}000}, \\dfrac{11{,}288}{42{,}000}, \\text{ and } \\dfrac{11{,}698}{42{,}000}", "__seed__": "0102"}}, {"seed": 103, "data": {"p1_how_many": "11", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}034}{35{,}000}, \\dfrac{7{,}554}{35{,}000}, \\dfrac{7{,}656}{35{,}000}, \\dfrac{7{,}946}{35{,}000}, \\dfrac{8{,}007}{35{,}000}, \\dfrac{8{,}132}{35{,}000}, \\dfrac{8{,}373}{35{,}000}, \\dfrac{9{,}373}{35{,}000}, \\dfrac{9{,}466}{35{,}000}, \\dfrac{9{,}523}{35{,}000}, \\dfrac{9{,}633}{35{,}000}, \\text{ and } \\dfrac{9{,}942}{35{,}000}", "__seed__": "0103"}}, {"seed": 104, "data": {"p1_how_many": "14", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.145, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135", "4.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}152}{63{,}000}, \\dfrac{27{,}269}{63{,}000}, \\dfrac{27{,}284}{63{,}000}, \\dfrac{27{,}298}{63{,}000}, \\dfrac{27{,}446}{63{,}000}, \\dfrac{27{,}519}{63{,}000}, \\dfrac{27{,}642}{63{,}000}, \\dfrac{27{,}650}{63{,}000}, \\dfrac{27{,}653}{63{,}000}, \\text{ and } \\dfrac{27{,}911}{63{,}000}", "__seed__": "0104"}}, {"seed": 105, "data": {"p1_how_many": "10", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}022}{20{,}000}, \\dfrac{4{,}111}{20{,}000}, \\dfrac{4{,}227}{20{,}000}, \\dfrac{4{,}520}{20{,}000}, \\dfrac{4{,}581}{20{,}000}, \\dfrac{4{,}774}{20{,}000}, \\dfrac{4{,}835}{20{,}000}, \\text{ and } \\dfrac{4{,}988}{20{,}000}", "__seed__": "0105"}}, {"seed": 106, "data": {"p1_how_many": "14", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.235, 9.24, 9.245, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225", "9.235", "9.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{52}{200}, \\dfrac{60}{200}, \\dfrac{61}{200}, \\dfrac{62}{200}, \\dfrac{63}{200}, \\dfrac{66}{200}, \\dfrac{68}{200}, \\dfrac{72}{200}, \\text{ and } \\dfrac{76}{200}", "__seed__": "0106"}}, {"seed": 107, "data": {"p1_how_many": "10", "p1_a": "4.52", "p1_b": "4.53", "p1_numbers": "4.5205, 4.521, 4.522, 4.523, 4.524, 4.525, 4.526, 4.527, 4.528, and 4.529", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.521", "4.521999999999999", "4.523", "4.523999999999999", "4.5249999999999995", "4.526", "4.526999999999999", "4.528", "4.529"], "p1_2_xs": ["4.520499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}715}{15{,}000}, \\dfrac{7{,}510}{15{,}000}, \\dfrac{7{,}725}{15{,}000}, \\dfrac{7{,}752}{15{,}000}, \\dfrac{7{,}867}{15{,}000}, \\dfrac{8{,}208}{15{,}000}, \\dfrac{8{,}698}{15{,}000}, \\dfrac{8{,}783}{15{,}000}, \\dfrac{9{,}309}{15{,}000}, \\dfrac{9{,}477}{15{,}000}, \\text{ and } \\dfrac{9{,}575}{15{,}000}", "__seed__": "0107"}}, {"seed": 108, "data": {"p1_how_many": "14", "p1_a": "8.57", "p1_b": "8.58", "p1_numbers": "8.5705, 8.571, 8.5715, 8.572, 8.5725, 8.573, 8.5735, 8.574, 8.5745, 8.575, 8.576, 8.577, 8.578, and 8.579", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.571", "8.572000000000001", "8.573", "8.574", "8.575000000000001", "8.576", "8.577", "8.578", "8.579"], "p1_2_xs": ["8.570500000000001", "8.5715", "8.572500000000002", "8.573500000000001", "8.5745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{123}{200}, \\dfrac{127}{200}, \\dfrac{134}{200}, \\dfrac{138}{200}, \\dfrac{139}{200}, \\dfrac{146}{200}, \\text{ and } \\dfrac{147}{200}", "__seed__": "0108"}}, {"seed": 109, "data": {"p1_how_many": "12", "p1_a": "1.16", "p1_b": "1.17", "p1_numbers": "1.1605, 1.161, 1.1615, 1.162, 1.1625, 1.163, 1.164, 1.165, 1.166, 1.167, 1.168, and 1.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.1609999999999998", "1.162", "1.1629999999999998", "1.164", "1.1649999999999998", "1.166", "1.1669999999999998", "1.168", "1.1689999999999998"], "p1_2_xs": ["1.1604999999999999", "1.1614999999999998", "1.1624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{78}{420}, \\dfrac{82}{420}, \\dfrac{88}{420}, \\dfrac{89}{420}, \\dfrac{95}{420}, \\dfrac{97}{420}, \\dfrac{101}{420}, \\dfrac{111}{420}, \\text{ and } \\dfrac{116}{420}", "__seed__": "0109"}}, {"seed": 110, "data": {"p1_how_many": "10", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.42, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}255}{2{,}000}, \\dfrac{1{,}284}{2{,}000}, \\dfrac{1{,}308}{2{,}000}, \\dfrac{1{,}346}{2{,}000}, \\dfrac{1{,}415}{2{,}000}, \\dfrac{1{,}427}{2{,}000}, \\text{ and } \\dfrac{1{,}478}{2{,}000}", "__seed__": "0110"}}, {"seed": 111, "data": {"p1_how_many": "12", "p1_a": "7.95", "p1_b": "7.96", "p1_numbers": "7.9505, 7.951, 7.9515, 7.952, 7.9525, 7.953, 7.954, 7.955, 7.956, 7.957, 7.958, and 7.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.9510000000000005", "7.952", "7.953", "7.954", "7.955", "7.956", "7.957", "7.958", "7.9590000000000005"], "p1_2_xs": ["7.9505", "7.9515", "7.9525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\dfrac{48}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0111"}}, {"seed": 112, "data": {"p1_how_many": "13", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.025, 1.03, 1.035, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015", "1.025", "1.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{505}{3{,}000}, \\dfrac{513}{3{,}000}, \\dfrac{521}{3{,}000}, \\dfrac{522}{3{,}000}, \\dfrac{530}{3{,}000}, \\dfrac{533}{3{,}000}, \\dfrac{539}{3{,}000}, \\dfrac{546}{3{,}000}, \\dfrac{566}{3{,}000}, \\text{ and } \\dfrac{580}{3{,}000}", "__seed__": "0112"}}, {"seed": 113, "data": {"p1_how_many": "11", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.6005, 5.601, 5.6015, 5.602, 5.603, 5.604, 5.605, 5.606, 5.607, 5.608, and 5.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.601", "5.601999999999999", "5.603", "5.603999999999999", "5.6049999999999995", "5.606", "5.606999999999999", "5.608", "5.609"], "p1_2_xs": ["5.600499999999999", "5.6015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}339}{56{,}000}, \\dfrac{32{,}540}{56{,}000}, \\dfrac{32{,}571}{56{,}000}, \\dfrac{32{,}891}{56{,}000}, \\dfrac{32{,}943}{56{,}000}, \\dfrac{33{,}193}{56{,}000}, \\dfrac{33{,}250}{56{,}000}, \\dfrac{33{,}444}{56{,}000}, \\dfrac{33{,}925}{56{,}000}, \\dfrac{34{,}082}{56{,}000}, \\text{ and } \\dfrac{34{,}122}{56{,}000}", "__seed__": "0113"}}, {"seed": 114, "data": {"p1_how_many": "10", "p1_a": "8.53", "p1_b": "8.54", "p1_numbers": "8.5305, 8.531, 8.532, 8.533, 8.534, 8.535, 8.536, 8.537, 8.538, and 8.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.530999999999999", "8.532", "8.533", "8.533999999999999", "8.535", "8.536", "8.536999999999999", "8.537999999999998", "8.539"], "p1_2_xs": ["8.5305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}042}{12{,}000}, \\dfrac{8{,}153}{12{,}000}, \\dfrac{8{,}265}{12{,}000}, \\dfrac{8{,}293}{12{,}000}, \\dfrac{8{,}341}{12{,}000}, \\dfrac{8{,}517}{12{,}000}, \\dfrac{8{,}761}{12{,}000}, \\dfrac{8{,}774}{12{,}000}, \\text{ and } \\dfrac{8{,}984}{12{,}000}", "__seed__": "0114"}}, {"seed": 115, "data": {"p1_how_many": "11", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.215, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205", "4.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{353}{560}, \\dfrac{361}{560}, \\dfrac{362}{560}, \\dfrac{365}{560}, \\dfrac{368}{560}, \\dfrac{372}{560}, \\dfrac{381}{560}, \\dfrac{384}{560}, \\text{ and } \\dfrac{393}{560}", "__seed__": "0115"}}, {"seed": 116, "data": {"p1_how_many": "10", "p1_a": "5.04", "p1_b": "5.05", "p1_numbers": "5.0405, 5.041, 5.042, 5.043, 5.044, 5.045, 5.046, 5.047, 5.048, and 5.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.041", "5.042", "5.043", "5.044", "5.045", "5.046", "5.047", "5.048", "5.049"], "p1_2_xs": ["5.0405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}730}{20{,}000}, \\dfrac{12{,}794}{20{,}000}, \\dfrac{13{,}303}{20{,}000}, \\dfrac{13{,}726}{20{,}000}, \\dfrac{13{,}843}{20{,}000}, \\dfrac{13{,}921}{20{,}000}, \\dfrac{14{,}165}{20{,}000}, \\text{ and } \\dfrac{14{,}819}{20{,}000}", "__seed__": "0116"}}, {"seed": 117, "data": {"p1_how_many": "10", "p1_a": "9.55", "p1_b": "9.56", "p1_numbers": "9.5505, 9.551, 9.552, 9.553, 9.554, 9.555, 9.556, 9.557, 9.558, and 9.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.551", "9.552000000000001", "9.553", "9.554", "9.555000000000001", "9.556000000000001", "9.557", "9.558", "9.559000000000001"], "p1_2_xs": ["9.550500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{729}{3{,}500}, \\dfrac{731}{3{,}500}, \\dfrac{794}{3{,}500}, \\dfrac{812}{3{,}500}, \\dfrac{814}{3{,}500}, \\dfrac{850}{3{,}500}, \\dfrac{854}{3{,}500}, \\dfrac{911}{3{,}500}, \\dfrac{938}{3{,}500}, \\dfrac{994}{3{,}500}, \\text{ and } \\dfrac{998}{3{,}500}", "__seed__": "0117"}}, {"seed": 118, "data": {"p1_how_many": "10", "p1_a": "2.55", "p1_b": "2.56", "p1_numbers": "2.5505, 2.551, 2.552, 2.553, 2.554, 2.555, 2.556, 2.557, 2.558, and 2.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5509999999999997", "2.5519999999999996", "2.553", "2.554", "2.5549999999999997", "2.5559999999999996", "2.557", "2.558", "2.5589999999999997"], "p1_2_xs": ["2.5505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}033}{42{,}000}, \\dfrac{35{,}037}{42{,}000}, \\dfrac{35{,}120}{42{,}000}, \\dfrac{35{,}232}{42{,}000}, \\dfrac{35{,}235}{42{,}000}, \\dfrac{35{,}680}{42{,}000}, \\dfrac{35{,}837}{42{,}000}, \\dfrac{35{,}844}{42{,}000}, \\dfrac{35{,}860}{42{,}000}, \\dfrac{35{,}914}{42{,}000}, \\text{ and } \\dfrac{35{,}983}{42{,}000}", "__seed__": "0118"}}, {"seed": 119, "data": {"p1_how_many": "11", "p1_a": "2.53", "p1_b": "2.54", "p1_numbers": "2.5305, 2.531, 2.5315, 2.532, 2.533, 2.534, 2.535, 2.536, 2.537, 2.538, and 2.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5309999999999997", "2.5319999999999996", "2.533", "2.534", "2.5349999999999997", "2.5359999999999996", "2.537", "2.538", "2.5389999999999997"], "p1_2_xs": ["2.5305", "2.5315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}010}{12{,}000}, \\dfrac{8{,}179}{12{,}000}, \\dfrac{8{,}413}{12{,}000}, \\dfrac{8{,}443}{12{,}000}, \\dfrac{8{,}606}{12{,}000}, \\dfrac{8{,}624}{12{,}000}, \\dfrac{8{,}745}{12{,}000}, \\dfrac{8{,}839}{12{,}000}, \\text{ and } \\dfrac{8{,}869}{12{,}000}", "__seed__": "0119"}}, {"seed": 120, "data": {"p1_how_many": "10", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}291}{2{,}000}, \\dfrac{1{,}295}{2{,}000}, \\dfrac{1{,}299}{2{,}000}, \\dfrac{1{,}324}{2{,}000}, \\dfrac{1{,}327}{2{,}000}, \\dfrac{1{,}355}{2{,}000}, \\dfrac{1{,}362}{2{,}000}, \\dfrac{1{,}378}{2{,}000}, \\dfrac{1{,}390}{2{,}000}, \\dfrac{1{,}440}{2{,}000}, \\dfrac{1{,}454}{2{,}000}, \\text{ and } \\dfrac{1{,}488}{2{,}000}", "__seed__": "0120"}}, {"seed": 121, "data": {"p1_how_many": "11", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{805}{1{,}200}, \\dfrac{810}{1{,}200}, \\dfrac{822}{1{,}200}, \\dfrac{824}{1{,}200}, \\dfrac{830}{1{,}200}, \\dfrac{837}{1{,}200}, \\dfrac{848}{1{,}200}, \\dfrac{851}{1{,}200}, \\dfrac{855}{1{,}200}, \\text{ and } \\dfrac{895}{1{,}200}", "__seed__": "0121"}}, {"seed": 122, "data": {"p1_how_many": "10", "p1_a": "3.22", "p1_b": "3.23", "p1_numbers": "3.2205, 3.221, 3.222, 3.223, 3.224, 3.225, 3.226, 3.227, 3.228, and 3.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.221", "3.222", "3.2230000000000003", "3.224", "3.225", "3.226", "3.2270000000000003", "3.228", "3.229"], "p1_2_xs": ["3.2205000000000004"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}504}{4{,}200}, \\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}520}{4{,}200}, \\dfrac{3{,}529}{4{,}200}, \\dfrac{3{,}532}{4{,}200}, \\dfrac{3{,}537}{4{,}200}, \\text{ and } \\dfrac{3{,}549}{4{,}200}", "__seed__": "0122"}}, {"seed": 123, "data": {"p1_how_many": "11", "p1_a": "2.85", "p1_b": "2.86", "p1_numbers": "2.8505, 2.851, 2.8515, 2.852, 2.853, 2.854, 2.855, 2.856, 2.857, 2.858, and 2.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.851", "2.852", "2.853", "2.854", "2.855", "2.856", "2.857", "2.858", "2.859"], "p1_2_xs": ["2.8505000000000003", "2.8515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}625}{5{,}600}, \\dfrac{1{,}642}{5{,}600}, \\dfrac{1{,}659}{5{,}600}, \\dfrac{1{,}678}{5{,}600}, \\dfrac{1{,}991}{5{,}600}, \\dfrac{1{,}996}{5{,}600}, \\text{ and } \\dfrac{2{,}006}{5{,}600}", "__seed__": "0123"}}, {"seed": 124, "data": {"p1_how_many": "13", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.735, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725", "6.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}164}{42{,}000}, \\dfrac{6{,}272}{42{,}000}, \\dfrac{6{,}301}{42{,}000}, \\dfrac{6{,}305}{42{,}000}, \\dfrac{6{,}342}{42{,}000}, \\dfrac{6{,}498}{42{,}000}, \\text{ and } \\dfrac{6{,}710}{42{,}000}", "__seed__": "0124"}}, {"seed": 125, "data": {"p1_how_many": "14", "p1_a": "9.07", "p1_b": "9.08", "p1_numbers": "9.0705, 9.071, 9.0715, 9.072, 9.0725, 9.073, 9.0735, 9.074, 9.0745, 9.075, 9.076, 9.077, 9.078, and 9.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.071", "9.072000000000001", "9.073", "9.074", "9.075000000000001", "9.076", "9.077", "9.078", "9.079"], "p1_2_xs": ["9.070500000000001", "9.0715", "9.072500000000002", "9.073500000000001", "9.0745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{512}{1{,}500}, \\dfrac{516}{1{,}500}, \\dfrac{525}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{536}{1{,}500}, \\dfrac{543}{1{,}500}, \\dfrac{572}{1{,}500}, \\dfrac{575}{1{,}500}, \\dfrac{580}{1{,}500}, \\dfrac{590}{1{,}500}, \\text{ and } \\dfrac{591}{1{,}500}", "__seed__": "0125"}}, {"seed": 126, "data": {"p1_how_many": "14", "p1_a": "5.85", "p1_b": "5.86", "p1_numbers": "5.8505, 5.851, 5.8515, 5.852, 5.8525, 5.853, 5.8535, 5.854, 5.8545, 5.855, 5.856, 5.857, 5.858, and 5.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.851", "5.851999999999999", "5.853", "5.853999999999999", "5.8549999999999995", "5.856", "5.856999999999999", "5.858", "5.859"], "p1_2_xs": ["5.850499999999999", "5.8515", "5.852499999999999", "5.8534999999999995", "5.854499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}693}{35{,}000}, \\dfrac{8{,}192}{35{,}000}, \\dfrac{8{,}263}{35{,}000}, \\dfrac{8{,}376}{35{,}000}, \\dfrac{8{,}491}{35{,}000}, \\dfrac{8{,}503}{35{,}000}, \\dfrac{8{,}552}{35{,}000}, \\dfrac{8{,}635}{35{,}000}, \\dfrac{9{,}088}{35{,}000}, \\dfrac{9{,}659}{35{,}000}, \\dfrac{9{,}762}{35{,}000}, \\text{ and } \\dfrac{9{,}838}{35{,}000}", "__seed__": "0126"}}, {"seed": 127, "data": {"p1_how_many": "10", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}313}{63{,}000}, \\dfrac{9{,}327}{63{,}000}, \\dfrac{10{,}381}{63{,}000}, \\dfrac{10{,}629}{63{,}000}, \\dfrac{11{,}043}{63{,}000}, \\dfrac{11{,}281}{63{,}000}, \\dfrac{11{,}286}{63{,}000}, \\dfrac{12{,}328}{63{,}000}, \\dfrac{12{,}630}{63{,}000}, \\text{ and } \\dfrac{13{,}572}{63{,}000}", "__seed__": "0127"}}, {"seed": 128, "data": {"p1_how_many": "13", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.005, 5.01, 5.015, 5.02, 5.025, 5.03, 5.035, 5.04, 5.05, 5.06, 5.07, 5.08, and 5.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005", "5.015", "5.0249999999999995", "5.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{92}{630}, \\dfrac{102}{630}, \\dfrac{118}{630}, \\dfrac{120}{630}, \\dfrac{131}{630}, \\dfrac{132}{630}, \\dfrac{134}{630}, \\dfrac{137}{630}, \\text{ and } \\dfrac{138}{630}", "__seed__": "0128"}}, {"seed": 129, "data": {"p1_how_many": "10", "p1_a": "6.61", "p1_b": "6.62", "p1_numbers": "6.6105, 6.611, 6.612, 6.613, 6.614, 6.615, 6.616, 6.617, 6.618, and 6.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.611000000000001", "6.612", "6.613", "6.614", "6.615", "6.6160000000000005", "6.617", "6.618", "6.619000000000001"], "p1_2_xs": ["6.6105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}046}{20{,}000}, \\dfrac{4{,}338}{20{,}000}, \\dfrac{4{,}486}{20{,}000}, \\dfrac{4{,}527}{20{,}000}, \\dfrac{4{,}742}{20{,}000}, \\dfrac{4{,}774}{20{,}000}, \\dfrac{4{,}776}{20{,}000}, \\dfrac{4{,}891}{20{,}000}, \\text{ and } \\dfrac{4{,}918}{20{,}000}", "__seed__": "0129"}}, {"seed": 130, "data": {"p1_how_many": "11", "p1_a": "4.37", "p1_b": "4.38", "p1_numbers": "4.3705, 4.371, 4.3715, 4.372, 4.373, 4.374, 4.375, 4.376, 4.377, 4.378, and 4.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.371", "4.372", "4.373", "4.374", "4.375", "4.376", "4.377", "4.378", "4.3790000000000004"], "p1_2_xs": ["4.3705", "4.3715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}074}{12{,}000}, \\dfrac{8{,}158}{12{,}000}, \\dfrac{8{,}168}{12{,}000}, \\dfrac{8{,}596}{12{,}000}, \\dfrac{8{,}654}{12{,}000}, \\dfrac{8{,}681}{12{,}000}, \\text{ and } \\dfrac{8{,}855}{12{,}000}", "__seed__": "0130"}}, {"seed": 131, "data": {"p1_how_many": "13", "p1_a": "4.63", "p1_b": "4.64", "p1_numbers": "4.6305, 4.631, 4.6315, 4.632, 4.6325, 4.633, 4.6335, 4.634, 4.635, 4.636, 4.637, 4.638, and 4.639", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.631", "4.632", "4.633", "4.6339999999999995", "4.635", "4.636", "4.637", "4.638", "4.639"], "p1_2_xs": ["4.6305", "4.6315", "4.632499999999999", "4.6335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{510}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{535}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{567}{1{,}500}, \\dfrac{572}{1{,}500}, \\dfrac{581}{1{,}500}, \\text{ and } \\dfrac{584}{1{,}500}", "__seed__": "0131"}}, {"seed": 132, "data": {"p1_how_many": "11", "p1_a": "8.16", "p1_b": "8.17", "p1_numbers": "8.1605, 8.161, 8.1615, 8.162, 8.163, 8.164, 8.165, 8.166, 8.167, 8.168, and 8.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.161", "8.162", "8.163", "8.164", "8.165000000000001", "8.166", "8.167", "8.168", "8.169"], "p1_2_xs": ["8.1605", "8.1615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}047}{42{,}000}, \\dfrac{6{,}193}{42{,}000}, \\dfrac{6{,}200}{42{,}000}, \\dfrac{6{,}231}{42{,}000}, \\dfrac{6{,}305}{42{,}000}, \\dfrac{6{,}524}{42{,}000}, \\dfrac{6{,}590}{42{,}000}, \\dfrac{6{,}631}{42{,}000}, \\dfrac{6{,}671}{42{,}000}, \\text{ and } \\dfrac{6{,}947}{42{,}000}", "__seed__": "0132"}}, {"seed": 133, "data": {"p1_how_many": "13", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725", "7.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}068}{35{,}000}, \\dfrac{14{,}168}{35{,}000}, \\dfrac{14{,}706}{35{,}000}, \\dfrac{14{,}715}{35{,}000}, \\dfrac{14{,}856}{35{,}000}, \\dfrac{14{,}889}{35{,}000}, \\dfrac{14{,}915}{35{,}000}, \\text{ and } \\dfrac{14{,}920}{35{,}000}", "__seed__": "0133"}}, {"seed": 134, "data": {"p1_how_many": "13", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{822}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{871}{1{,}200}, \\dfrac{872}{1{,}200}, \\dfrac{886}{1{,}200}, \\dfrac{887}{1{,}200}, \\text{ and } \\dfrac{890}{1{,}200}", "__seed__": "0134"}}, {"seed": 135, "data": {"p1_how_many": "10", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{604}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{646}{4{,}200}, \\dfrac{651}{4{,}200}, \\dfrac{669}{4{,}200}, \\text{ and } \\dfrac{670}{4{,}200}", "__seed__": "0135"}}, {"seed": 136, "data": {"p1_how_many": "13", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{706}{3{,}500}, \\dfrac{726}{3{,}500}, \\dfrac{750}{3{,}500}, \\dfrac{761}{3{,}500}, \\dfrac{768}{3{,}500}, \\dfrac{856}{3{,}500}, \\dfrac{867}{3{,}500}, \\dfrac{893}{3{,}500}, \\dfrac{912}{3{,}500}, \\dfrac{925}{3{,}500}, \\dfrac{934}{3{,}500}, \\text{ and } \\dfrac{989}{3{,}500}", "__seed__": "0136"}}, {"seed": 137, "data": {"p1_how_many": "10", "p1_a": "7.44", "p1_b": "7.45", "p1_numbers": "7.4405, 7.441, 7.442, 7.443, 7.444, 7.445, 7.446, 7.447, 7.448, and 7.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.441000000000001", "7.442", "7.4430000000000005", "7.444", "7.445", "7.446000000000001", "7.447", "7.448", "7.449000000000001"], "p1_2_xs": ["7.4405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}067}{20{,}000}, \\dfrac{4{,}212}{20{,}000}, \\dfrac{4{,}273}{20{,}000}, \\dfrac{4{,}306}{20{,}000}, \\dfrac{4{,}324}{20{,}000}, \\dfrac{4{,}423}{20{,}000}, \\dfrac{4{,}602}{20{,}000}, \\dfrac{4{,}623}{20{,}000}, \\text{ and } \\dfrac{4{,}990}{20{,}000}", "__seed__": "0137"}}, {"seed": 138, "data": {"p1_how_many": "12", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}244}{2{,}000}, \\dfrac{1{,}277}{2{,}000}, \\dfrac{1{,}313}{2{,}000}, \\dfrac{1{,}359}{2{,}000}, \\dfrac{1{,}379}{2{,}000}, \\dfrac{1{,}383}{2{,}000}, \\dfrac{1{,}405}{2{,}000}, \\dfrac{1{,}475}{2{,}000}, \\text{ and } \\dfrac{1{,}488}{2{,}000}", "__seed__": "0138"}}, {"seed": 139, "data": {"p1_how_many": "11", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.13, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}018}{15{,}000}, \\dfrac{5{,}101}{15{,}000}, \\dfrac{5{,}167}{15{,}000}, \\dfrac{5{,}301}{15{,}000}, \\dfrac{5{,}307}{15{,}000}, \\dfrac{5{,}384}{15{,}000}, \\dfrac{5{,}451}{15{,}000}, \\dfrac{5{,}533}{15{,}000}, \\dfrac{5{,}560}{15{,}000}, \\dfrac{5{,}645}{15{,}000}, \\text{ and } \\dfrac{5{,}781}{15{,}000}", "__seed__": "0139"}}, {"seed": 140, "data": {"p1_how_many": "10", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0140"}}, {"seed": 141, "data": {"p1_how_many": "12", "p1_a": "8.76", "p1_b": "8.77", "p1_numbers": "8.7605, 8.761, 8.7615, 8.762, 8.7625, 8.763, 8.764, 8.765, 8.766, 8.767, 8.768, and 8.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.761", "8.762", "8.763", "8.764", "8.765", "8.766", "8.767", "8.767999999999999", "8.769"], "p1_2_xs": ["8.7605", "8.7615", "8.762500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}886}{42{,}000}, \\dfrac{8{,}572}{42{,}000}, \\dfrac{8{,}617}{42{,}000}, \\dfrac{8{,}791}{42{,}000}, \\dfrac{9{,}367}{42{,}000}, \\dfrac{9{,}719}{42{,}000}, \\dfrac{9{,}808}{42{,}000}, \\dfrac{10{,}076}{42{,}000}, \\dfrac{10{,}592}{42{,}000}, \\dfrac{11{,}074}{42{,}000}, \\dfrac{11{,}403}{42{,}000}, \\text{ and } \\dfrac{11{,}407}{42{,}000}", "__seed__": "0141"}}, {"seed": 142, "data": {"p1_how_many": "12", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.325, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995", "3.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{107}{350}, \\dfrac{112}{350}, \\dfrac{113}{350}, \\dfrac{117}{350}, \\dfrac{120}{350}, \\dfrac{125}{350}, \\text{ and } \\dfrac{131}{350}", "__seed__": "0142"}}, {"seed": 143, "data": {"p1_how_many": "13", "p1_a": "1.95", "p1_b": "1.96", "p1_numbers": "1.9505, 1.951, 1.9515, 1.952, 1.9525, 1.953, 1.9535, 1.954, 1.955, 1.956, 1.957, 1.958, and 1.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9509999999999998", "1.952", "1.9529999999999998", "1.954", "1.9549999999999998", "1.956", "1.9569999999999999", "1.958", "1.9589999999999999"], "p1_2_xs": ["1.9505", "1.9514999999999998", "1.9525", "1.9534999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}812}{5{,}600}, \\dfrac{4{,}817}{5{,}600}, \\dfrac{4{,}819}{5{,}600}, \\dfrac{4{,}826}{5{,}600}, \\dfrac{4{,}831}{5{,}600}, \\dfrac{4{,}843}{5{,}600}, \\dfrac{4{,}847}{5{,}600}, \\dfrac{4{,}856}{5{,}600}, \\dfrac{4{,}862}{5{,}600}, \\text{ and } \\dfrac{4{,}880}{5{,}600}", "__seed__": "0143"}}, {"seed": 144, "data": {"p1_how_many": "11", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{504}{2{,}000}, \\dfrac{522}{2{,}000}, \\dfrac{546}{2{,}000}, \\dfrac{548}{2{,}000}, \\dfrac{564}{2{,}000}, \\dfrac{610}{2{,}000}, \\dfrac{667}{2{,}000}, \\dfrac{675}{2{,}000}, \\dfrac{714}{2{,}000}, \\dfrac{716}{2{,}000}, \\text{ and } \\dfrac{781}{2{,}000}", "__seed__": "0144"}}, {"seed": 145, "data": {"p1_how_many": "10", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, \\dfrac{243}{300}, \\dfrac{245}{300}, \\dfrac{247}{300}, \\dfrac{248}{300}, \\text{ and } \\dfrac{249}{300}", "__seed__": "0145"}}, {"seed": 146, "data": {"p1_how_many": "10", "p1_a": "1.07", "p1_b": "1.08", "p1_numbers": "1.0705, 1.071, 1.072, 1.073, 1.074, 1.075, 1.076, 1.077, 1.078, and 1.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.071", "1.072", "1.073", "1.074", "1.075", "1.076", "1.077", "1.078", "1.079"], "p1_2_xs": ["1.0705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{2{,}000}, \\dfrac{549}{2{,}000}, \\dfrac{566}{2{,}000}, \\dfrac{569}{2{,}000}, \\dfrac{607}{2{,}000}, \\dfrac{658}{2{,}000}, \\dfrac{715}{2{,}000}, \\text{ and } \\dfrac{751}{2{,}000}", "__seed__": "0146"}}, {"seed": 147, "data": {"p1_how_many": "13", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{506}{1{,}500}, \\dfrac{524}{1{,}500}, \\dfrac{534}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{564}{1{,}500}, \\dfrac{587}{1{,}500}, \\text{ and } \\dfrac{592}{1{,}500}", "__seed__": "0147"}}, {"seed": 148, "data": {"p1_how_many": "14", "p1_a": "7.26", "p1_b": "7.27", "p1_numbers": "7.2605, 7.261, 7.2615, 7.262, 7.2625, 7.263, 7.2635, 7.264, 7.2645, 7.265, 7.266, 7.267, 7.268, and 7.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.261", "7.262", "7.263", "7.263999999999999", "7.265", "7.266", "7.2669999999999995", "7.268", "7.269"], "p1_2_xs": ["7.2604999999999995", "7.2615", "7.262499999999999", "7.2635", "7.264499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}098}{15{,}000}, \\dfrac{5{,}258}{15{,}000}, \\dfrac{5{,}384}{15{,}000}, \\dfrac{5{,}435}{15{,}000}, \\dfrac{5{,}466}{15{,}000}, \\dfrac{5{,}477}{15{,}000}, \\dfrac{5{,}620}{15{,}000}, \\dfrac{5{,}738}{15{,}000}, \\text{ and } \\dfrac{5{,}868}{15{,}000}", "__seed__": "0148"}}, {"seed": 149, "data": {"p1_how_many": "11", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.215, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205", "4.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}491}{42{,}000}, \\dfrac{31{,}310}{42{,}000}, \\dfrac{32{,}240}{42{,}000}, \\dfrac{32{,}674}{42{,}000}, \\dfrac{33{,}363}{42{,}000}, \\dfrac{34{,}099}{42{,}000}, \\dfrac{34{,}441}{42{,}000}, \\dfrac{34{,}528}{42{,}000}, \\text{ and } \\dfrac{34{,}659}{42{,}000}", "__seed__": "0149"}}, {"seed": 150, "data": {"p1_how_many": "14", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.025, 1.03, 1.035, 1.04, 1.045, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015", "1.025", "1.035", "1.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}120}{20{,}000}, \\dfrac{4{,}422}{20{,}000}, \\dfrac{4{,}445}{20{,}000}, \\dfrac{4{,}466}{20{,}000}, \\dfrac{4{,}630}{20{,}000}, \\dfrac{4{,}671}{20{,}000}, \\dfrac{4{,}738}{20{,}000}, \\text{ and } \\dfrac{4{,}927}{20{,}000}", "__seed__": "0150"}}, {"seed": 151, "data": {"p1_how_many": "14", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.545, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535", "9.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}290}{7{,}700}, \\dfrac{4{,}386}{7{,}700}, \\dfrac{4{,}699}{7{,}700}, \\dfrac{5{,}119}{7{,}700}, \\dfrac{5{,}228}{7{,}700}, \\dfrac{5{,}439}{7{,}700}, \\dfrac{5{,}639}{7{,}700}, \\dfrac{5{,}698}{7{,}700}, \\dfrac{5{,}838}{7{,}700}, \\dfrac{6{,}019}{7{,}700}, \\dfrac{6{,}392}{7{,}700}, \\text{ and } \\dfrac{6{,}560}{7{,}700}", "__seed__": "0151"}}, {"seed": 152, "data": {"p1_how_many": "14", "p1_a": "3.67", "p1_b": "3.68", "p1_numbers": "3.6705, 3.671, 3.6715, 3.672, 3.6725, 3.673, 3.6735, 3.674, 3.6745, 3.675, 3.676, 3.677, 3.678, and 3.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.671", "3.6719999999999997", "3.673", "3.674", "3.675", "3.6759999999999997", "3.677", "3.678", "3.679"], "p1_2_xs": ["3.6705", "3.6715", "3.6725", "3.6735", "3.6745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0152"}}, {"seed": 153, "data": {"p1_how_many": "12", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{54}{200}, \\dfrac{55}{200}, \\dfrac{56}{200}, \\dfrac{61}{200}, \\dfrac{65}{200}, \\dfrac{67}{200}, \\dfrac{70}{200}, \\dfrac{76}{200}, \\text{ and } \\dfrac{78}{200}", "__seed__": "0153"}}, {"seed": 154, "data": {"p1_how_many": "14", "p1_a": "2.01", "p1_b": "2.02", "p1_numbers": "2.0105, 2.011, 2.0115, 2.012, 2.0125, 2.013, 2.0135, 2.014, 2.0145, 2.015, 2.016, 2.017, 2.018, and 2.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.0109999999999997", "2.0119999999999996", "2.013", "2.014", "2.0149999999999997", "2.0159999999999996", "2.017", "2.018", "2.0189999999999997"], "p1_2_xs": ["2.0105", "2.0115", "2.0124999999999997", "2.0135", "2.0145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{150}, \\dfrac{52}{150}, \\dfrac{53}{150}, \\dfrac{54}{150}, \\dfrac{55}{150}, \\dfrac{56}{150}, \\text{ and } \\dfrac{58}{150}", "__seed__": "0154"}}, {"seed": 155, "data": {"p1_how_many": "13", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.635, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625", "8.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}266}{7{,}700}, \\dfrac{4{,}652}{7{,}700}, \\dfrac{4{,}657}{7{,}700}, \\dfrac{4{,}700}{7{,}700}, \\dfrac{4{,}917}{7{,}700}, \\dfrac{5{,}017}{7{,}700}, \\dfrac{5{,}139}{7{,}700}, \\text{ and } \\dfrac{5{,}192}{7{,}700}", "__seed__": "0155"}}, {"seed": 156, "data": {"p1_how_many": "11", "p1_a": "4.17", "p1_b": "4.18", "p1_numbers": "4.1705, 4.171, 4.1715, 4.172, 4.173, 4.174, 4.175, 4.176, 4.177, 4.178, and 4.179", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.171", "4.172", "4.173", "4.1739999999999995", "4.175", "4.176", "4.177", "4.178", "4.179"], "p1_2_xs": ["4.1705", "4.1715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{544}{2{,}000}, \\dfrac{552}{2{,}000}, \\dfrac{559}{2{,}000}, \\dfrac{572}{2{,}000}, \\dfrac{585}{2{,}000}, \\dfrac{603}{2{,}000}, \\dfrac{626}{2{,}000}, \\dfrac{663}{2{,}000}, \\dfrac{685}{2{,}000}, \\dfrac{761}{2{,}000}, \\dfrac{762}{2{,}000}, \\text{ and } \\dfrac{794}{2{,}000}", "__seed__": "0156"}}, {"seed": 157, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{516}{1{,}500}, \\dfrac{521}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{536}{1{,}500}, \\dfrac{538}{1{,}500}, \\dfrac{559}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{563}{1{,}500}, \\dfrac{578}{1{,}500}, \\text{ and } \\dfrac{579}{1{,}500}", "__seed__": "0157"}}, {"seed": 158, "data": {"p1_how_many": "10", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}404}{3{,}000}, \\dfrac{2{,}407}{3{,}000}, \\dfrac{2{,}409}{3{,}000}, \\dfrac{2{,}432}{3{,}000}, \\dfrac{2{,}437}{3{,}000}, \\dfrac{2{,}452}{3{,}000}, \\dfrac{2{,}467}{3{,}000}, \\dfrac{2{,}478}{3{,}000}, \\dfrac{2{,}483}{3{,}000}, \\text{ and } \\dfrac{2{,}498}{3{,}000}", "__seed__": "0158"}}, {"seed": 159, "data": {"p1_how_many": "14", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.125, 1.13, 1.135, 1.14, 1.145, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115", "1.125", "1.135", "1.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}141}{5{,}600}, \\dfrac{2{,}151}{5{,}600}, \\dfrac{2{,}169}{5{,}600}, \\dfrac{2{,}210}{5{,}600}, \\dfrac{2{,}235}{5{,}600}, \\dfrac{2{,}304}{5{,}600}, \\text{ and } \\dfrac{2{,}326}{5{,}600}", "__seed__": "0159"}}, {"seed": 160, "data": {"p1_how_many": "14", "p1_a": "6.4", "p1_b": "6.5", "p1_numbers": "6.4005, 6.401, 6.4015, 6.402, 6.4025, 6.403, 6.4035, 6.404, 6.4045, 6.405, 6.406, 6.407, 6.408, and 6.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.401000000000001", "6.402", "6.4030000000000005", "6.404", "6.405", "6.406000000000001", "6.407", "6.408", "6.409000000000001"], "p1_2_xs": ["6.4005", "6.4015", "6.4025", "6.4035", "6.4045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}513}{4{,}200}, \\dfrac{3{,}527}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}543}{4{,}200}, \\dfrac{3{,}550}{4{,}200}, \\text{ and } \\dfrac{3{,}560}{4{,}200}", "__seed__": "0160"}}, {"seed": 161, "data": {"p1_how_many": "13", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.435, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425", "7.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{321}{560}, \\dfrac{324}{560}, \\dfrac{331}{560}, \\dfrac{332}{560}, \\dfrac{334}{560}, \\dfrac{337}{560}, \\dfrac{343}{560}, \\dfrac{344}{560}, \\text{ and } \\dfrac{346}{560}", "__seed__": "0161"}}, {"seed": 162, "data": {"p1_how_many": "11", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}870}{20{,}000}, \\dfrac{5{,}873}{20{,}000}, \\dfrac{5{,}900}{20{,}000}, \\dfrac{6{,}161}{20{,}000}, \\dfrac{6{,}443}{20{,}000}, \\dfrac{6{,}542}{20{,}000}, \\dfrac{6{,}640}{20{,}000}, \\dfrac{7{,}039}{20{,}000}, \\dfrac{7{,}611}{20{,}000}, \\dfrac{7{,}673}{20{,}000}, \\text{ and } \\dfrac{7{,}807}{20{,}000}", "__seed__": "0162"}}, {"seed": 163, "data": {"p1_how_many": "11", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}079}{3{,}500}, \\dfrac{1{,}116}{3{,}500}, \\dfrac{1{,}171}{3{,}500}, \\dfrac{1{,}189}{3{,}500}, \\dfrac{1{,}191}{3{,}500}, \\dfrac{1{,}258}{3{,}500}, \\dfrac{1{,}269}{3{,}500}, \\dfrac{1{,}316}{3{,}500}, \\dfrac{1{,}325}{3{,}500}, \\dfrac{1{,}353}{3{,}500}, \\text{ and } \\dfrac{1{,}354}{3{,}500}", "__seed__": "0163"}}, {"seed": 164, "data": {"p1_how_many": "10", "p1_a": "5.14", "p1_b": "5.15", "p1_numbers": "5.1405, 5.141, 5.142, 5.143, 5.144, 5.145, 5.146, 5.147, 5.148, and 5.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.141", "5.1419999999999995", "5.143", "5.143999999999999", "5.145", "5.146", "5.146999999999999", "5.148", "5.149"], "p1_2_xs": ["5.140499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{151}{350}, \\dfrac{168}{350}, \\dfrac{179}{350}, \\dfrac{181}{350}, \\dfrac{185}{350}, \\dfrac{187}{350}, \\dfrac{191}{350}, \\dfrac{205}{350}, \\text{ and } \\dfrac{207}{350}", "__seed__": "0164"}}, {"seed": 165, "data": {"p1_how_many": "13", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.535, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995", "4.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}266}{20{,}000}, \\dfrac{15{,}267}{20{,}000}, \\dfrac{15{,}457}{20{,}000}, \\dfrac{15{,}486}{20{,}000}, \\dfrac{15{,}581}{20{,}000}, \\dfrac{15{,}756}{20{,}000}, \\dfrac{15{,}857}{20{,}000}, \\dfrac{15{,}889}{20{,}000}, \\dfrac{15{,}906}{20{,}000}, \\text{ and } \\dfrac{15{,}988}{20{,}000}", "__seed__": "0165"}}, {"seed": 166, "data": {"p1_how_many": "14", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.3005, 2.301, 2.3015, 2.302, 2.3025, 2.303, 2.3035, 2.304, 2.3045, 2.305, 2.306, 2.307, 2.308, and 2.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3009999999999997", "2.3019999999999996", "2.303", "2.304", "2.3049999999999997", "2.3059999999999996", "2.307", "2.308", "2.3089999999999997"], "p1_2_xs": ["2.3005", "2.3015", "2.3024999999999998", "2.3035", "2.3045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{509}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{533}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{570}{1{,}500}, \\text{ and } \\dfrac{592}{1{,}500}", "__seed__": "0166"}}, {"seed": 167, "data": {"p1_how_many": "12", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number 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\\dfrac{35{,}272}{42{,}000}, \\dfrac{35{,}369}{42{,}000}, \\dfrac{35{,}433}{42{,}000}, \\dfrac{35{,}463}{42{,}000}, \\dfrac{35{,}912}{42{,}000}, \\text{ and } \\dfrac{35{,}915}{42{,}000}", "__seed__": "0168"}}, {"seed": 169, "data": {"p1_how_many": "10", "p1_a": "9.66", "p1_b": "9.67", "p1_numbers": "9.6605, 9.661, 9.662, 9.663, 9.664, 9.665, 9.666, 9.667, 9.668, and 9.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.661", "9.662", "9.663", "9.664", "9.665000000000001", "9.666", "9.667", "9.668", "9.669"], "p1_2_xs": ["9.6605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{656}{1{,}500}, \\dfrac{692}{1{,}500}, \\dfrac{721}{1{,}500}, \\dfrac{722}{1{,}500}, \\dfrac{728}{1{,}500}, \\dfrac{744}{1{,}500}, \\dfrac{777}{1{,}500}, \\dfrac{900}{1{,}500}, \\dfrac{972}{1{,}500}, \\text{ and } \\dfrac{982}{1{,}500}", "__seed__": "0169"}}, {"seed": 170, "data": {"p1_how_many": "11", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}145}{20{,}000}, \\dfrac{4{,}196}{20{,}000}, \\dfrac{4{,}242}{20{,}000}, \\dfrac{4{,}258}{20{,}000}, \\dfrac{4{,}412}{20{,}000}, \\dfrac{4{,}534}{20{,}000}, \\dfrac{4{,}590}{20{,}000}, \\dfrac{4{,}678}{20{,}000}, \\dfrac{4{,}741}{20{,}000}, \\dfrac{4{,}832}{20{,}000}, \\text{ and } \\dfrac{4{,}871}{20{,}000}", "__seed__": "0170"}}, {"seed": 171, "data": {"p1_how_many": "11", "p1_a": "5.03", "p1_b": "5.04", "p1_numbers": "5.0305, 5.031, 5.0315, 5.032, 5.033, 5.034, 5.035, 5.036, 5.037, 5.038, and 5.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.031000000000001", "5.032", "5.033", "5.034", "5.035", "5.0360000000000005", "5.037", "5.038", "5.039000000000001"], "p1_2_xs": ["5.0305", "5.0315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0171"}}, {"seed": 172, "data": {"p1_how_many": "12", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}505}{4{,}200}, \\dfrac{3{,}516}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}541}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}555}{4{,}200}, \\dfrac{3{,}559}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}573}{4{,}200}, \\text{ and } \\dfrac{3{,}595}{4{,}200}", "__seed__": "0172"}}, {"seed": 173, "data": {"p1_how_many": "10", "p1_a": "8.12", "p1_b": "8.13", "p1_numbers": "8.1205, 8.121, 8.122, 8.123, 8.124, 8.125, 8.126, 8.127, 8.128, and 8.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.120999999999999", "8.122", "8.123", "8.123999999999999", "8.125", "8.126", "8.126999999999999", "8.127999999999998", "8.129"], "p1_2_xs": ["8.1205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0173"}}, {"seed": 174, "data": {"p1_how_many": "11", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}514}{2{,}000}, \\dfrac{1{,}546}{2{,}000}, \\dfrac{1{,}557}{2{,}000}, \\dfrac{1{,}558}{2{,}000}, \\dfrac{1{,}567}{2{,}000}, \\dfrac{1{,}576}{2{,}000}, \\text{ and } \\dfrac{1{,}592}{2{,}000}", "__seed__": "0174"}}, {"seed": 175, "data": {"p1_how_many": "10", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.42, 5.43, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{602}{4{,}200}, \\dfrac{605}{4{,}200}, \\dfrac{617}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{656}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{682}{4{,}200}, \\dfrac{687}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0175"}}, {"seed": 176, "data": {"p1_how_many": "14", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.125, 5.13, 5.135, 5.14, 5.145, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999", "5.124999999999999", "5.135", "5.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}968}{35{,}000}, \\dfrac{8{,}071}{35{,}000}, \\dfrac{8{,}149}{35{,}000}, \\dfrac{8{,}243}{35{,}000}, \\dfrac{8{,}640}{35{,}000}, \\dfrac{8{,}710}{35{,}000}, \\dfrac{8{,}955}{35{,}000}, \\dfrac{9{,}075}{35{,}000}, \\dfrac{9{,}300}{35{,}000}, \\text{ and } \\dfrac{9{,}879}{35{,}000}", "__seed__": "0176"}}, {"seed": 177, "data": {"p1_how_many": "14", "p1_a": "4.43", "p1_b": "4.44", "p1_numbers": "4.4305, 4.431, 4.4315, 4.432, 4.4325, 4.433, 4.4335, 4.434, 4.4345, 4.435, 4.436, 4.437, 4.438, and 4.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.431", "4.4319999999999995", "4.433", "4.433999999999999", "4.435", "4.436", "4.436999999999999", "4.438", "4.439"], "p1_2_xs": ["4.430499999999999", "4.4315", "4.432499999999999", "4.4334999999999996", "4.434499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}057}{42{,}000}, \\dfrac{35{,}082}{42{,}000}, \\dfrac{35{,}254}{42{,}000}, \\dfrac{35{,}262}{42{,}000}, \\dfrac{35{,}319}{42{,}000}, \\dfrac{35{,}361}{42{,}000}, \\dfrac{35{,}374}{42{,}000}, \\dfrac{35{,}402}{42{,}000}, \\dfrac{35{,}738}{42{,}000}, \\dfrac{35{,}860}{42{,}000}, \\text{ and } \\dfrac{35{,}948}{42{,}000}", "__seed__": "0177"}}, {"seed": 178, "data": {"p1_how_many": "13", "p1_a": "4.65", "p1_b": "4.66", "p1_numbers": "4.6505, 4.651, 4.6515, 4.652, 4.6525, 4.653, 4.6535, 4.654, 4.655, 4.656, 4.657, 4.658, and 4.659", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.651000000000001", "4.652", "4.6530000000000005", "4.654", "4.655", "4.656000000000001", "4.657", "4.658", "4.659000000000001"], "p1_2_xs": ["4.6505", "4.6515", "4.6525", "4.6535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}215}{7{,}700}, \\dfrac{4{,}382}{7{,}700}, \\dfrac{4{,}460}{7{,}700}, \\dfrac{4{,}476}{7{,}700}, \\dfrac{4{,}630}{7{,}700}, \\dfrac{4{,}728}{7{,}700}, \\dfrac{4{,}799}{7{,}700}, \\dfrac{5{,}294}{7{,}700}, \\dfrac{5{,}307}{7{,}700}, \\text{ and } \\dfrac{5{,}337}{7{,}700}", "__seed__": 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"0179"}}, {"seed": 180, "data": {"p1_how_many": "14", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.635, 4.64, 4.645, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999", "4.635", "4.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{413}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{419}{2{,}000}, \\dfrac{441}{2{,}000}, \\dfrac{447}{2{,}000}, \\dfrac{458}{2{,}000}, \\dfrac{472}{2{,}000}, \\dfrac{483}{2{,}000}, \\dfrac{485}{2{,}000}, \\dfrac{486}{2{,}000}, \\dfrac{490}{2{,}000}, \\text{ and } \\dfrac{498}{2{,}000}", "__seed__": "0180"}}, {"seed": 181, "data": {"p1_how_many": "10", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}169}{30{,}000}, \\dfrac{24{,}351}{30{,}000}, \\dfrac{24{,}386}{30{,}000}, \\dfrac{24{,}408}{30{,}000}, \\dfrac{24{,}512}{30{,}000}, \\dfrac{24{,}569}{30{,}000}, \\dfrac{24{,}610}{30{,}000}, \\dfrac{24{,}754}{30{,}000}, \\text{ and } \\dfrac{24{,}816}{30{,}000}", "__seed__": "0181"}}, {"seed": 182, "data": {"p1_how_many": "11", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{603}{1{,}500}, \\dfrac{655}{1{,}500}, \\dfrac{672}{1{,}500}, \\dfrac{688}{1{,}500}, \\dfrac{691}{1{,}500}, \\dfrac{700}{1{,}500}, \\dfrac{771}{1{,}500}, \\dfrac{904}{1{,}500}, \\dfrac{917}{1{,}500}, \\dfrac{931}{1{,}500}, \\dfrac{942}{1{,}500}, \\text{ and } \\dfrac{962}{1{,}500}", "__seed__": "0182"}}, {"seed": 183, "data": {"p1_how_many": "10", "p1_a": "3.91", "p1_b": "3.92", "p1_numbers": "3.9105, 3.911, 3.912, 3.913, 3.914, 3.915, 3.916, 3.917, 3.918, and 3.919", "p1_decimal_vals": "2", "p1_increment": 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on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}029}{3{,}500}, \\dfrac{1{,}042}{3{,}500}, \\dfrac{1{,}085}{3{,}500}, \\dfrac{1{,}134}{3{,}500}, \\dfrac{1{,}141}{3{,}500}, \\dfrac{1{,}193}{3{,}500}, \\dfrac{1{,}199}{3{,}500}, \\dfrac{1{,}313}{3{,}500}, \\text{ and } \\dfrac{1{,}331}{3{,}500}", "__seed__": "0185"}}, {"seed": 186, "data": {"p1_how_many": "12", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}020}{15{,}000}, \\dfrac{6{,}659}{15{,}000}, \\dfrac{7{,}395}{15{,}000}, \\dfrac{7{,}514}{15{,}000}, \\dfrac{7{,}746}{15{,}000}, \\dfrac{8{,}297}{15{,}000}, \\dfrac{8{,}363}{15{,}000}, \\dfrac{8{,}440}{15{,}000}, \\dfrac{8{,}499}{15{,}000}, \\text{ and } \\dfrac{9{,}247}{15{,}000}", "__seed__": "0186"}}, {"seed": 187, "data": {"p1_how_many": "12", "p1_a": "3.93", "p1_b": "3.94", "p1_numbers": "3.9305, 3.931, 3.9315, 3.932, 3.9325, 3.933, 3.934, 3.935, 3.936, 3.937, 3.938, and 3.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.931", "3.932", "3.9330000000000003", "3.934", "3.935", "3.936", "3.9370000000000003", "3.938", "3.939"], "p1_2_xs": ["3.9305000000000003", "3.9315", "3.9325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}039}{42{,}000}, \\dfrac{6{,}044}{42{,}000}, \\dfrac{6{,}057}{42{,}000}, \\dfrac{6{,}377}{42{,}000}, \\dfrac{6{,}403}{42{,}000}, \\dfrac{6{,}427}{42{,}000}, \\dfrac{6{,}479}{42{,}000}, \\dfrac{6{,}638}{42{,}000}, \\dfrac{6{,}686}{42{,}000}, \\text{ and } \\dfrac{6{,}794}{42{,}000}", "__seed__": "0187"}}, {"seed": 188, "data": {"p1_how_many": "14", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.235, 9.24, 9.245, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225", "9.235", "9.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}257}{7{,}700}, \\dfrac{4{,}579}{7{,}700}, \\dfrac{4{,}764}{7{,}700}, \\dfrac{5{,}239}{7{,}700}, \\dfrac{5{,}393}{7{,}700}, \\dfrac{5{,}661}{7{,}700}, \\dfrac{5{,}778}{7{,}700}, \\dfrac{6{,}003}{7{,}700}, \\dfrac{6{,}009}{7{,}700}, \\dfrac{6{,}233}{7{,}700}, \\text{ and } \\dfrac{6{,}326}{7{,}700}", "__seed__": "0188"}}, {"seed": 189, "data": {"p1_how_many": "12", "p1_a": "8.25", "p1_b": "8.26", "p1_numbers": "8.2505, 8.251, 8.2515, 8.252, 8.2525, 8.253, 8.254, 8.255, 8.256, 8.257, 8.258, and 8.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.251", "8.252", "8.253", "8.254", "8.255", "8.256", "8.257", "8.258", "8.259"], "p1_2_xs": ["8.2505", "8.2515", "8.252500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0189"}}, {"seed": 190, "data": 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7.125, 7.13, 7.135, 7.14, 7.145, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135", "7.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}125}{20{,}000}, \\dfrac{4{,}137}{20{,}000}, \\dfrac{4{,}206}{20{,}000}, \\dfrac{4{,}289}{20{,}000}, \\dfrac{4{,}496}{20{,}000}, \\dfrac{4{,}511}{20{,}000}, \\dfrac{4{,}514}{20{,}000}, \\dfrac{4{,}524}{20{,}000}, \\dfrac{4{,}624}{20{,}000}, \\dfrac{4{,}727}{20{,}000}, \\text{ and } \\dfrac{4{,}949}{20{,}000}", "__seed__": "0191"}}, {"seed": 192, "data": {"p1_how_many": "10", "p1_a": "7.03", "p1_b": "7.04", "p1_numbers": "7.0305, 7.031, 7.032, 7.033, 7.034, 7.035, 7.036, 7.037, 7.038, and 7.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.031000000000001", "7.032", "7.033", "7.034", "7.035", "7.0360000000000005", "7.037", "7.038", "7.039000000000001"], "p1_2_xs": ["7.0305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}235}{7{,}700}, \\dfrac{4{,}281}{7{,}700}, \\dfrac{4{,}694}{7{,}700}, \\dfrac{4{,}940}{7{,}700}, \\dfrac{5{,}378}{7{,}700}, \\dfrac{5{,}419}{7{,}700}, \\dfrac{5{,}431}{7{,}700}, \\dfrac{5{,}493}{7{,}700}, \\dfrac{5{,}539}{7{,}700}, \\dfrac{5{,}816}{7{,}700}, \\text{ and } \\dfrac{6{,}088}{7{,}700}", "__seed__": "0192"}}, {"seed": 193, "data": {"p1_how_many": "12", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}014}{20{,}000}, \\dfrac{5{,}019}{20{,}000}, \\dfrac{5{,}608}{20{,}000}, \\dfrac{6{,}113}{20{,}000}, \\dfrac{6{,}129}{20{,}000}, \\dfrac{7{,}092}{20{,}000}, \\dfrac{7{,}643}{20{,}000}, \\dfrac{7{,}705}{20{,}000}, \\dfrac{7{,}768}{20{,}000}, \\dfrac{7{,}868}{20{,}000}, \\text{ and } \\dfrac{7{,}953}{20{,}000}", "__seed__": "0193"}}, {"seed": 194, "data": {"p1_how_many": "10", "p1_a": "3.87", "p1_b": "3.88", "p1_numbers": "3.8705, 3.871, 3.872, 3.873, 3.874, 3.875, 3.876, 3.877, 3.878, and 3.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.871", "3.872", "3.873", "3.874", "3.875", "3.876", "3.8770000000000002", "3.878", "3.879"], "p1_2_xs": ["3.8705000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{126}{200}, \\dfrac{127}{200}, \\dfrac{128}{200}, \\dfrac{131}{200}, \\dfrac{133}{200}, \\dfrac{140}{200}, \\dfrac{144}{200}, \\dfrac{145}{200}, \\text{ and } \\dfrac{146}{200}", "__seed__": "0194"}}, {"seed": 195, "data": {"p1_how_many": "11", "p1_a": "3.72", "p1_b": "3.73", "p1_numbers": "3.7205, 3.721, 3.7215, 3.722, 3.723, 3.724, 3.725, 3.726, 3.727, 3.728, and 3.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.721", "3.722", "3.7230000000000003", "3.724", "3.725", "3.726", "3.7270000000000003", "3.728", "3.729"], "p1_2_xs": ["3.7205000000000004", "3.7215000000000003"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}537}{4{,}200}, \\dfrac{3{,}544}{4{,}200}, \\dfrac{3{,}548}{4{,}200}, \\dfrac{3{,}560}{4{,}200}, \\dfrac{3{,}563}{4{,}200}, \\dfrac{3{,}567}{4{,}200}, \\text{ and } \\dfrac{3{,}587}{4{,}200}", "__seed__": "0195"}}, {"seed": 196, "data": {"p1_how_many": "13", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.005, 5.01, 5.015, 5.02, 5.025, 5.03, 5.035, 5.04, 5.05, 5.06, 5.07, 5.08, and 5.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005", "5.015", "5.0249999999999995", "5.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}543}{3{,}500}, \\dfrac{1{,}588}{3{,}500}, \\dfrac{1{,}632}{3{,}500}, \\dfrac{1{,}634}{3{,}500}, \\dfrac{1{,}703}{3{,}500}, \\dfrac{1{,}806}{3{,}500}, \\dfrac{1{,}830}{3{,}500}, \\dfrac{1{,}992}{3{,}500}, \\text{ and } \\dfrac{2{,}086}{3{,}500}", "__seed__": "0196"}}, {"seed": 197, "data": {"p1_how_many": "12", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{747}{4{,}200}, \\dfrac{772}{4{,}200}, \\dfrac{784}{4{,}200}, \\dfrac{805}{4{,}200}, \\dfrac{862}{4{,}200}, \\dfrac{868}{4{,}200}, \\dfrac{881}{4{,}200}, \\dfrac{931}{4{,}200}, \\dfrac{935}{4{,}200}, \\dfrac{1{,}117}{4{,}200}, \\dfrac{1{,}135}{4{,}200}, \\text{ and } \\dfrac{1{,}188}{4{,}200}", "__seed__": "0197"}}, {"seed": 198, "data": {"p1_how_many": "10", "p1_a": "3.27", "p1_b": "3.28", "p1_numbers": "3.2705, 3.271, 3.272, 3.273, 3.274, 3.275, 3.276, 3.277, 3.278, and 3.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.271", "3.272", "3.273", "3.274", "3.275", "3.276", "3.277", "3.278", "3.279"], "p1_2_xs": ["3.2705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}663}{63{,}000}, \\dfrac{28{,}914}{63{,}000}, \\dfrac{29{,}229}{63{,}000}, \\dfrac{29{,}513}{63{,}000}, \\dfrac{29{,}855}{63{,}000}, \\dfrac{32{,}010}{63{,}000}, \\dfrac{33{,}570}{63{,}000}, \\dfrac{34{,}556}{63{,}000}, \\text{ and } \\dfrac{34{,}793}{63{,}000}", "__seed__": "0198"}}, {"seed": 199, "data": {"p1_how_many": "11", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.015, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{61}{420}, \\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0199"}}, {"seed": 200, "data": {"p1_how_many": "14", "p1_a": "4.06", "p1_b": "4.07", "p1_numbers": "4.0605, 4.061, 4.0615, 4.062, 4.0625, 4.063, 4.0635, 4.064, 4.0645, 4.065, 4.066, 4.067, 4.068, and 4.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.061", "4.061999999999999", "4.063", "4.063999999999999", "4.0649999999999995", "4.066", "4.066999999999999", "4.068", "4.069"], "p1_2_xs": ["4.060499999999999", "4.0615", "4.062499999999999", "4.0634999999999994", "4.064499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{67}{150}, \\dfrac{69}{150}, \\dfrac{74}{150}, \\dfrac{77}{150}, \\dfrac{84}{150}, \\dfrac{90}{150}, \\dfrac{95}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0200"}}, {"seed": 201, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}026}{35{,}000}, \\dfrac{7{,}989}{35{,}000}, \\dfrac{8{,}378}{35{,}000}, \\dfrac{8{,}670}{35{,}000}, \\dfrac{8{,}918}{35{,}000}, \\dfrac{8{,}967}{35{,}000}, \\dfrac{9{,}528}{35{,}000}, \\dfrac{9{,}530}{35{,}000}, \\dfrac{9{,}659}{35{,}000}, \\text{ and } \\dfrac{9{,}851}{35{,}000}", "__seed__": "0201"}}, {"seed": 202, "data": {"p1_how_many": "12", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.215, 1.22, 1.225, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998", "1.2149999999999999", "1.2249999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}111}{12{,}000}, \\dfrac{3{,}348}{12{,}000}, \\dfrac{3{,}402}{12{,}000}, \\dfrac{3{,}519}{12{,}000}, \\dfrac{3{,}548}{12{,}000}, \\dfrac{3{,}591}{12{,}000}, \\dfrac{3{,}735}{12{,}000}, \\dfrac{3{,}771}{12{,}000}, \\dfrac{3{,}809}{12{,}000}, \\dfrac{3{,}893}{12{,}000}, \\dfrac{3{,}949}{12{,}000}, \\text{ and } \\dfrac{3{,}956}{12{,}000}", "__seed__": "0202"}}, {"seed": 203, "data": {"p1_how_many": "14", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.025, 3.03, 3.035, 3.04, 3.045, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997", "3.025", "3.0349999999999997", "3.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{732}{3{,}500}, \\dfrac{740}{3{,}500}, \\dfrac{760}{3{,}500}, \\dfrac{794}{3{,}500}, \\dfrac{957}{3{,}500}, \\dfrac{963}{3{,}500}, \\dfrac{977}{3{,}500}, \\text{ and } \\dfrac{995}{3{,}500}", "__seed__": "0203"}}, {"seed": 204, "data": {"p1_how_many": "12", "p1_a": "2.91", "p1_b": "2.92", "p1_numbers": "2.9105, 2.911, 2.9115, 2.912, 2.9125, 2.913, 2.914, 2.915, 2.916, 2.917, 2.918, and 2.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.911", "2.912", "2.9130000000000003", "2.914", "2.915", "2.916", "2.9170000000000003", "2.918", "2.919"], "p1_2_xs": ["2.9105000000000003", "2.9115", "2.9125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}102}{20{,}000}, \\dfrac{4{,}108}{20{,}000}, \\dfrac{4{,}215}{20{,}000}, \\dfrac{4{,}220}{20{,}000}, \\dfrac{4{,}543}{20{,}000}, \\dfrac{4{,}545}{20{,}000}, \\text{ and } \\dfrac{4{,}728}{20{,}000}", "__seed__": "0204"}}, {"seed": 205, "data": {"p1_how_many": "10", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{1{,}099}{6{,}300}, \\dfrac{1{,}107}{6{,}300}, \\dfrac{1{,}127}{6{,}300}, \\dfrac{1{,}168}{6{,}300}, \\dfrac{1{,}177}{6{,}300}, \\dfrac{1{,}194}{6{,}300}, \\dfrac{1{,}200}{6{,}300}, \\text{ and } \\dfrac{1{,}395}{6{,}300}", "__seed__": "0205"}}, {"seed": 206, "data": {"p1_how_many": "11", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{518}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{538}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{557}{1{,}500}, \\dfrac{565}{1{,}500}, \\dfrac{585}{1{,}500}, \\text{ and } \\dfrac{596}{1{,}500}", "__seed__": "0206"}}, {"seed": 207, "data": {"p1_how_many": "11", "p1_a": "8.94", "p1_b": "8.95", "p1_numbers": "8.9405, 8.941, 8.9415, 8.942, 8.943, 8.944, 8.945, 8.946, 8.947, 8.948, and 8.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.940999999999999", "8.942", "8.943", "8.943999999999999", "8.945", "8.946", "8.947", "8.947999999999999", "8.949"], "p1_2_xs": ["8.9405", "8.9415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{202}{350}, \\dfrac{205}{350}, \\dfrac{218}{350}, \\dfrac{236}{350}, \\dfrac{248}{350}, \\dfrac{256}{350}, \\dfrac{263}{350}, \\text{ and } \\dfrac{275}{350}", "__seed__": "0207"}}, {"seed": 208, "data": {"p1_how_many": "14", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.545, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535", "7.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{73}{420}, \\dfrac{83}{420}, \\dfrac{85}{420}, \\dfrac{94}{420}, \\dfrac{99}{420}, \\dfrac{100}{420}, \\text{ and } \\dfrac{107}{420}", "__seed__": "0208"}}, {"seed": 209, "data": {"p1_how_many": "13", "p1_a": "6.74", "p1_b": "6.75", "p1_numbers": "6.7405, 6.741, 6.7415, 6.742, 6.7425, 6.743, 6.7435, 6.744, 6.745, 6.746, 6.747, 6.748, and 6.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.7410000000000005", "6.742", "6.743", "6.744", "6.745", "6.746", "6.747", "6.748", "6.7490000000000006"], "p1_2_xs": ["6.7405", "6.7415", "6.7425", "6.7435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{241}{350}, \\dfrac{242}{350}, \\dfrac{256}{350}, \\dfrac{257}{350}, \\dfrac{260}{350}, \\dfrac{267}{350}, \\dfrac{268}{350}, \\text{ and } \\dfrac{276}{350}", "__seed__": "0209"}}, {"seed": 210, "data": {"p1_how_many": "10", "p1_a": "9.66", "p1_b": "9.67", "p1_numbers": "9.6605, 9.661, 9.662, 9.663, 9.664, 9.665, 9.666, 9.667, 9.668, and 9.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.661", "9.662", "9.663", "9.664", "9.665000000000001", "9.666", "9.667", "9.668", "9.669"], "p1_2_xs": ["9.6605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}109}{4{,}200}, \\dfrac{3{,}148}{4{,}200}, \\dfrac{3{,}209}{4{,}200}, \\dfrac{3{,}248}{4{,}200}, \\dfrac{3{,}333}{4{,}200}, \\dfrac{3{,}461}{4{,}200}, \\text{ and } \\dfrac{3{,}463}{4{,}200}", "__seed__": "0210"}}, {"seed": 211, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}508}{2{,}000}, \\dfrac{1{,}514}{2{,}000}, \\dfrac{1{,}525}{2{,}000}, \\dfrac{1{,}538}{2{,}000}, \\dfrac{1{,}546}{2{,}000}, \\dfrac{1{,}575}{2{,}000}, \\text{ and } \\dfrac{1{,}581}{2{,}000}", "__seed__": "0211"}}, {"seed": 212, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}702}{6{,}300}, \\dfrac{2{,}707}{6{,}300}, \\dfrac{2{,}723}{6{,}300}, \\dfrac{2{,}724}{6{,}300}, \\dfrac{2{,}727}{6{,}300}, \\dfrac{2{,}728}{6{,}300}, \\dfrac{2{,}732}{6{,}300}, \\dfrac{2{,}754}{6{,}300}, \\dfrac{2{,}775}{6{,}300}, \\dfrac{2{,}788}{6{,}300}, \\text{ and } \\dfrac{2{,}791}{6{,}300}", "__seed__": "0212"}}, {"seed": 213, "data": {"p1_how_many": "11", "p1_a": "8.43", "p1_b": "8.44", "p1_numbers": "8.4305, 8.431, 8.4315, 8.432, 8.433, 8.434, 8.435, 8.436, 8.437, 8.438, and 8.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.431", "8.432", "8.433", "8.434", "8.435", "8.436", "8.437", "8.437999999999999", "8.439"], "p1_2_xs": ["8.4305", "8.4315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}128}{5{,}600}, \\dfrac{2{,}132}{5{,}600}, \\dfrac{2{,}149}{5{,}600}, \\dfrac{2{,}236}{5{,}600}, \\dfrac{2{,}252}{5{,}600}, \\dfrac{2{,}265}{5{,}600}, \\dfrac{2{,}289}{5{,}600}, \\dfrac{2{,}297}{5{,}600}, \\dfrac{2{,}302}{5{,}600}, \\text{ and } \\dfrac{2{,}379}{5{,}600}", "__seed__": "0213"}}, {"seed": 214, "data": {"p1_how_many": "12", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.015, 9.02, 9.025, 9.03, 9.04, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005", "9.015", "9.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{512}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{531}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{540}{1{,}500}, \\dfrac{571}{1{,}500}, \\dfrac{577}{1{,}500}, \\dfrac{581}{1{,}500}, \\dfrac{588}{1{,}500}, \\dfrac{590}{1{,}500}, \\text{ and } \\dfrac{598}{1{,}500}", "__seed__": "0214"}}, {"seed": 215, "data": {"p1_how_many": "14", "p1_a": "2.41", "p1_b": "2.42", "p1_numbers": "2.4105, 2.411, 2.4115, 2.412, 2.4125, 2.413, 2.4135, 2.414, 2.4145, 2.415, 2.416, 2.417, 2.418, and 2.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.411", "2.412", "2.4130000000000003", "2.414", "2.415", "2.416", "2.4170000000000003", "2.418", "2.419"], "p1_2_xs": ["2.4105000000000003", "2.4115", "2.4125", "2.4135000000000004", "2.4145000000000003"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}057}{12{,}000}, \\dfrac{3{,}243}{12{,}000}, \\dfrac{3{,}263}{12{,}000}, \\dfrac{3{,}405}{12{,}000}, \\dfrac{3{,}455}{12{,}000}, \\dfrac{3{,}494}{12{,}000}, \\dfrac{3{,}785}{12{,}000}, \\dfrac{3{,}854}{12{,}000}, \\dfrac{3{,}894}{12{,}000}, \\dfrac{3{,}915}{12{,}000}, \\text{ and } \\dfrac{3{,}929}{12{,}000}", "__seed__": "0215"}}, {"seed": 216, "data": {"p1_how_many": "11", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}021}{15{,}000}, \\dfrac{5{,}059}{15{,}000}, \\dfrac{5{,}225}{15{,}000}, \\dfrac{5{,}472}{15{,}000}, \\dfrac{5{,}517}{15{,}000}, \\dfrac{5{,}610}{15{,}000}, \\dfrac{5{,}654}{15{,}000}, \\dfrac{5{,}700}{15{,}000}, \\dfrac{5{,}728}{15{,}000}, \\dfrac{5{,}758}{15{,}000}, \\text{ and } \\dfrac{5{,}851}{15{,}000}", "__seed__": "0216"}}, {"seed": 217, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}097}{63{,}000}, \\dfrac{27{,}287}{63{,}000}, \\dfrac{27{,}479}{63{,}000}, \\dfrac{27{,}563}{63{,}000}, \\dfrac{27{,}649}{63{,}000}, \\dfrac{27{,}686}{63{,}000}, \\dfrac{27{,}768}{63{,}000}, \\dfrac{27{,}922}{63{,}000}, \\text{ and } \\dfrac{27{,}991}{63{,}000}", "__seed__": "0217"}}, {"seed": 218, "data": {"p1_how_many": "10", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.0005, 5.001, 5.002, 5.003, 5.004, 5.005, 5.006, 5.007, 5.008, and 5.009", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.001", "5.002", "5.003", "5.004", "5.005", "5.006", "5.007", "5.008", "5.009"], "p1_2_xs": ["5.0005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}049}{30{,}000}, \\dfrac{5{,}060}{30{,}000}, \\dfrac{5{,}080}{30{,}000}, \\dfrac{5{,}082}{30{,}000}, \\dfrac{5{,}131}{30{,}000}, \\dfrac{5{,}237}{30{,}000}, \\dfrac{5{,}294}{30{,}000}, \\dfrac{5{,}315}{30{,}000}, \\dfrac{5{,}383}{30{,}000}, \\dfrac{5{,}428}{30{,}000}, \\dfrac{5{,}816}{30{,}000}, \\text{ and } \\dfrac{5{,}996}{30{,}000}", "__seed__": "0218"}}, {"seed": 219, "data": {"p1_how_many": "13", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.2005, 8.201, 8.2015, 8.202, 8.2025, 8.203, 8.2035, 8.204, 8.205, 8.206, 8.207, 8.208, and 8.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.200999999999999", "8.202", "8.203", "8.203999999999999", "8.205", "8.206", "8.206999999999999", "8.207999999999998", "8.209"], "p1_2_xs": ["8.2005", "8.2015", "8.2025", "8.2035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}108}{63{,}000}, \\dfrac{14{,}109}{63{,}000}, \\dfrac{14{,}308}{63{,}000}, \\dfrac{15{,}114}{63{,}000}, \\dfrac{15{,}310}{63{,}000}, \\dfrac{15{,}672}{63{,}000}, \\dfrac{16{,}385}{63{,}000}, \\dfrac{17{,}037}{63{,}000}, \\dfrac{17{,}091}{63{,}000}, \\text{ and } \\dfrac{17{,}326}{63{,}000}", "__seed__": "0219"}}, {"seed": 220, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}413}{15{,}000}, \\dfrac{7{,}217}{15{,}000}, \\dfrac{7{,}264}{15{,}000}, \\dfrac{7{,}386}{15{,}000}, \\dfrac{7{,}581}{15{,}000}, \\dfrac{7{,}805}{15{,}000}, \\dfrac{8{,}031}{15{,}000}, \\dfrac{8{,}151}{15{,}000}, \\dfrac{8{,}828}{15{,}000}, \\dfrac{9{,}495}{15{,}000}, \\dfrac{9{,}837}{15{,}000}, \\text{ and } \\dfrac{9{,}893}{15{,}000}", "__seed__": "0220"}}, {"seed": 221, "data": {"p1_how_many": "10", "p1_a": "5.51", "p1_b": "5.52", "p1_numbers": "5.5105, 5.511, 5.512, 5.513, 5.514, 5.515, 5.516, 5.517, 5.518, and 5.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.511", "5.512", "5.513", "5.513999999999999", "5.515", "5.516", "5.5169999999999995", "5.518", "5.519"], "p1_2_xs": ["5.5104999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}054}{35{,}000}, \\dfrac{20{,}126}{35{,}000}, \\dfrac{20{,}219}{35{,}000}, \\dfrac{20{,}221}{35{,}000}, \\dfrac{20{,}407}{35{,}000}, \\dfrac{20{,}546}{35{,}000}, \\dfrac{20{,}564}{35{,}000}, \\dfrac{20{,}588}{35{,}000}, \\dfrac{20{,}641}{35{,}000}, \\dfrac{20{,}897}{35{,}000}, \\text{ and } \\dfrac{20{,}968}{35{,}000}", "__seed__": "0221"}}, {"seed": 222, "data": {"p1_how_many": "12", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0222"}}, {"seed": 223, "data": {"p1_how_many": "12", "p1_a": "7.13", "p1_b": "7.14", "p1_numbers": "7.1305, 7.131, 7.1315, 7.132, 7.1325, 7.133, 7.134, 7.135, 7.136, 7.137, 7.138, and 7.139", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.131", "7.132", "7.133", "7.1339999999999995", "7.135", "7.136", "7.137", "7.138", "7.139"], "p1_2_xs": ["7.1305", "7.1315", "7.132499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{731}{4{,}200}, \\dfrac{745}{4{,}200}, \\dfrac{780}{4{,}200}, \\dfrac{782}{4{,}200}, \\dfrac{823}{4{,}200}, \\dfrac{834}{4{,}200}, \\dfrac{910}{4{,}200}, \\dfrac{932}{4{,}200}, \\text{ and } \\dfrac{1{,}051}{4{,}200}", "__seed__": "0223"}}, {"seed": 224, "data": {"p1_how_many": "10", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.22, 6.23, 6.24, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{607}{4{,}200}, \\dfrac{613}{4{,}200}, \\dfrac{621}{4{,}200}, \\dfrac{629}{4{,}200}, \\dfrac{631}{4{,}200}, \\dfrac{635}{4{,}200}, \\dfrac{666}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{669}{4{,}200}, \\text{ and } \\dfrac{682}{4{,}200}", "__seed__": "0224"}}, {"seed": 225, "data": {"p1_how_many": "12", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}551}{35{,}000}, \\dfrac{7{,}671}{35{,}000}, \\dfrac{8{,}324}{35{,}000}, \\dfrac{8{,}859}{35{,}000}, \\dfrac{9{,}326}{35{,}000}, \\dfrac{9{,}399}{35{,}000}, \\text{ and } \\dfrac{9{,}856}{35{,}000}", "__seed__": "0225"}}, {"seed": 226, "data": {"p1_how_many": "12", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{723}{5{,}600}, \\dfrac{724}{5{,}600}, \\dfrac{725}{5{,}600}, \\dfrac{735}{5{,}600}, \\dfrac{737}{5{,}600}, \\dfrac{744}{5{,}600}, \\dfrac{746}{5{,}600}, \\dfrac{752}{5{,}600}, \\dfrac{781}{5{,}600}, \\text{ and } \\dfrac{789}{5{,}600}", "__seed__": "0226"}}, {"seed": 227, "data": {"p1_how_many": "14", "p1_a": "4.02", "p1_b": "4.03", "p1_numbers": "4.0205, 4.021, 4.0215, 4.022, 4.0225, 4.023, 4.0235, 4.024, 4.0245, 4.025, 4.026, 4.027, 4.028, and 4.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.021", "4.021999999999999", "4.023", "4.023999999999999", "4.0249999999999995", "4.026", "4.026999999999999", "4.028", "4.029"], "p1_2_xs": ["4.020499999999999", "4.0215", "4.022499999999999", "4.023499999999999", "4.024499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{501}{2{,}000}, \\dfrac{514}{2{,}000}, \\dfrac{597}{2{,}000}, \\dfrac{643}{2{,}000}, \\dfrac{644}{2{,}000}, \\dfrac{663}{2{,}000}, \\dfrac{722}{2{,}000}, \\dfrac{771}{2{,}000}, \\dfrac{779}{2{,}000}, \\text{ and } \\dfrac{797}{2{,}000}", "__seed__": "0227"}}, {"seed": 228, "data": {"p1_how_many": "14", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.425, 5.43, 5.435, 5.44, 5.445, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415", "5.425", "5.4350000000000005", "5.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{809}{1{,}200}, \\dfrac{811}{1{,}200}, \\dfrac{821}{1{,}200}, \\dfrac{840}{1{,}200}, \\dfrac{843}{1{,}200}, \\dfrac{849}{1{,}200}, \\dfrac{869}{1{,}200}, \\dfrac{878}{1{,}200}, \\text{ and } \\dfrac{891}{1{,}200}", "__seed__": "0228"}}, {"seed": 229, "data": {"p1_how_many": "14", "p1_a": "5.11", "p1_b": "5.12", "p1_numbers": "5.1105, 5.111, 5.1115, 5.112, 5.1125, 5.113, 5.1135, 5.114, 5.1145, 5.115, 5.116, 5.117, 5.118, and 5.119", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.111000000000001", "5.112", "5.113", "5.114", "5.115", "5.1160000000000005", "5.117", "5.118", "5.119000000000001"], "p1_2_xs": ["5.1105", "5.1115", "5.1125", "5.1135", "5.1145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}648}{15{,}000}, \\dfrac{6{,}872}{15{,}000}, \\dfrac{6{,}917}{15{,}000}, \\dfrac{6{,}930}{15{,}000}, \\dfrac{7{,}387}{15{,}000}, \\dfrac{7{,}564}{15{,}000}, \\dfrac{8{,}044}{15{,}000}, \\dfrac{8{,}219}{15{,}000}, \\dfrac{8{,}630}{15{,}000}, \\dfrac{8{,}679}{15{,}000}, \\dfrac{8{,}775}{15{,}000}, \\text{ and } \\dfrac{9{,}155}{15{,}000}", "__seed__": "0229"}}, {"seed": 230, "data": {"p1_how_many": "12", "p1_a": "1.8", "p1_b": "1.9", "p1_numbers": "1.8005, 1.801, 1.8015, 1.802, 1.8025, 1.803, 1.804, 1.805, 1.806, 1.807, 1.808, and 1.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.801", "1.802", "1.803", "1.804", "1.805", "1.806", "1.807", "1.808", "1.809"], "p1_2_xs": ["1.8005", "1.8014999999999999", "1.8025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}074}{4{,}200}, \\dfrac{3{,}126}{4{,}200}, \\dfrac{3{,}171}{4{,}200}, \\dfrac{3{,}173}{4{,}200}, \\dfrac{3{,}245}{4{,}200}, \\dfrac{3{,}259}{4{,}200}, \\dfrac{3{,}383}{4{,}200}, \\dfrac{3{,}391}{4{,}200}, \\dfrac{3{,}432}{4{,}200}, \\dfrac{3{,}442}{4{,}200}, \\dfrac{3{,}481}{4{,}200}, \\text{ and } \\dfrac{3{,}495}{4{,}200}", "__seed__": "0230"}}, {"seed": 231, "data": {"p1_how_many": "14", "p1_a": "7.57", "p1_b": "7.58", "p1_numbers": "7.5705, 7.571, 7.5715, 7.572, 7.5725, 7.573, 7.5735, 7.574, 7.5745, 7.575, 7.576, 7.577, 7.578, and 7.579", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.571000000000001", "7.572", "7.573", "7.574", "7.575", "7.5760000000000005", "7.577", "7.578", "7.579000000000001"], "p1_2_xs": ["7.5705", "7.5715", "7.5725", "7.5735", "7.5745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}223}{2{,}000}, \\dfrac{1{,}225}{2{,}000}, \\dfrac{1{,}256}{2{,}000}, \\dfrac{1{,}281}{2{,}000}, \\dfrac{1{,}290}{2{,}000}, \\dfrac{1{,}355}{2{,}000}, \\dfrac{1{,}384}{2{,}000}, \\dfrac{1{,}452}{2{,}000}, \\text{ and } \\dfrac{1{,}499}{2{,}000}", "__seed__": "0231"}}, {"seed": 232, "data": {"p1_how_many": "12", "p1_a": "9.27", "p1_b": "9.28", "p1_numbers": "9.2705, 9.271, 9.2715, 9.272, 9.2725, 9.273, 9.274, 9.275, 9.276, 9.277, 9.278, and 9.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.270999999999999", "9.272", "9.273", "9.274", "9.275", "9.276", "9.277", "9.277999999999999", "9.279"], "p1_2_xs": ["9.2705", "9.2715", "9.2725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}017}{35{,}000}, \\dfrac{14{,}250}{35{,}000}, \\dfrac{14{,}266}{35{,}000}, \\dfrac{14{,}439}{35{,}000}, \\dfrac{14{,}623}{35{,}000}, \\dfrac{14{,}664}{35{,}000}, \\dfrac{14{,}814}{35{,}000}, \\dfrac{14{,}869}{35{,}000}, \\dfrac{14{,}894}{35{,}000}, \\dfrac{14{,}976}{35{,}000}, \\text{ and } \\dfrac{14{,}989}{35{,}000}", "__seed__": "0232"}}, {"seed": 233, "data": {"p1_how_many": "10", "p1_a": "5.07", "p1_b": "5.08", "p1_numbers": "5.0705, 5.071, 5.072, 5.073, 5.074, 5.075, 5.076, 5.077, 5.078, and 5.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.071000000000001", "5.072", "5.073", "5.074", "5.075", "5.0760000000000005", "5.077", "5.078", "5.079000000000001"], "p1_2_xs": ["5.0705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}116}{35{,}000}, \\dfrac{8{,}306}{35{,}000}, \\dfrac{8{,}472}{35{,}000}, \\dfrac{8{,}634}{35{,}000}, \\dfrac{9{,}104}{35{,}000}, \\dfrac{9{,}621}{35{,}000}, \\text{ and } \\dfrac{9{,}685}{35{,}000}", "__seed__": "0233"}}, {"seed": 234, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}045}{35{,}000}, \\dfrac{20{,}193}{35{,}000}, \\dfrac{20{,}203}{35{,}000}, \\dfrac{20{,}368}{35{,}000}, \\dfrac{20{,}395}{35{,}000}, \\dfrac{20{,}479}{35{,}000}, \\dfrac{20{,}732}{35{,}000}, \\dfrac{20{,}757}{35{,}000}, \\dfrac{20{,}927}{35{,}000}, \\dfrac{20{,}970}{35{,}000}, \\text{ and } \\dfrac{20{,}996}{35{,}000}", "__seed__": "0234"}}, {"seed": 235, "data": {"p1_how_many": "13", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{315}{1{,}200}, \\dfrac{318}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{349}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{353}{1{,}200}, \\dfrac{356}{1{,}200}, \\dfrac{359}{1{,}200}, \\dfrac{388}{1{,}200}, \\text{ and } \\dfrac{396}{1{,}200}", "__seed__": "0235"}}, {"seed": 236, "data": {"p1_how_many": "14", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.235, 8.24, 8.245, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225", "8.235", "8.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}320}{20{,}000}, \\dfrac{12{,}476}{20{,}000}, \\dfrac{12{,}599}{20{,}000}, \\dfrac{12{,}781}{20{,}000}, \\dfrac{12{,}968}{20{,}000}, \\dfrac{13{,}463}{20{,}000}, \\dfrac{13{,}485}{20{,}000}, \\dfrac{13{,}672}{20{,}000}, \\dfrac{14{,}191}{20{,}000}, \\dfrac{14{,}586}{20{,}000}, \\text{ and } \\dfrac{14{,}998}{20{,}000}", "__seed__": "0236"}}, {"seed": 237, "data": {"p1_how_many": "14", "p1_a": "9.27", "p1_b": "9.28", "p1_numbers": "9.2705, 9.271, 9.2715, 9.272, 9.2725, 9.273, 9.2735, 9.274, 9.2745, 9.275, 9.276, 9.277, 9.278, and 9.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.270999999999999", "9.272", "9.273", "9.274", "9.275", "9.276", "9.277", "9.277999999999999", "9.279"], "p1_2_xs": ["9.2705", "9.2715", "9.2725", "9.2735", "9.2745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}146}{35{,}000}, \\dfrac{20{,}164}{35{,}000}, \\dfrac{20{,}175}{35{,}000}, \\dfrac{20{,}188}{35{,}000}, \\dfrac{20{,}307}{35{,}000}, \\dfrac{20{,}381}{35{,}000}, \\dfrac{20{,}395}{35{,}000}, \\dfrac{20{,}440}{35{,}000}, \\dfrac{20{,}631}{35{,}000}, \\text{ and } \\dfrac{20{,}998}{35{,}000}", "__seed__": "0237"}}, {"seed": 238, "data": {"p1_how_many": "10", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{424}{2{,}000}, \\dfrac{428}{2{,}000}, \\dfrac{448}{2{,}000}, \\dfrac{458}{2{,}000}, \\dfrac{463}{2{,}000}, \\dfrac{467}{2{,}000}, \\dfrac{469}{2{,}000}, \\dfrac{476}{2{,}000}, \\text{ and } \\dfrac{490}{2{,}000}", "__seed__": "0238"}}, {"seed": 239, "data": {"p1_how_many": "11", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.1005, 1.101, 1.1015, 1.102, 1.103, 1.104, 1.105, 1.106, 1.107, 1.108, and 1.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.101", "1.102", "1.103", "1.104", "1.105", "1.106", "1.107", "1.108", "1.109"], "p1_2_xs": ["1.1005", "1.1015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}523}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}531}{2{,}000}, \\dfrac{1{,}533}{2{,}000}, \\dfrac{1{,}563}{2{,}000}, \\dfrac{1{,}568}{2{,}000}, \\dfrac{1{,}569}{2{,}000}, \\dfrac{1{,}582}{2{,}000}, \\dfrac{1{,}589}{2{,}000}, \\text{ and } \\dfrac{1{,}593}{2{,}000}", "__seed__": "0239"}}, {"seed": 240, "data": {"p1_how_many": "10", "p1_a": "4.24", "p1_b": "4.25", 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7.9445, 7.945, 7.946, 7.947, 7.948, and 7.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.941000000000001", "7.942", "7.9430000000000005", "7.944", "7.945", "7.946000000000001", "7.947", "7.948", "7.949000000000001"], "p1_2_xs": ["7.9405", "7.9415000000000004", "7.9425", "7.9435", "7.9445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}020}{15{,}000}, \\dfrac{5{,}278}{15{,}000}, \\dfrac{5{,}405}{15{,}000}, \\dfrac{5{,}486}{15{,}000}, \\dfrac{5{,}558}{15{,}000}, \\dfrac{5{,}630}{15{,}000}, \\text{ and } \\dfrac{5{,}837}{15{,}000}", "__seed__": "0241"}}, {"seed": 242, "data": {"p1_how_many": "10", "p1_a": "8.35", "p1_b": "8.36", "p1_numbers": "8.3505, 8.351, 8.352, 8.353, 8.354, 8.355, 8.356, 8.357, 8.358, and 8.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.350999999999999", "8.352", "8.353", "8.354", "8.355", "8.356", "8.357", "8.357999999999999", "8.359"], "p1_2_xs": ["8.3505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{411}{2{,}000}, \\dfrac{445}{2{,}000}, \\dfrac{459}{2{,}000}, \\dfrac{465}{2{,}000}, \\dfrac{477}{2{,}000}, \\dfrac{483}{2{,}000}, \\dfrac{486}{2{,}000}, \\dfrac{494}{2{,}000}, \\dfrac{495}{2{,}000}, \\text{ and } \\dfrac{498}{2{,}000}", "__seed__": "0242"}}, {"seed": 243, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{521}{3{,}000}, \\dfrac{539}{3{,}000}, \\dfrac{545}{3{,}000}, \\dfrac{552}{3{,}000}, \\dfrac{554}{3{,}000}, \\dfrac{557}{3{,}000}, \\dfrac{567}{3{,}000}, \\dfrac{582}{3{,}000}, \\text{ and } \\dfrac{585}{3{,}000}", "__seed__": "0243"}}, {"seed": 244, "data": {"p1_how_many": "14", "p1_a": "7.77", "p1_b": "7.78", "p1_numbers": "7.7705, 7.771, 7.7715, 7.772, 7.7725, 7.773, 7.7735, 7.774, 7.7745, 7.775, 7.776, 7.777, 7.778, and 7.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.771", "7.771999999999999", "7.773", "7.773999999999999", "7.7749999999999995", "7.776", "7.776999999999999", "7.778", "7.779"], "p1_2_xs": ["7.770499999999999", "7.7715", "7.772499999999999", "7.773499999999999", "7.774499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}137}{42{,}000}, \\dfrac{7{,}443}{42{,}000}, \\dfrac{7{,}462}{42{,}000}, \\dfrac{9{,}263}{42{,}000}, \\dfrac{10{,}281}{42{,}000}, \\dfrac{10{,}371}{42{,}000}, \\dfrac{10{,}678}{42{,}000}, \\dfrac{10{,}987}{42{,}000}, \\text{ and } \\dfrac{11{,}008}{42{,}000}", "__seed__": "0244"}}, {"seed": 245, "data": {"p1_how_many": "14", "p1_a": "8.75", "p1_b": "8.76", "p1_numbers": "8.7505, 8.751, 8.7515, 8.752, 8.7525, 8.753, 8.7535, 8.754, 8.7545, 8.755, 8.756, 8.757, 8.758, and 8.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.751", "8.752", "8.753", "8.754", "8.755", "8.756", "8.757", "8.758", "8.759"], "p1_2_xs": ["8.7505", "8.7515", "8.752500000000001", "8.7535", "8.7545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}360}{35{,}000}, \\dfrac{7{,}565}{35{,}000}, \\dfrac{7{,}652}{35{,}000}, \\dfrac{8{,}149}{35{,}000}, \\dfrac{9{,}190}{35{,}000}, \\dfrac{9{,}366}{35{,}000}, \\dfrac{9{,}478}{35{,}000}, \\dfrac{9{,}852}{35{,}000}, \\text{ and } \\dfrac{9{,}913}{35{,}000}", "__seed__": "0245"}}, {"seed": 246, "data": {"p1_how_many": "11", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.415, 3.42, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}083}{4{,}200}, \\dfrac{3{,}121}{4{,}200}, \\dfrac{3{,}164}{4{,}200}, \\dfrac{3{,}172}{4{,}200}, \\dfrac{3{,}178}{4{,}200}, \\dfrac{3{,}290}{4{,}200}, \\dfrac{3{,}367}{4{,}200}, \\dfrac{3{,}410}{4{,}200}, \\dfrac{3{,}469}{4{,}200}, \\dfrac{3{,}494}{4{,}200}, \\text{ and } \\dfrac{3{,}496}{4{,}200}", "__seed__": "0246"}}, {"seed": 247, "data": {"p1_how_many": "10", "p1_a": "4.92", "p1_b": "4.93", "p1_numbers": "4.9205, 4.921, 4.922, 4.923, 4.924, 4.925, 4.926, 4.927, 4.928, and 4.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.921", "4.922", "4.923", "4.9239999999999995", "4.925", "4.926", "4.927", "4.928", "4.929"], "p1_2_xs": ["4.9205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0247"}}, {"seed": 248, "data": {"p1_how_many": "12", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}779}{35{,}000}, \\dfrac{16{,}776}{35{,}000}, \\dfrac{16{,}998}{35{,}000}, \\dfrac{17{,}362}{35{,}000}, \\dfrac{18{,}923}{35{,}000}, \\dfrac{20{,}483}{35{,}000}, \\dfrac{20{,}569}{35{,}000}, \\dfrac{20{,}625}{35{,}000}, \\text{ and } \\dfrac{20{,}908}{35{,}000}", "__seed__": "0248"}}, {"seed": 249, "data": {"p1_how_many": "10", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}197}{12{,}000}, \\dfrac{8{,}206}{12{,}000}, \\dfrac{8{,}208}{12{,}000}, \\dfrac{8{,}281}{12{,}000}, \\dfrac{8{,}757}{12{,}000}, \\dfrac{8{,}802}{12{,}000}, \\dfrac{8{,}828}{12{,}000}, \\dfrac{8{,}832}{12{,}000}, \\dfrac{8{,}844}{12{,}000}, \\text{ and } \\dfrac{8{,}904}{12{,}000}", "__seed__": "0249"}}, {"seed": 250, "data": {"p1_how_many": "11", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{762}{3{,}500}, \\dfrac{780}{3{,}500}, \\dfrac{789}{3{,}500}, \\dfrac{829}{3{,}500}, \\dfrac{887}{3{,}500}, \\dfrac{922}{3{,}500}, \\dfrac{929}{3{,}500}, \\text{ and } \\dfrac{945}{3{,}500}", "__seed__": "0250"}}, {"seed": 251, "data": {"p1_how_many": "13", "p1_a": "7.93", "p1_b": "7.94", "p1_numbers": "7.9305, 7.931, 7.9315, 7.932, 7.9325, 7.933, 7.9335, 7.934, 7.935, 7.936, 7.937, 7.938, and 7.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.931", "7.9319999999999995", "7.933", "7.933999999999999", "7.935", "7.936", "7.936999999999999", "7.938", "7.939"], "p1_2_xs": ["7.930499999999999", "7.9315", "7.932499999999999", "7.9334999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{2{,}008}{3{,}500}, \\dfrac{2{,}021}{3{,}500}, \\dfrac{2{,}023}{3{,}500}, \\dfrac{2{,}029}{3{,}500}, \\dfrac{2{,}039}{3{,}500}, \\dfrac{2{,}052}{3{,}500}, \\dfrac{2{,}053}{3{,}500}, \\dfrac{2{,}061}{3{,}500}, \\dfrac{2{,}077}{3{,}500}, \\text{ and } \\dfrac{2{,}095}{3{,}500}", "__seed__": "0251"}}, {"seed": 252, "data": {"p1_how_many": "14", "p1_a": "2.75", "p1_b": "2.76", "p1_numbers": "2.7505, 2.751, 2.7515, 2.752, 2.7525, 2.753, 2.7535, 2.754, 2.7545, 2.755, 2.756, 2.757, 2.758, and 2.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.751", "2.752", "2.753", "2.754", "2.755", "2.756", "2.757", "2.758", "2.759"], "p1_2_xs": ["2.7505", "2.7515", "2.7525", "2.7535000000000003", "2.7545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}705}{6{,}300}, \\dfrac{2{,}706}{6{,}300}, \\dfrac{2{,}745}{6{,}300}, \\dfrac{2{,}749}{6{,}300}, \\dfrac{2{,}760}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}785}{6{,}300}, \\dfrac{2{,}794}{6{,}300}, \\dfrac{2{,}795}{6{,}300}, \\text{ and } \\dfrac{2{,}797}{6{,}300}", "__seed__": "0252"}}, {"seed": 253, "data": {"p1_how_many": "13", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.3005, 3.301, 3.3015, 3.302, 3.3025, 3.303, 3.3035, 3.304, 3.305, 3.306, 3.307, 3.308, and 3.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.3009999999999997", "3.3019999999999996", "3.303", "3.304", "3.3049999999999997", "3.3059999999999996", "3.307", "3.308", "3.3089999999999997"], "p1_2_xs": ["3.3005", "3.3015", "3.3024999999999998", "3.3035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}506}{2{,}000}, \\dfrac{1{,}520}{2{,}000}, \\dfrac{1{,}529}{2{,}000}, \\dfrac{1{,}536}{2{,}000}, \\dfrac{1{,}538}{2{,}000}, \\dfrac{1{,}552}{2{,}000}, \\dfrac{1{,}555}{2{,}000}, \\dfrac{1{,}558}{2{,}000}, \\dfrac{1{,}561}{2{,}000}, \\text{ and } \\dfrac{1{,}582}{2{,}000}", "__seed__": "0253"}}, {"seed": 254, "data": {"p1_how_many": "13", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.535, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525", "1.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{271}{630}, \\dfrac{272}{630}, \\dfrac{273}{630}, \\dfrac{274}{630}, \\dfrac{275}{630}, \\dfrac{276}{630}, \\dfrac{278}{630}, \\text{ and } \\dfrac{279}{630}", "__seed__": "0254"}}, {"seed": 255, "data": {"p1_how_many": "12", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{141}{350}, \\dfrac{142}{350}, \\dfrac{143}{350}, \\dfrac{144}{350}, \\dfrac{145}{350}, \\dfrac{146}{350}, \\dfrac{147}{350}, \\dfrac{148}{350}, \\text{ and } \\dfrac{149}{350}", "__seed__": "0255"}}, {"seed": 256, "data": {"p1_how_many": "12", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0256"}}, {"seed": 257, "data": {"p1_how_many": "12", "p1_a": "4.3", "p1_b": "4.4", "p1_numbers": "4.3005, 4.301, 4.3015, 4.302, 4.3025, 4.303, 4.304, 4.305, 4.306, 4.307, 4.308, and 4.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.301", "4.302", "4.303", "4.303999999999999", "4.305", "4.306", "4.3069999999999995", "4.308", "4.309"], "p1_2_xs": ["4.3004999999999995", "4.3015", "4.302499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{622}{4{,}200}, \\dfrac{624}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{633}{4{,}200}, \\dfrac{646}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{673}{4{,}200}, \\dfrac{677}{4{,}200}, \\dfrac{693}{4{,}200}, \\text{ and } \\dfrac{695}{4{,}200}", "__seed__": "0257"}}, {"seed": 258, "data": {"p1_how_many": "14", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.135, 3.14, 3.145, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125", "3.135", "3.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}402}{3{,}000}, \\dfrac{2{,}405}{3{,}000}, \\dfrac{2{,}420}{3{,}000}, \\dfrac{2{,}424}{3{,}000}, \\dfrac{2{,}432}{3{,}000}, \\dfrac{2{,}446}{3{,}000}, \\dfrac{2{,}456}{3{,}000}, \\dfrac{2{,}483}{3{,}000}, \\dfrac{2{,}495}{3{,}000}, \\text{ and } \\dfrac{2{,}499}{3{,}000}", "__seed__": "0258"}}, {"seed": 259, "data": {"p1_how_many": "14", "p1_a": "5.22", "p1_b": "5.23", "p1_numbers": "5.2205, 5.221, 5.2215, 5.222, 5.2225, 5.223, 5.2235, 5.224, 5.2245, 5.225, 5.226, 5.227, 5.228, and 5.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.221", "5.2219999999999995", "5.223", "5.223999999999999", "5.225", "5.226", "5.226999999999999", "5.228", "5.229"], "p1_2_xs": ["5.2204999999999995", "5.2215", "5.222499999999999", "5.2235", "5.224499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}105}{12{,}000}, \\dfrac{3{,}222}{12{,}000}, \\dfrac{3{,}610}{12{,}000}, \\dfrac{3{,}733}{12{,}000}, \\dfrac{3{,}753}{12{,}000}, \\dfrac{3{,}878}{12{,}000}, \\dfrac{3{,}883}{12{,}000}, \\dfrac{3{,}893}{12{,}000}, \\text{ and } \\dfrac{3{,}955}{12{,}000}", "__seed__": "0259"}}, {"seed": 260, "data": {"p1_how_many": "10", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}527}{63{,}000}, \\dfrac{14{,}639}{63{,}000}, \\dfrac{15{,}369}{63{,}000}, \\dfrac{15{,}969}{63{,}000}, \\dfrac{16{,}738}{63{,}000}, \\dfrac{16{,}759}{63{,}000}, \\dfrac{17{,}633}{63{,}000}, \\text{ and } \\dfrac{17{,}787}{63{,}000}", "__seed__": "0260"}}, {"seed": 261, "data": {"p1_how_many": "10", "p1_a": "9.75", "p1_b": "9.76", "p1_numbers": "9.7505, 9.751, 9.752, 9.753, 9.754, 9.755, 9.756, 9.757, 9.758, and 9.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.751", "9.752", "9.753", "9.754", "9.755", "9.756", "9.757", "9.758", "9.759"], "p1_2_xs": ["9.7505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}061}{42{,}000}, \\dfrac{6{,}071}{42{,}000}, \\dfrac{6{,}146}{42{,}000}, \\dfrac{6{,}196}{42{,}000}, \\dfrac{6{,}726}{42{,}000}, \\dfrac{6{,}741}{42{,}000}, \\dfrac{6{,}814}{42{,}000}, \\dfrac{6{,}836}{42{,}000}, \\dfrac{6{,}883}{42{,}000}, \\dfrac{6{,}939}{42{,}000}, \\text{ and } \\dfrac{6{,}941}{42{,}000}", "__seed__": "0261"}}, {"seed": 262, "data": {"p1_how_many": "14", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.035, 7.04, 7.045, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995", "7.035", "7.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{55}{200}, \\dfrac{61}{200}, \\dfrac{64}{200}, \\dfrac{69}{200}, \\dfrac{73}{200}, \\dfrac{75}{200}, \\dfrac{76}{200}, \\dfrac{78}{200}, \\text{ and } \\dfrac{79}{200}", "__seed__": "0262"}}, {"seed": 263, "data": {"p1_how_many": "13", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.335, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999", "7.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{52}{200}, \\dfrac{53}{200}, \\dfrac{56}{200}, \\dfrac{58}{200}, \\dfrac{70}{200}, \\dfrac{73}{200}, \\text{ and } \\dfrac{79}{200}", "__seed__": "0263"}}, {"seed": 264, "data": {"p1_how_many": "10", "p1_a": "9.72", "p1_b": "9.73", "p1_numbers": "9.7205, 9.721, 9.722, 9.723, 9.724, 9.725, 9.726, 9.727, 9.728, and 9.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.721", "9.722000000000001", "9.723", "9.724", "9.725000000000001", "9.726", "9.727", "9.728", "9.729000000000001"], "p1_2_xs": ["9.720500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}508}{4{,}200}, \\dfrac{3{,}529}{4{,}200}, \\dfrac{3{,}542}{4{,}200}, \\dfrac{3{,}543}{4{,}200}, \\dfrac{3{,}557}{4{,}200}, \\dfrac{3{,}568}{4{,}200}, \\dfrac{3{,}571}{4{,}200}, \\text{ and } \\dfrac{3{,}593}{4{,}200}", "__seed__": "0264"}}, {"seed": 265, "data": {"p1_how_many": "14", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.125, 5.13, 5.135, 5.14, 5.145, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999", "5.124999999999999", "5.135", "5.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{102}{350}, \\dfrac{112}{350}, \\dfrac{118}{350}, \\dfrac{121}{350}, \\dfrac{128}{350}, \\dfrac{129}{350}, \\dfrac{131}{350}, \\dfrac{136}{350}, \\text{ and } \\dfrac{137}{350}", "__seed__": "0265"}}, {"seed": 266, "data": {"p1_how_many": "10", "p1_a": "5.65", "p1_b": "5.66", "p1_numbers": "5.6505, 5.651, 5.652, 5.653, 5.654, 5.655, 5.656, 5.657, 5.658, and 5.659", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.651000000000001", "5.652", "5.6530000000000005", "5.654", "5.655", "5.656000000000001", "5.657", "5.658", "5.659000000000001"], "p1_2_xs": ["5.6505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}290}{35{,}000}, \\dfrac{7{,}315}{35{,}000}, \\dfrac{7{,}317}{35{,}000}, \\dfrac{7{,}846}{35{,}000}, \\dfrac{7{,}875}{35{,}000}, \\dfrac{7{,}903}{35{,}000}, \\dfrac{7{,}956}{35{,}000}, \\dfrac{8{,}355}{35{,}000}, \\dfrac{8{,}647}{35{,}000}, \\dfrac{9{,}235}{35{,}000}, \\text{ and } \\dfrac{9{,}621}{35{,}000}", "__seed__": "0266"}}, {"seed": 267, "data": {"p1_how_many": "12", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.325, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001", "8.325000000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}145}{5{,}600}, \\dfrac{2{,}159}{5{,}600}, \\dfrac{2{,}162}{5{,}600}, \\dfrac{2{,}166}{5{,}600}, \\dfrac{2{,}198}{5{,}600}, \\dfrac{2{,}215}{5{,}600}, \\dfrac{2{,}239}{5{,}600}, \\dfrac{2{,}251}{5{,}600}, \\dfrac{2{,}271}{5{,}600}, \\dfrac{2{,}281}{5{,}600}, \\dfrac{2{,}282}{5{,}600}, \\text{ and } \\dfrac{2{,}346}{5{,}600}", "__seed__": "0267"}}, {"seed": 268, "data": {"p1_how_many": "12", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.325, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001", "9.325000000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}010}{30{,}000}, \\dfrac{24{,}389}{30{,}000}, \\dfrac{24{,}480}{30{,}000}, \\dfrac{24{,}545}{30{,}000}, \\dfrac{24{,}703}{30{,}000}, \\dfrac{24{,}720}{30{,}000}, \\dfrac{24{,}827}{30{,}000}, \\dfrac{24{,}855}{30{,}000}, \\dfrac{24{,}870}{30{,}000}, \\dfrac{24{,}941}{30{,}000}, \\text{ and } \\dfrac{24{,}942}{30{,}000}", "__seed__": "0268"}}, {"seed": 269, "data": {"p1_how_many": "10", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}880}{15{,}000}, \\dfrac{7{,}082}{15{,}000}, \\dfrac{7{,}144}{15{,}000}, \\dfrac{7{,}946}{15{,}000}, \\dfrac{8{,}345}{15{,}000}, \\dfrac{8{,}490}{15{,}000}, \\dfrac{8{,}867}{15{,}000}, \\dfrac{9{,}015}{15{,}000}, \\dfrac{9{,}843}{15{,}000}, \\dfrac{9{,}848}{15{,}000}, \\text{ and } \\dfrac{9{,}994}{15{,}000}", "__seed__": "0269"}}, {"seed": 270, "data": {"p1_how_many": "11", "p1_a": "7.26", "p1_b": "7.27", "p1_numbers": "7.2605, 7.261, 7.2615, 7.262, 7.263, 7.264, 7.265, 7.266, 7.267, 7.268, and 7.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.261", "7.262", "7.263", "7.263999999999999", "7.265", "7.266", "7.2669999999999995", "7.268", "7.269"], "p1_2_xs": ["7.2604999999999995", "7.2615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{820}{1{,}200}, \\dfrac{822}{1{,}200}, \\dfrac{826}{1{,}200}, \\dfrac{850}{1{,}200}, \\dfrac{851}{1{,}200}, \\dfrac{883}{1{,}200}, \\dfrac{885}{1{,}200}, \\dfrac{888}{1{,}200}, \\text{ and } \\dfrac{894}{1{,}200}", "__seed__": "0270"}}, {"seed": 271, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}085}{20{,}000}, \\dfrac{12{,}441}{20{,}000}, \\dfrac{12{,}477}{20{,}000}, \\dfrac{13{,}084}{20{,}000}, \\dfrac{13{,}591}{20{,}000}, \\dfrac{14{,}957}{20{,}000}, \\text{ and } \\dfrac{14{,}983}{20{,}000}", "__seed__": "0271"}}, {"seed": 272, "data": {"p1_how_many": "10", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{611}{1{,}500}, \\dfrac{616}{1{,}500}, \\dfrac{679}{1{,}500}, \\dfrac{682}{1{,}500}, \\dfrac{705}{1{,}500}, \\dfrac{721}{1{,}500}, \\dfrac{894}{1{,}500}, \\text{ and } \\dfrac{950}{1{,}500}", "__seed__": "0272"}}, {"seed": 273, "data": {"p1_how_many": "10", "p1_a": "3.36", "p1_b": "3.37", "p1_numbers": "3.3605, 3.361, 3.362, 3.363, 3.364, 3.365, 3.366, 3.367, 3.368, and 3.369", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.3609999999999998", "3.3619999999999997", "3.363", "3.364", "3.3649999999999998", "3.3659999999999997", "3.367", "3.368", "3.3689999999999998"], "p1_2_xs": ["3.3605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}010}{4{,}200}, \\dfrac{3{,}037}{4{,}200}, \\dfrac{3{,}051}{4{,}200}, \\dfrac{3{,}057}{4{,}200}, \\dfrac{3{,}085}{4{,}200}, \\dfrac{3{,}093}{4{,}200}, \\dfrac{3{,}113}{4{,}200}, \\dfrac{3{,}131}{4{,}200}, \\dfrac{3{,}184}{4{,}200}, \\dfrac{3{,}380}{4{,}200}, \\dfrac{3{,}424}{4{,}200}, \\text{ and } \\dfrac{3{,}441}{4{,}200}", "__seed__": "0273"}}, {"seed": 274, "data": {"p1_how_many": "11", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{321}{560}, \\dfrac{325}{560}, \\dfrac{328}{560}, \\dfrac{332}{560}, \\dfrac{334}{560}, \\dfrac{338}{560}, \\dfrac{345}{560}, \\dfrac{348}{560}, \\text{ and } \\dfrac{349}{560}", "__seed__": "0274"}}, {"seed": 275, "data": {"p1_how_many": "10", "p1_a": "5.41", "p1_b": "5.42", "p1_numbers": "5.4105, 5.411, 5.412, 5.413, 5.414, 5.415, 5.416, 5.417, 5.418, and 5.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.4110000000000005", "5.412", "5.413", "5.414", "5.415", "5.416", "5.417", "5.418", "5.4190000000000005"], "p1_2_xs": ["5.4105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}039}{12{,}000}, \\dfrac{3{,}052}{12{,}000}, \\dfrac{3{,}171}{12{,}000}, \\dfrac{3{,}272}{12{,}000}, \\dfrac{3{,}362}{12{,}000}, \\dfrac{3{,}368}{12{,}000}, \\dfrac{3{,}466}{12{,}000}, \\dfrac{3{,}487}{12{,}000}, \\dfrac{3{,}489}{12{,}000}, \\dfrac{3{,}563}{12{,}000}, \\dfrac{3{,}651}{12{,}000}, \\text{ and } \\dfrac{3{,}917}{12{,}000}", "__seed__": "0275"}}, {"seed": 276, "data": {"p1_how_many": "14", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.745, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725", "7.735", "7.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}846}{42{,}000}, \\dfrac{30{,}874}{42{,}000}, \\dfrac{32{,}314}{42{,}000}, \\dfrac{33{,}233}{42{,}000}, \\dfrac{33{,}763}{42{,}000}, \\dfrac{34{,}053}{42{,}000}, \\dfrac{34{,}088}{42{,}000}, \\dfrac{34{,}430}{42{,}000}, \\text{ and } \\dfrac{34{,}759}{42{,}000}", "__seed__": "0276"}}, {"seed": 277, "data": {"p1_how_many": "14", "p1_a": "2.06", "p1_b": "2.07", "p1_numbers": "2.0605, 2.061, 2.0615, 2.062, 2.0625, 2.063, 2.0635, 2.064, 2.0645, 2.065, 2.066, 2.067, 2.068, and 2.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.061", "2.062", "2.063", "2.064", "2.065", "2.066", "2.067", "2.068", "2.069"], "p1_2_xs": ["2.0605", "2.0615", "2.0625", "2.0635000000000003", "2.0645000000000002"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}701}{6{,}300}, \\dfrac{2{,}716}{6{,}300}, \\dfrac{2{,}722}{6{,}300}, \\dfrac{2{,}742}{6{,}300}, \\dfrac{2{,}750}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}766}{6{,}300}, \\dfrac{2{,}774}{6{,}300}, \\dfrac{2{,}782}{6{,}300}, \\text{ and } \\dfrac{2{,}793}{6{,}300}", "__seed__": "0277"}}, {"seed": 278, "data": {"p1_how_many": "14", "p1_a": "1.47", "p1_b": "1.48", "p1_numbers": "1.4705, 1.471, 1.4715, 1.472, 1.4725, 1.473, 1.4735, 1.474, 1.4745, 1.475, 1.476, 1.477, 1.478, and 1.479", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4709999999999999", "1.472", "1.4729999999999999", "1.474", "1.4749999999999999", "1.476", "1.4769999999999999", "1.478", "1.4789999999999999"], "p1_2_xs": ["1.4705", "1.4714999999999998", "1.4725", "1.4734999999999998", "1.4745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{353}{560}, \\dfrac{361}{560}, \\dfrac{365}{560}, \\dfrac{388}{560}, \\dfrac{392}{560}, \\dfrac{396}{560}, \\text{ and } \\dfrac{398}{560}", "__seed__": "0278"}}, {"seed": 279, "data": {"p1_how_many": "12", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}515}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}526}{4{,}200}, \\dfrac{3{,}537}{4{,}200}, \\dfrac{3{,}540}{4{,}200}, \\dfrac{3{,}543}{4{,}200}, \\dfrac{3{,}566}{4{,}200}, \\dfrac{3{,}569}{4{,}200}, \\dfrac{3{,}587}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0279"}}, {"seed": 280, "data": {"p1_how_many": "12", "p1_a": "4.86", "p1_b": "4.87", "p1_numbers": "4.8605, 4.861, 4.8615, 4.862, 4.8625, 4.863, 4.864, 4.865, 4.866, 4.867, 4.868, and 4.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.861000000000001", "4.862", "4.863", "4.864", "4.865", "4.8660000000000005", "4.867", "4.868", "4.869000000000001"], "p1_2_xs": ["4.8605", "4.8615", "4.8625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{308}{1{,}200}, \\dfrac{313}{1{,}200}, \\dfrac{326}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{362}{1{,}200}, \\dfrac{371}{1{,}200}, \\text{ and } \\dfrac{387}{1{,}200}", "__seed__": "0280"}}, {"seed": 281, "data": {"p1_how_many": "12", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}371}{42{,}000}, \\dfrac{6{,}420}{42{,}000}, \\dfrac{6{,}486}{42{,}000}, \\dfrac{6{,}514}{42{,}000}, \\dfrac{6{,}517}{42{,}000}, \\dfrac{6{,}531}{42{,}000}, \\dfrac{6{,}548}{42{,}000}, \\dfrac{6{,}626}{42{,}000}, \\dfrac{6{,}744}{42{,}000}, \\dfrac{6{,}795}{42{,}000}, \\dfrac{6{,}865}{42{,}000}, \\text{ and } \\dfrac{6{,}867}{42{,}000}", "__seed__": "0281"}}, {"seed": 282, "data": {"p1_how_many": "14", "p1_a": "2.23", "p1_b": "2.24", "p1_numbers": "2.2305, 2.231, 2.2315, 2.232, 2.2325, 2.233, 2.2335, 2.234, 2.2345, 2.235, 2.236, 2.237, 2.238, and 2.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.231", "2.2319999999999998", "2.233", "2.234", "2.235", "2.2359999999999998", "2.237", "2.238", "2.239"], "p1_2_xs": ["2.2305", "2.2315", "2.2325", "2.2335000000000003", "2.2345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}081}{63{,}000}, \\dfrac{14{,}368}{63{,}000}, \\dfrac{14{,}541}{63{,}000}, \\dfrac{15{,}134}{63{,}000}, \\dfrac{15{,}478}{63{,}000}, \\dfrac{15{,}558}{63{,}000}, \\dfrac{16{,}412}{63{,}000}, \\dfrac{16{,}671}{63{,}000}, \\dfrac{17{,}220}{63{,}000}, \\dfrac{17{,}225}{63{,}000}, \\dfrac{17{,}372}{63{,}000}, \\text{ and } \\dfrac{17{,}626}{63{,}000}", "__seed__": "0282"}}, {"seed": 283, "data": {"p1_how_many": "14", "p1_a": "1.94", "p1_b": "1.95", "p1_numbers": "1.9405, 1.941, 1.9415, 1.942, 1.9425, 1.943, 1.9435, 1.944, 1.9445, 1.945, 1.946, 1.947, 1.948, and 1.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9409999999999998", "1.942", "1.9429999999999998", "1.944", "1.9449999999999998", "1.946", "1.9469999999999998", "1.948", "1.9489999999999998"], "p1_2_xs": ["1.9405", "1.9414999999999998", "1.9425", "1.9434999999999998", "1.9445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{127}{200}, \\dfrac{130}{200}, \\dfrac{131}{200}, \\dfrac{138}{200}, \\dfrac{141}{200}, \\dfrac{143}{200}, \\dfrac{145}{200}, \\text{ and } \\dfrac{147}{200}", "__seed__": "0283"}}, {"seed": 284, "data": {"p1_how_many": "12", "p1_a": "9.31", "p1_b": "9.32", "p1_numbers": "9.3105, 9.311, 9.3115, 9.312, 9.3125, 9.313, 9.314, 9.315, 9.316, 9.317, 9.318, and 9.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.311", "9.312000000000001", "9.313", "9.314", "9.315000000000001", "9.316", "9.317", "9.318", "9.319"], "p1_2_xs": ["9.310500000000001", "9.3115", "9.312500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{667}{1{,}500}, \\dfrac{672}{1{,}500}, \\dfrac{681}{1{,}500}, \\dfrac{717}{1{,}500}, \\dfrac{778}{1{,}500}, \\dfrac{908}{1{,}500}, \\text{ and } \\dfrac{982}{1{,}500}", "__seed__": "0284"}}, {"seed": 285, "data": {"p1_how_many": "14", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.335, 2.34, 2.345, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997", "2.3349999999999995", "2.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}094}{35{,}000}, \\dfrac{10{,}894}{35{,}000}, \\dfrac{11{,}144}{35{,}000}, \\dfrac{11{,}356}{35{,}000}, \\dfrac{11{,}538}{35{,}000}, \\dfrac{12{,}021}{35{,}000}, \\dfrac{12{,}203}{35{,}000}, \\dfrac{12{,}493}{35{,}000}, \\dfrac{13{,}220}{35{,}000}, \\dfrac{13{,}317}{35{,}000}, \\dfrac{13{,}323}{35{,}000}, \\text{ and } \\dfrac{13{,}998}{35{,}000}", "__seed__": "0285"}}, {"seed": 286, "data": {"p1_how_many": "14", "p1_a": "5.5", "p1_b": "5.6", "p1_numbers": "5.505, 5.51, 5.515, 5.52, 5.525, 5.53, 5.535, 5.54, 5.545, 5.55, 5.56, 5.57, 5.58, and 5.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.51", "5.52", "5.53", "5.54", "5.55", "5.56", "5.57", "5.58", "5.59"], "p1_2_xs": ["5.505", "5.515", "5.5249999999999995", "5.535", "5.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}075}{42{,}000}, \\dfrac{35{,}142}{42{,}000}, \\dfrac{35{,}158}{42{,}000}, \\dfrac{35{,}189}{42{,}000}, \\dfrac{35{,}223}{42{,}000}, \\dfrac{35{,}487}{42{,}000}, \\dfrac{35{,}623}{42{,}000}, \\dfrac{35{,}662}{42{,}000}, \\dfrac{35{,}757}{42{,}000}, \\text{ and } \\dfrac{35{,}971}{42{,}000}", "__seed__": "0286"}}, {"seed": 287, "data": {"p1_how_many": "13", "p1_a": "5.51", "p1_b": "5.52", "p1_numbers": "5.5105, 5.511, 5.5115, 5.512, 5.5125, 5.513, 5.5135, 5.514, 5.515, 5.516, 5.517, 5.518, and 5.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.511", "5.512", "5.513", "5.513999999999999", "5.515", "5.516", "5.5169999999999995", "5.518", "5.519"], "p1_2_xs": ["5.5104999999999995", "5.5115", "5.512499999999999", "5.5135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}253}{35{,}000}, \\dfrac{10{,}479}{35{,}000}, \\dfrac{10{,}696}{35{,}000}, \\dfrac{10{,}703}{35{,}000}, \\dfrac{10{,}997}{35{,}000}, \\dfrac{11{,}001}{35{,}000}, \\dfrac{11{,}279}{35{,}000}, \\dfrac{11{,}463}{35{,}000}, \\dfrac{12{,}247}{35{,}000}, \\dfrac{12{,}572}{35{,}000}, \\text{ and } \\dfrac{13{,}259}{35{,}000}", "__seed__": "0287"}}, {"seed": 288, "data": {"p1_how_many": "14", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.215, 6.22, 6.225, 6.23, 6.235, 6.24, 6.245, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205", "6.215", "6.225", "6.235", "6.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0288"}}, {"seed": 289, "data": {"p1_how_many": "12", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.225, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215", "8.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{301}{1{,}200}, \\dfrac{303}{1{,}200}, \\dfrac{304}{1{,}200}, \\dfrac{307}{1{,}200}, \\dfrac{334}{1{,}200}, \\dfrac{337}{1{,}200}, \\dfrac{367}{1{,}200}, \\dfrac{381}{1{,}200}, \\text{ and } \\dfrac{383}{1{,}200}", "__seed__": "0289"}}, {"seed": 290, "data": {"p1_how_many": "13", "p1_a": "7.77", "p1_b": "7.78", "p1_numbers": "7.7705, 7.771, 7.7715, 7.772, 7.7725, 7.773, 7.7735, 7.774, 7.775, 7.776, 7.777, 7.778, and 7.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.771", "7.771999999999999", "7.773", "7.773999999999999", "7.7749999999999995", "7.776", "7.776999999999999", "7.778", "7.779"], "p1_2_xs": ["7.770499999999999", "7.7715", "7.772499999999999", "7.773499999999999"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{717}{3{,}500}, \\dfrac{718}{3{,}500}, \\dfrac{752}{3{,}500}, \\dfrac{889}{3{,}500}, \\dfrac{937}{3{,}500}, \\dfrac{940}{3{,}500}, \\dfrac{964}{3{,}500}, \\text{ and } \\dfrac{979}{3{,}500}", "__seed__": "0290"}}, {"seed": 291, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}014}{42{,}000}, \\dfrac{7{,}041}{42{,}000}, \\dfrac{7{,}451}{42{,}000}, \\dfrac{8{,}136}{42{,}000}, \\dfrac{8{,}675}{42{,}000}, \\dfrac{9{,}422}{42{,}000}, \\dfrac{9{,}471}{42{,}000}, \\dfrac{9{,}494}{42{,}000}, \\dfrac{10{,}981}{42{,}000}, \\dfrac{11{,}445}{42{,}000}, \\dfrac{11{,}510}{42{,}000}, \\text{ and } \\dfrac{11{,}612}{42{,}000}", "__seed__": "0291"}}, {"seed": 292, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}103}{42{,}000}, \\dfrac{6{,}155}{42{,}000}, \\dfrac{6{,}237}{42{,}000}, \\dfrac{6{,}526}{42{,}000}, \\dfrac{6{,}535}{42{,}000}, \\dfrac{6{,}545}{42{,}000}, \\dfrac{6{,}546}{42{,}000}, \\dfrac{6{,}762}{42{,}000}, \\dfrac{6{,}807}{42{,}000}, \\dfrac{6{,}817}{42{,}000}, \\dfrac{6{,}938}{42{,}000}, \\text{ and } \\dfrac{6{,}958}{42{,}000}", "__seed__": "0292"}}, {"seed": 293, "data": {"p1_how_many": "11", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0293"}}, {"seed": 294, "data": {"p1_how_many": "10", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.6005, 4.601, 4.602, 4.603, 4.604, 4.605, 4.606, 4.607, 4.608, and 4.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.601", "4.601999999999999", "4.603", "4.603999999999999", "4.6049999999999995", "4.606", "4.606999999999999", "4.608", "4.609"], "p1_2_xs": ["4.600499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}507}{3{,}500}, \\dfrac{1{,}525}{3{,}500}, \\dfrac{1{,}569}{3{,}500}, \\dfrac{1{,}734}{3{,}500}, \\dfrac{1{,}781}{3{,}500}, \\dfrac{1{,}815}{3{,}500}, \\dfrac{1{,}854}{3{,}500}, \\dfrac{1{,}909}{3{,}500}, \\dfrac{2{,}006}{3{,}500}, \\text{ and } \\dfrac{2{,}095}{3{,}500}", "__seed__": "0294"}}, {"seed": 295, "data": {"p1_how_many": "12", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}154}{35{,}000}, \\dfrac{7{,}721}{35{,}000}, \\dfrac{8{,}013}{35{,}000}, \\dfrac{8{,}026}{35{,}000}, \\dfrac{8{,}878}{35{,}000}, \\dfrac{9{,}014}{35{,}000}, \\dfrac{9{,}160}{35{,}000}, \\dfrac{9{,}339}{35{,}000}, \\text{ and } \\dfrac{9{,}998}{35{,}000}", "__seed__": "0295"}}, {"seed": 296, "data": {"p1_how_many": "11", "p1_a": "7.52", "p1_b": "7.53", "p1_numbers": "7.5205, 7.521, 7.5215, 7.522, 7.523, 7.524, 7.525, 7.526, 7.527, 7.528, and 7.529", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.521", "7.521999999999999", "7.523", "7.523999999999999", "7.5249999999999995", "7.526", "7.526999999999999", "7.528", "7.529"], "p1_2_xs": ["7.520499999999999", "7.5215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}047}{35{,}000}, \\dfrac{14{,}116}{35{,}000}, \\dfrac{14{,}340}{35{,}000}, \\dfrac{14{,}433}{35{,}000}, \\dfrac{14{,}508}{35{,}000}, \\dfrac{14{,}560}{35{,}000}, \\dfrac{14{,}570}{35{,}000}, \\dfrac{14{,}628}{35{,}000}, \\text{ and } \\dfrac{14{,}645}{35{,}000}", "__seed__": "0296"}}, {"seed": 297, "data": {"p1_how_many": "12", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.415, 3.42, 3.425, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996", "3.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}144}{42{,}000}, \\dfrac{7{,}736}{42{,}000}, \\dfrac{8{,}360}{42{,}000}, \\dfrac{8{,}461}{42{,}000}, \\dfrac{9{,}478}{42{,}000}, \\dfrac{9{,}678}{42{,}000}, \\dfrac{10{,}143}{42{,}000}, \\dfrac{10{,}214}{42{,}000}, \\dfrac{11{,}799}{42{,}000}, \\text{ and } \\dfrac{11{,}941}{42{,}000}", "__seed__": "0297"}}, {"seed": 298, "data": {"p1_how_many": "10", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.42, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}503}{4{,}200}, \\dfrac{3{,}518}{4{,}200}, \\dfrac{3{,}523}{4{,}200}, \\dfrac{3{,}546}{4{,}200}, \\dfrac{3{,}554}{4{,}200}, \\dfrac{3{,}564}{4{,}200}, \\text{ and } \\dfrac{3{,}580}{4{,}200}", "__seed__": "0298"}}, {"seed": 299, "data": {"p1_how_many": "11", "p1_a": "6.73", "p1_b": "6.74", "p1_numbers": "6.7305, 6.731, 6.7315, 6.732, 6.733, 6.734, 6.735, 6.736, 6.737, 6.738, and 6.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.731000000000001", "6.732", "6.7330000000000005", "6.734", "6.735", "6.736000000000001", "6.737", "6.738", "6.739000000000001"], "p1_2_xs": ["6.7305", "6.7315000000000005"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}092}{42{,}000}, \\dfrac{6{,}251}{42{,}000}, \\dfrac{6{,}285}{42{,}000}, \\dfrac{6{,}389}{42{,}000}, \\dfrac{6{,}444}{42{,}000}, \\dfrac{6{,}528}{42{,}000}, \\dfrac{6{,}796}{42{,}000}, \\text{ and } \\dfrac{6{,}886}{42{,}000}", "__seed__": "0299"}}, {"seed": 300, "data": {"p1_how_many": "11", "p1_a": "9.73", "p1_b": "9.74", "p1_numbers": "9.7305, 9.731, 9.7315, 9.732, 9.733, 9.734, 9.735, 9.736, 9.737, 9.738, and 9.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.731", "9.732000000000001", "9.733", "9.734", "9.735000000000001", "9.736", "9.737", "9.738", "9.739"], "p1_2_xs": ["9.730500000000001", "9.7315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}552}{3{,}500}, \\dfrac{1{,}666}{3{,}500}, \\dfrac{1{,}675}{3{,}500}, \\dfrac{1{,}682}{3{,}500}, \\dfrac{1{,}710}{3{,}500}, \\dfrac{1{,}748}{3{,}500}, \\dfrac{1{,}867}{3{,}500}, \\dfrac{1{,}992}{3{,}500}, \\dfrac{2{,}060}{3{,}500}, \\dfrac{2{,}079}{3{,}500}, \\text{ and } \\dfrac{2{,}085}{3{,}500}", "__seed__": "0300"}}, {"seed": 301, "data": {"p1_how_many": "12", "p1_a": "9.22", "p1_b": "9.23", "p1_numbers": "9.2205, 9.221, 9.2215, 9.222, 9.2225, 9.223, 9.224, 9.225, 9.226, 9.227, 9.228, and 9.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.221", "9.222000000000001", "9.223", "9.224", "9.225000000000001", "9.226", "9.227", "9.228", "9.229000000000001"], "p1_2_xs": ["9.220500000000001", "9.2215", "9.222500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}401}{3{,}000}, \\dfrac{2{,}425}{3{,}000}, \\dfrac{2{,}432}{3{,}000}, \\dfrac{2{,}474}{3{,}000}, \\dfrac{2{,}475}{3{,}000}, \\dfrac{2{,}478}{3{,}000}, \\text{ and } \\dfrac{2{,}491}{3{,}000}", "__seed__": "0301"}}, {"seed": 302, "data": {"p1_how_many": "13", "p1_a": "5.5", "p1_b": "5.6", "p1_numbers": "5.505, 5.51, 5.515, 5.52, 5.525, 5.53, 5.535, 5.54, 5.55, 5.56, 5.57, 5.58, and 5.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.51", "5.52", "5.53", "5.54", "5.55", "5.56", "5.57", "5.58", "5.59"], "p1_2_xs": ["5.505", "5.515", "5.5249999999999995", "5.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}129}{42{,}000}, \\dfrac{7{,}254}{42{,}000}, \\dfrac{7{,}644}{42{,}000}, \\dfrac{8{,}166}{42{,}000}, \\dfrac{8{,}290}{42{,}000}, \\dfrac{8{,}358}{42{,}000}, \\dfrac{8{,}979}{42{,}000}, \\dfrac{9{,}336}{42{,}000}, \\dfrac{10{,}054}{42{,}000}, \\dfrac{10{,}067}{42{,}000}, \\dfrac{10{,}255}{42{,}000}, \\text{ and } \\dfrac{10{,}421}{42{,}000}", "__seed__": "0302"}}, {"seed": 303, "data": {"p1_how_many": "12", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.025, 3.03, 3.04, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997", "3.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}503}{2{,}000}, \\dfrac{1{,}511}{2{,}000}, \\dfrac{1{,}515}{2{,}000}, \\dfrac{1{,}518}{2{,}000}, \\dfrac{1{,}525}{2{,}000}, \\dfrac{1{,}526}{2{,}000}, \\dfrac{1{,}535}{2{,}000}, \\dfrac{1{,}540}{2{,}000}, \\dfrac{1{,}541}{2{,}000}, \\dfrac{1{,}555}{2{,}000}, \\dfrac{1{,}557}{2{,}000}, \\text{ and } \\dfrac{1{,}574}{2{,}000}", "__seed__": "0303"}}, {"seed": 304, "data": {"p1_how_many": "11", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{95}{630}, \\dfrac{97}{630}, \\dfrac{107}{630}, \\dfrac{108}{630}, \\dfrac{112}{630}, \\dfrac{114}{630}, \\dfrac{131}{630}, \\dfrac{135}{630}, \\text{ and } \\dfrac{138}{630}", "__seed__": "0304"}}, {"seed": 305, "data": {"p1_how_many": "12", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{42{,}043}{77{,}000}, \\dfrac{43{,}117}{77{,}000}, \\dfrac{50{,}651}{77{,}000}, \\dfrac{51{,}345}{77{,}000}, \\dfrac{51{,}890}{77{,}000}, \\dfrac{53{,}036}{77{,}000}, \\dfrac{56{,}346}{77{,}000}, \\dfrac{60{,}768}{77{,}000}, \\dfrac{63{,}689}{77{,}000}, \\text{ and } \\dfrac{64{,}413}{77{,}000}", "__seed__": "0305"}}, {"seed": 306, "data": {"p1_how_many": "13", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.325, 9.33, 9.335, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001", "9.325000000000001", "9.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}009}{20{,}000}, \\dfrac{5{,}448}{20{,}000}, \\dfrac{5{,}461}{20{,}000}, \\dfrac{5{,}746}{20{,}000}, \\dfrac{6{,}014}{20{,}000}, \\dfrac{6{,}464}{20{,}000}, \\dfrac{6{,}579}{20{,}000}, \\dfrac{7{,}025}{20{,}000}, \\dfrac{7{,}119}{20{,}000}, \\text{ and } \\dfrac{7{,}658}{20{,}000}", "__seed__": "0306"}}, {"seed": 307, "data": {"p1_how_many": "14", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.445, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998", "1.4449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}043}{12{,}000}, \\dfrac{3{,}378}{12{,}000}, \\dfrac{3{,}561}{12{,}000}, \\dfrac{3{,}586}{12{,}000}, \\dfrac{3{,}603}{12{,}000}, \\dfrac{3{,}763}{12{,}000}, \\dfrac{3{,}778}{12{,}000}, \\dfrac{3{,}780}{12{,}000}, \\dfrac{3{,}825}{12{,}000}, \\dfrac{3{,}832}{12{,}000}, \\text{ and } \\dfrac{3{,}955}{12{,}000}", "__seed__": "0307"}}, {"seed": 308, "data": {"p1_how_many": "12", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.54, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}444}{20{,}000}, \\dfrac{6{,}270}{20{,}000}, \\dfrac{6{,}275}{20{,}000}, \\dfrac{6{,}282}{20{,}000}, \\dfrac{6{,}650}{20{,}000}, \\dfrac{6{,}819}{20{,}000}, \\dfrac{7{,}088}{20{,}000}, \\dfrac{7{,}243}{20{,}000}, \\dfrac{7{,}527}{20{,}000}, \\text{ and } \\dfrac{7{,}769}{20{,}000}", "__seed__": "0308"}}, {"seed": 309, "data": {"p1_how_many": "13", "p1_a": "5.04", "p1_b": "5.05", "p1_numbers": "5.0405, 5.041, 5.0415, 5.042, 5.0425, 5.043, 5.0435, 5.044, 5.045, 5.046, 5.047, 5.048, and 5.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.041", "5.042", "5.043", "5.044", "5.045", "5.046", "5.047", "5.048", "5.049"], "p1_2_xs": ["5.0405", "5.0415", "5.0424999999999995", "5.0435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}033}{35{,}000}, \\dfrac{20{,}037}{35{,}000}, \\dfrac{20{,}120}{35{,}000}, \\dfrac{20{,}203}{35{,}000}, \\dfrac{20{,}323}{35{,}000}, \\dfrac{20{,}362}{35{,}000}, \\dfrac{20{,}632}{35{,}000}, \\dfrac{20{,}722}{35{,}000}, \\text{ and } \\dfrac{20{,}953}{35{,}000}", "__seed__": "0309"}}, {"seed": 310, "data": {"p1_how_many": "13", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.015, 2.02, 2.025, 2.03, 2.035, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997", "2.025", "2.0349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{545}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{554}{1{,}500}, \\dfrac{575}{1{,}500}, \\dfrac{594}{1{,}500}, \\text{ and } \\dfrac{596}{1{,}500}", "__seed__": "0310"}}, {"seed": 311, "data": {"p1_how_many": "12", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}267}{35{,}000}, \\dfrac{10{,}312}{35{,}000}, \\dfrac{10{,}757}{35{,}000}, \\dfrac{10{,}825}{35{,}000}, \\dfrac{10{,}845}{35{,}000}, \\dfrac{12{,}494}{35{,}000}, \\dfrac{12{,}674}{35{,}000}, \\dfrac{13{,}185}{35{,}000}, \\dfrac{13{,}539}{35{,}000}, \\text{ and } \\dfrac{13{,}615}{35{,}000}", "__seed__": "0311"}}, {"seed": 312, "data": {"p1_how_many": "14", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.635, 6.64, 6.645, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999", "6.635", "6.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0312"}}, {"seed": 313, "data": {"p1_how_many": "10", "p1_a": "1.73", "p1_b": "1.74", "p1_numbers": "1.7305, 1.731, 1.732, 1.733, 1.734, 1.735, 1.736, 1.737, 1.738, and 1.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.7309999999999999", "1.732", "1.7329999999999999", "1.734", "1.7349999999999999", "1.736", "1.7369999999999999", "1.738", "1.7389999999999999"], "p1_2_xs": ["1.7305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{621}{4{,}200}, \\dfrac{636}{4{,}200}, \\dfrac{641}{4{,}200}, \\dfrac{643}{4{,}200}, \\dfrac{654}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{661}{4{,}200}, \\dfrac{672}{4{,}200}, \\dfrac{675}{4{,}200}, \\dfrac{694}{4{,}200}, \\text{ and } \\dfrac{698}{4{,}200}", "__seed__": "0313"}}, {"seed": 314, "data": {"p1_how_many": "14", "p1_a": "1.86", "p1_b": "1.87", "p1_numbers": "1.8605, 1.861, 1.8615, 1.862, 1.8625, 1.863, 1.8635, 1.864, 1.8645, 1.865, 1.866, 1.867, 1.868, and 1.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.861", "1.862", "1.863", "1.864", "1.865", "1.866", "1.867", "1.868", "1.869"], "p1_2_xs": ["1.8605", "1.8615", "1.8625", "1.8635", "1.8645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}519}{6{,}300}, \\dfrac{1{,}592}{6{,}300}, \\dfrac{1{,}595}{6{,}300}, \\dfrac{1{,}643}{6{,}300}, \\dfrac{1{,}718}{6{,}300}, \\dfrac{1{,}719}{6{,}300}, \\dfrac{1{,}751}{6{,}300}, \\text{ and } \\dfrac{1{,}755}{6{,}300}", "__seed__": "0314"}}, {"seed": 315, "data": {"p1_how_many": "11", "p1_a": "8.26", "p1_b": "8.27", "p1_numbers": "8.2605, 8.261, 8.2615, 8.262, 8.263, 8.264, 8.265, 8.266, 8.267, 8.268, and 8.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.261", "8.262", "8.263", "8.264", "8.265", "8.266", "8.267", "8.267999999999999", "8.269"], "p1_2_xs": ["8.2605", "8.2615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{802}{1{,}200}, \\dfrac{813}{1{,}200}, \\dfrac{820}{1{,}200}, \\dfrac{828}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{836}{1{,}200}, \\dfrac{849}{1{,}200}, \\dfrac{857}{1{,}200}, \\dfrac{876}{1{,}200}, \\dfrac{882}{1{,}200}, \\dfrac{885}{1{,}200}, \\text{ and } \\dfrac{899}{1{,}200}", "__seed__": "0315"}}, {"seed": 316, "data": {"p1_how_many": "14", "p1_a": "2.32", "p1_b": "2.33", "p1_numbers": "2.3205, 2.321, 2.3215, 2.322, 2.3225, 2.323, 2.3235, 2.324, 2.3245, 2.325, 2.326, 2.327, 2.328, and 2.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3209999999999997", "2.3219999999999996", "2.323", "2.324", "2.3249999999999997", "2.3259999999999996", "2.327", "2.328", "2.3289999999999997"], "p1_2_xs": ["2.3205", "2.3215", "2.3225", "2.3235", "2.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}408}{3{,}000}, \\dfrac{2{,}416}{3{,}000}, \\dfrac{2{,}418}{3{,}000}, \\dfrac{2{,}428}{3{,}000}, \\dfrac{2{,}430}{3{,}000}, \\dfrac{2{,}440}{3{,}000}, \\dfrac{2{,}457}{3{,}000}, \\dfrac{2{,}473}{3{,}000}, \\dfrac{2{,}480}{3{,}000}, \\dfrac{2{,}482}{3{,}000}, \\dfrac{2{,}485}{3{,}000}, \\text{ and } \\dfrac{2{,}497}{3{,}000}", "__seed__": "0316"}}, {"seed": 317, "data": {"p1_how_many": "13", "p1_a": "6.9", "p1_b": "6.1", "p1_numbers": "6.9005, 6.901, 6.9015, 6.902, 6.9025, 6.903, 6.9035, 6.904, 6.905, 6.906, 6.907, 6.908, and 6.909", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.901000000000001", "6.902", "6.9030000000000005", "6.904", "6.905", "6.906000000000001", "6.907", "6.908", "6.909000000000001"], "p1_2_xs": ["6.9005", "6.9015", "6.9025", "6.9035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}037}{12{,}000}, \\dfrac{3{,}306}{12{,}000}, \\dfrac{3{,}389}{12{,}000}, \\dfrac{3{,}456}{12{,}000}, \\dfrac{3{,}543}{12{,}000}, \\dfrac{3{,}600}{12{,}000}, \\dfrac{3{,}606}{12{,}000}, \\dfrac{3{,}621}{12{,}000}, \\dfrac{3{,}739}{12{,}000}, \\dfrac{3{,}762}{12{,}000}, \\text{ and } \\dfrac{3{,}894}{12{,}000}", "__seed__": "0317"}}, {"seed": 318, "data": {"p1_how_many": "14", "p1_a": "8.21", "p1_b": "8.22", "p1_numbers": "8.2105, 8.211, 8.2115, 8.212, 8.2125, 8.213, 8.2135, 8.214, 8.2145, 8.215, 8.216, 8.217, 8.218, and 8.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.211", "8.212000000000002", "8.213000000000001", "8.214", "8.215000000000002", "8.216000000000001", "8.217", "8.218", "8.219000000000001"], "p1_2_xs": ["8.210500000000001", "8.211500000000001", "8.212500000000002", "8.213500000000002", "8.214500000000001"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{731}{4{,}200}, \\dfrac{734}{4{,}200}, \\dfrac{740}{4{,}200}, \\dfrac{795}{4{,}200}, \\dfrac{809}{4{,}200}, \\dfrac{884}{4{,}200}, \\dfrac{912}{4{,}200}, \\dfrac{999}{4{,}200}, \\dfrac{1{,}046}{4{,}200}, \\dfrac{1{,}126}{4{,}200}, \\dfrac{1{,}138}{4{,}200}, \\text{ and } \\dfrac{1{,}157}{4{,}200}", "__seed__": "0318"}}, {"seed": 319, "data": {"p1_how_many": "11", "p1_a": "1.93", "p1_b": "1.94", "p1_numbers": "1.9305, 1.931, 1.9315, 1.932, 1.933, 1.934, 1.935, 1.936, 1.937, 1.938, and 1.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9309999999999998", "1.932", "1.9329999999999998", "1.934", "1.9349999999999998", "1.936", "1.9369999999999998", "1.938", "1.9389999999999998"], "p1_2_xs": ["1.9304999999999999", "1.9314999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{307}{1{,}200}, \\dfrac{323}{1{,}200}, \\dfrac{327}{1{,}200}, \\dfrac{355}{1{,}200}, \\dfrac{363}{1{,}200}, \\dfrac{364}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{385}{1{,}200}, \\dfrac{388}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0319"}}, {"seed": 320, "data": {"p1_how_many": "14", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.245, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235", "5.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}034}{56{,}000}, \\dfrac{48{,}039}{56{,}000}, \\dfrac{48{,}207}{56{,}000}, \\dfrac{48{,}386}{56{,}000}, \\dfrac{48{,}601}{56{,}000}, \\dfrac{48{,}693}{56{,}000}, \\dfrac{48{,}788}{56{,}000}, \\dfrac{48{,}831}{56{,}000}, \\dfrac{48{,}875}{56{,}000}, \\dfrac{48{,}878}{56{,}000}, \\text{ and } \\dfrac{48{,}880}{56{,}000}", "__seed__": "0320"}}, {"seed": 321, "data": {"p1_how_many": "13", "p1_a": "5.31", "p1_b": "5.32", "p1_numbers": "5.3105, 5.311, 5.3115, 5.312, 5.3125, 5.313, 5.3135, 5.314, 5.315, 5.316, 5.317, 5.318, and 5.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.311", "5.311999999999999", "5.313", "5.313999999999999", "5.3149999999999995", "5.316", "5.316999999999999", "5.318", "5.319"], "p1_2_xs": ["5.310499999999999", "5.3115", "5.312499999999999", "5.3134999999999994"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}141}{42{,}000}, \\dfrac{30{,}202}{42{,}000}, \\dfrac{30{,}322}{42{,}000}, \\dfrac{30{,}326}{42{,}000}, \\dfrac{31{,}024}{42{,}000}, \\dfrac{31{,}351}{42{,}000}, \\dfrac{31{,}813}{42{,}000}, \\dfrac{32{,}865}{42{,}000}, \\dfrac{33{,}074}{42{,}000}, \\dfrac{33{,}933}{42{,}000}, \\dfrac{34{,}415}{42{,}000}, \\text{ and } \\dfrac{34{,}872}{42{,}000}", "__seed__": "0321"}}, {"seed": 322, "data": {"p1_how_many": "10", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.62, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}312}{63{,}000}, \\dfrac{30{,}278}{63{,}000}, \\dfrac{30{,}371}{63{,}000}, \\dfrac{31{,}655}{63{,}000}, \\dfrac{31{,}891}{63{,}000}, \\dfrac{31{,}977}{63{,}000}, \\text{ and } \\dfrac{34{,}804}{63{,}000}", "__seed__": "0322"}}, {"seed": 323, "data": {"p1_how_many": "14", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.725, 4.73, 4.735, 4.74, 4.745, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715", "4.725", "4.735", "4.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}031}{30{,}000}, \\dfrac{5{,}121}{30{,}000}, \\dfrac{5{,}162}{30{,}000}, \\dfrac{5{,}383}{30{,}000}, \\dfrac{5{,}598}{30{,}000}, \\dfrac{5{,}625}{30{,}000}, \\dfrac{5{,}653}{30{,}000}, \\dfrac{5{,}701}{30{,}000}, \\dfrac{5{,}725}{30{,}000}, \\dfrac{5{,}774}{30{,}000}, \\text{ and } \\dfrac{5{,}911}{30{,}000}", "__seed__": "0323"}}, {"seed": 324, "data": {"p1_how_many": "14", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135", "2.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}502}{2{,}000}, \\dfrac{1{,}529}{2{,}000}, \\dfrac{1{,}539}{2{,}000}, \\dfrac{1{,}543}{2{,}000}, \\dfrac{1{,}547}{2{,}000}, \\dfrac{1{,}548}{2{,}000}, \\dfrac{1{,}549}{2{,}000}, \\dfrac{1{,}573}{2{,}000}, \\dfrac{1{,}586}{2{,}000}, \\dfrac{1{,}589}{2{,}000}, \\text{ and } \\dfrac{1{,}592}{2{,}000}", "__seed__": "0324"}}, {"seed": 325, "data": {"p1_how_many": "13", "p1_a": "7.55", "p1_b": "7.56", "p1_numbers": "7.5505, 7.551, 7.5515, 7.552, 7.5525, 7.553, 7.5535, 7.554, 7.555, 7.556, 7.557, 7.558, and 7.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.551", "7.552", "7.553", "7.553999999999999", "7.555", "7.556", "7.5569999999999995", "7.558", "7.559"], "p1_2_xs": ["7.5504999999999995", "7.5515", "7.552499999999999", "7.5535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}207}{2{,}000}, \\dfrac{1{,}217}{2{,}000}, \\dfrac{1{,}244}{2{,}000}, \\dfrac{1{,}267}{2{,}000}, \\dfrac{1{,}348}{2{,}000}, \\dfrac{1{,}389}{2{,}000}, \\text{ and } \\dfrac{1{,}431}{2{,}000}", "__seed__": "0325"}}, {"seed": 326, "data": {"p1_how_many": "12", "p1_a": "2.34", "p1_b": "2.35", "p1_numbers": "2.3405, 2.341, 2.3415, 2.342, 2.3425, 2.343, 2.344, 2.345, 2.346, 2.347, 2.348, and 2.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3409999999999997", "2.3419999999999996", "2.343", "2.344", "2.3449999999999998", "2.3459999999999996", "2.347", "2.348", "2.3489999999999998"], "p1_2_xs": ["2.3405", "2.3415", "2.3425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{524}{1{,}500}, \\dfrac{531}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{559}{1{,}500}, \\dfrac{560}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{566}{1{,}500}, \\dfrac{568}{1{,}500}, \\dfrac{579}{1{,}500}, \\dfrac{588}{1{,}500}, \\dfrac{596}{1{,}500}, \\text{ and } \\dfrac{598}{1{,}500}", "__seed__": "0326"}}, {"seed": 327, "data": {"p1_how_many": "11", "p1_a": "3.11", "p1_b": "3.12", "p1_numbers": "3.1105, 3.111, 3.1115, 3.112, 3.113, 3.114, 3.115, 3.116, 3.117, 3.118, and 3.119", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.1109999999999998", "3.1119999999999997", "3.113", "3.114", "3.1149999999999998", "3.1159999999999997", "3.117", "3.118", "3.1189999999999998"], "p1_2_xs": ["3.1105", "3.1115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}728}{6{,}300}, \\dfrac{2{,}729}{6{,}300}, \\dfrac{2{,}738}{6{,}300}, \\dfrac{2{,}753}{6{,}300}, \\dfrac{2{,}756}{6{,}300}, \\dfrac{2{,}758}{6{,}300}, \\dfrac{2{,}771}{6{,}300}, \\dfrac{2{,}774}{6{,}300}, \\dfrac{2{,}781}{6{,}300}, \\text{ and } \\dfrac{2{,}784}{6{,}300}", "__seed__": "0327"}}, {"seed": 328, "data": {"p1_how_many": "12", "p1_a": "2.75", "p1_b": "2.76", "p1_numbers": "2.7505, 2.751, 2.7515, 2.752, 2.7525, 2.753, 2.754, 2.755, 2.756, 2.757, 2.758, and 2.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.751", "2.752", "2.753", "2.754", "2.755", "2.756", "2.757", "2.758", "2.759"], "p1_2_xs": ["2.7505", "2.7515", "2.7525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}881}{56{,}000}, \\dfrac{36{,}108}{56{,}000}, \\dfrac{36{,}447}{56{,}000}, \\dfrac{36{,}623}{56{,}000}, \\dfrac{38{,}376}{56{,}000}, \\dfrac{38{,}564}{56{,}000}, \\dfrac{38{,}808}{56{,}000}, \\text{ and } \\dfrac{39{,}744}{56{,}000}", "__seed__": "0328"}}, {"seed": 329, "data": {"p1_how_many": "10", "p1_a": "8.56", "p1_b": "8.57", "p1_numbers": "8.5605, 8.561, 8.562, 8.563, 8.564, 8.565, 8.566, 8.567, 8.568, and 8.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.561", "8.562000000000001", "8.563", "8.564", "8.565000000000001", "8.566", "8.567", "8.568", "8.569"], "p1_2_xs": ["8.560500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{2{,}000}, \\dfrac{546}{2{,}000}, \\dfrac{552}{2{,}000}, \\dfrac{586}{2{,}000}, \\dfrac{601}{2{,}000}, \\dfrac{659}{2{,}000}, \\dfrac{750}{2{,}000}, \\dfrac{761}{2{,}000}, \\text{ and } \\dfrac{780}{2{,}000}", "__seed__": "0329"}}, {"seed": 330, "data": {"p1_how_many": "10", "p1_a": "6.93", "p1_b": "6.94", "p1_numbers": "6.9305, 6.931, 6.932, 6.933, 6.934, 6.935, 6.936, 6.937, 6.938, and 6.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.931", "6.9319999999999995", "6.933", "6.933999999999999", "6.935", "6.936", "6.936999999999999", "6.938", "6.939"], "p1_2_xs": ["6.930499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}032}{3{,}500}, \\dfrac{1{,}060}{3{,}500}, \\dfrac{1{,}123}{3{,}500}, \\dfrac{1{,}167}{3{,}500}, \\dfrac{1{,}219}{3{,}500}, \\dfrac{1{,}336}{3{,}500}, \\text{ and } \\dfrac{1{,}358}{3{,}500}", "__seed__": "0330"}}, {"seed": 331, "data": {"p1_how_many": "12", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}214}{30{,}000}, \\dfrac{24{,}315}{30{,}000}, \\dfrac{24{,}352}{30{,}000}, \\dfrac{24{,}539}{30{,}000}, \\dfrac{24{,}643}{30{,}000}, \\dfrac{24{,}791}{30{,}000}, \\dfrac{24{,}916}{30{,}000}, \\text{ and } \\dfrac{24{,}974}{30{,}000}", "__seed__": "0331"}}, {"seed": 332, "data": {"p1_how_many": "14", "p1_a": "3.22", "p1_b": "3.23", "p1_numbers": "3.2205, 3.221, 3.2215, 3.222, 3.2225, 3.223, 3.2235, 3.224, 3.2245, 3.225, 3.226, 3.227, 3.228, and 3.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.221", "3.222", "3.2230000000000003", "3.224", "3.225", "3.226", "3.2270000000000003", "3.228", "3.229"], "p1_2_xs": ["3.2205000000000004", "3.2215000000000003", "3.2225", "3.2235000000000005", "3.2245000000000004"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}803}{5{,}600}, \\dfrac{4{,}814}{5{,}600}, \\dfrac{4{,}823}{5{,}600}, \\dfrac{4{,}873}{5{,}600}, \\dfrac{4{,}877}{5{,}600}, \\dfrac{4{,}886}{5{,}600}, \\text{ and } \\dfrac{4{,}891}{5{,}600}", "__seed__": "0332"}}, {"seed": 333, "data": {"p1_how_many": "13", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.235, 9.24, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225", "9.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}585}{42{,}000}, \\dfrac{7{,}743}{42{,}000}, \\dfrac{7{,}778}{42{,}000}, \\dfrac{7{,}994}{42{,}000}, \\dfrac{8{,}941}{42{,}000}, \\dfrac{9{,}731}{42{,}000}, \\dfrac{9{,}986}{42{,}000}, \\dfrac{10{,}364}{42{,}000}, \\dfrac{11{,}012}{42{,}000}, \\dfrac{11{,}111}{42{,}000}, \\dfrac{11{,}430}{42{,}000}, \\text{ and } \\dfrac{11{,}476}{42{,}000}", "__seed__": "0333"}}, {"seed": 334, "data": {"p1_how_many": "11", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{143}{630}, \\dfrac{146}{630}, \\dfrac{155}{630}, \\dfrac{159}{630}, \\dfrac{170}{630}, \\dfrac{175}{630}, \\text{ and } \\dfrac{179}{630}", "__seed__": "0334"}}, {"seed": 335, "data": {"p1_how_many": "13", "p1_a": "5.74", "p1_b": "5.75", "p1_numbers": "5.7405, 5.741, 5.7415, 5.742, 5.7425, 5.743, 5.7435, 5.744, 5.745, 5.746, 5.747, 5.748, and 5.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7410000000000005", "5.742", "5.743", "5.744", "5.745", "5.746", "5.747", "5.748", "5.7490000000000006"], "p1_2_xs": ["5.7405", "5.7415", "5.7425", "5.7435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{603}{4{,}200}, \\dfrac{625}{4{,}200}, \\dfrac{638}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{652}{4{,}200}, \\dfrac{658}{4{,}200}, \\dfrac{667}{4{,}200}, \\dfrac{687}{4{,}200}, \\dfrac{693}{4{,}200}, \\text{ and } \\dfrac{695}{4{,}200}", "__seed__": "0335"}}, {"seed": 336, "data": {"p1_how_many": "14", "p1_a": "9.34", "p1_b": "9.35", "p1_numbers": "9.3405, 9.341, 9.3415, 9.342, 9.3425, 9.343, 9.3435, 9.344, 9.3445, 9.345, 9.346, 9.347, 9.348, and 9.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.341", "9.342", "9.343", "9.344", "9.345", "9.346", "9.347", "9.347999999999999", "9.349"], "p1_2_xs": ["9.3405", "9.3415", "9.342500000000001", "9.3435", "9.3445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{745}{4{,}200}, \\dfrac{754}{4{,}200}, \\dfrac{848}{4{,}200}, \\dfrac{889}{4{,}200}, \\dfrac{958}{4{,}200}, \\dfrac{999}{4{,}200}, \\dfrac{1{,}013}{4{,}200}, \\dfrac{1{,}057}{4{,}200}, \\dfrac{1{,}135}{4{,}200}, \\text{ and } \\dfrac{1{,}154}{4{,}200}", "__seed__": "0336"}}, {"seed": 337, "data": {"p1_how_many": "13", "p1_a": "1.97", "p1_b": "1.98", "p1_numbers": "1.9705, 1.971, 1.9715, 1.972, 1.9725, 1.973, 1.9735, 1.974, 1.975, 1.976, 1.977, 1.978, and 1.979", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9709999999999999", "1.972", "1.9729999999999999", "1.974", "1.9749999999999999", "1.976", "1.9769999999999999", "1.978", "1.9789999999999999"], "p1_2_xs": ["1.9705", "1.9714999999999998", "1.9725", "1.9734999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}129}{3{,}500}, \\dfrac{2{,}135}{3{,}500}, \\dfrac{2{,}192}{3{,}500}, \\dfrac{2{,}328}{3{,}500}, \\dfrac{2{,}338}{3{,}500}, \\dfrac{2{,}413}{3{,}500}, \\dfrac{2{,}461}{3{,}500}, \\dfrac{2{,}483}{3{,}500}, \\dfrac{2{,}533}{3{,}500}, \\dfrac{2{,}566}{3{,}500}, \\dfrac{2{,}710}{3{,}500}, \\text{ and } \\dfrac{2{,}777}{3{,}500}", "__seed__": "0337"}}, {"seed": 338, "data": {"p1_how_many": "12", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.4005, 1.401, 1.4015, 1.402, 1.4025, 1.403, 1.404, 1.405, 1.406, 1.407, 1.408, and 1.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4009999999999998", "1.402", "1.4029999999999998", "1.404", "1.4049999999999998", "1.406", "1.4069999999999998", "1.408", "1.4089999999999998"], "p1_2_xs": ["1.4004999999999999", "1.4014999999999997", "1.4024999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}012}{20{,}000}, \\dfrac{4{,}040}{20{,}000}, \\dfrac{4{,}057}{20{,}000}, \\dfrac{4{,}103}{20{,}000}, \\dfrac{4{,}424}{20{,}000}, \\dfrac{4{,}428}{20{,}000}, \\dfrac{4{,}432}{20{,}000}, \\dfrac{4{,}515}{20{,}000}, \\dfrac{4{,}608}{20{,}000}, \\dfrac{4{,}679}{20{,}000}, \\text{ and } \\dfrac{4{,}854}{20{,}000}", "__seed__": "0338"}}, {"seed": 339, "data": {"p1_how_many": "13", "p1_a": "7.33", "p1_b": "7.34", "p1_numbers": "7.3305, 7.331, 7.3315, 7.332, 7.3325, 7.333, 7.3335, 7.334, 7.335, 7.336, 7.337, 7.338, and 7.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.331", "7.332", "7.333", "7.334", "7.335", "7.336", "7.337", "7.338", "7.339"], "p1_2_xs": ["7.3305", "7.3315", "7.3325", "7.3335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{1{,}736}{3{,}500}, \\dfrac{1{,}785}{3{,}500}, \\dfrac{1{,}787}{3{,}500}, \\dfrac{1{,}926}{3{,}500}, \\dfrac{1{,}943}{3{,}500}, \\dfrac{1{,}996}{3{,}500}, \\dfrac{1{,}998}{3{,}500}, \\dfrac{2{,}019}{3{,}500}, 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and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}061}{42{,}000}, \\dfrac{7{,}891}{42{,}000}, \\dfrac{8{,}037}{42{,}000}, \\dfrac{9{,}295}{42{,}000}, \\dfrac{9{,}815}{42{,}000}, \\dfrac{10{,}188}{42{,}000}, \\dfrac{10{,}253}{42{,}000}, \\dfrac{11{,}202}{42{,}000}, \\text{ and } \\dfrac{11{,}403}{42{,}000}", "__seed__": "0346"}}, {"seed": 347, "data": {"p1_how_many": "10", "p1_a": "4.61", "p1_b": "4.62", "p1_numbers": "4.6105, 4.611, 4.612, 4.613, 4.614, 4.615, 4.616, 4.617, 4.618, and 4.619", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.611000000000001", "4.612", "4.613", "4.614", "4.615", "4.6160000000000005", "4.617", "4.618", "4.619000000000001"], "p1_2_xs": ["4.6105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}127}{4{,}200}, \\dfrac{3{,}173}{4{,}200}, \\dfrac{3{,}186}{4{,}200}, \\dfrac{3{,}204}{4{,}200}, \\dfrac{3{,}328}{4{,}200}, \\dfrac{3{,}423}{4{,}200}, \\text{ and } \\dfrac{3{,}451}{4{,}200}", "__seed__": "0347"}}, {"seed": 348, "data": {"p1_how_many": "12", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.24, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}266}{20{,}000}, \\dfrac{5{,}307}{20{,}000}, \\dfrac{6{,}488}{20{,}000}, \\dfrac{6{,}530}{20{,}000}, \\dfrac{6{,}540}{20{,}000}, \\dfrac{6{,}577}{20{,}000}, \\dfrac{6{,}635}{20{,}000}, \\dfrac{6{,}909}{20{,}000}, \\dfrac{7{,}046}{20{,}000}, \\dfrac{7{,}415}{20{,}000}, \\text{ and } \\dfrac{7{,}477}{20{,}000}", "__seed__": "0348"}}, {"seed": 349, "data": {"p1_how_many": "12", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}236}{2{,}000}, \\dfrac{1{,}269}{2{,}000}, \\dfrac{1{,}336}{2{,}000}, \\dfrac{1{,}346}{2{,}000}, \\dfrac{1{,}361}{2{,}000}, \\dfrac{1{,}380}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\text{ and } \\dfrac{1{,}499}{2{,}000}", 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3.415, 3.42, 3.425, 3.43, 3.435, 3.44, 3.445, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996", "3.425", "3.4349999999999996", "3.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}450}{63{,}000}, \\dfrac{10{,}665}{63{,}000}, \\dfrac{10{,}758}{63{,}000}, \\dfrac{11{,}086}{63{,}000}, \\dfrac{11{,}317}{63{,}000}, \\dfrac{11{,}424}{63{,}000}, \\dfrac{11{,}740}{63{,}000}, \\dfrac{11{,}978}{63{,}000}, \\dfrac{12{,}110}{63{,}000}, \\dfrac{12{,}206}{63{,}000}, \\text{ and } \\dfrac{13{,}720}{63{,}000}", "__seed__": "0351"}}, {"seed": 352, "data": {"p1_how_many": "11", "p1_a": "9.1", "p1_b": 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"p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.621", "7.622", "7.623", "7.624", "7.625", "7.626", "7.627", "7.628", "7.6290000000000004"], "p1_2_xs": ["7.6205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}085}{12{,}000}, \\dfrac{8{,}394}{12{,}000}, \\dfrac{8{,}462}{12{,}000}, \\dfrac{8{,}585}{12{,}000}, \\dfrac{8{,}621}{12{,}000}, \\dfrac{8{,}713}{12{,}000}, \\dfrac{8{,}777}{12{,}000}, \\text{ and } \\dfrac{8{,}940}{12{,}000}", "__seed__": "0353"}}, {"seed": 354, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{310}{1{,}200}, \\dfrac{326}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{339}{1{,}200}, \\dfrac{356}{1{,}200}, \\dfrac{361}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{388}{1{,}200}, \\text{ and } \\dfrac{399}{1{,}200}", "__seed__": "0354"}}, {"seed": 355, "data": {"p1_how_many": "13", "p1_a": "2.67", "p1_b": "2.68", "p1_numbers": "2.6705, 2.671, 2.6715, 2.672, 2.6725, 2.673, 2.6735, 2.674, 2.675, 2.676, 2.677, 2.678, and 2.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.671", "2.6719999999999997", "2.673", "2.674", "2.675", "2.6759999999999997", "2.677", "2.678", "2.679"], "p1_2_xs": ["2.6705", "2.6715", "2.6725", "2.6735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}056}{15{,}000}, \\dfrac{5{,}305}{15{,}000}, \\dfrac{5{,}448}{15{,}000}, \\dfrac{5{,}522}{15{,}000}, \\dfrac{5{,}618}{15{,}000}, \\dfrac{5{,}689}{15{,}000}, \\dfrac{5{,}793}{15{,}000}, \\text{ and } \\dfrac{5{,}838}{15{,}000}", "__seed__": "0355"}}, {"seed": 356, "data": {"p1_how_many": "14", "p1_a": "4.43", "p1_b": "4.44", "p1_numbers": "4.4305, 4.431, 4.4315, 4.432, 4.4325, 4.433, 4.4335, 4.434, 4.4345, 4.435, 4.436, 4.437, 4.438, and 4.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.431", "4.4319999999999995", "4.433", "4.433999999999999", "4.435", "4.436", "4.436999999999999", "4.438", "4.439"], "p1_2_xs": ["4.430499999999999", "4.4315", "4.432499999999999", "4.4334999999999996", "4.434499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{309}{1{,}200}, \\dfrac{312}{1{,}200}, \\dfrac{315}{1{,}200}, \\dfrac{333}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{345}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{370}{1{,}200}, \\dfrac{380}{1{,}200}, \\text{ and } \\dfrac{390}{1{,}200}", "__seed__": "0356"}}, {"seed": 357, "data": {"p1_how_many": "10", "p1_a": "7.22", "p1_b": "7.23", "p1_numbers": "7.2205, 7.221, 7.222, 7.223, 7.224, 7.225, 7.226, 7.227, 7.228, and 7.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.221", "7.2219999999999995", "7.223", "7.223999999999999", "7.225", "7.226", "7.226999999999999", "7.228", "7.229"], "p1_2_xs": ["7.2204999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0357"}}, {"seed": 358, "data": {"p1_how_many": "14", "p1_a": "2.37", "p1_b": "2.38", "p1_numbers": "2.3705, 2.371, 2.3715, 2.372, 2.3725, 2.373, 2.3735, 2.374, 2.3745, 2.375, 2.376, 2.377, 2.378, and 2.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.371", "2.372", "2.373", "2.374", "2.375", "2.376", "2.3770000000000002", "2.378", "2.379"], "p1_2_xs": ["2.3705000000000003", "2.3715", "2.3725", "2.3735000000000004", "2.3745000000000003"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}159}{20{,}000}, \\dfrac{12{,}286}{20{,}000}, \\dfrac{12{,}568}{20{,}000}, \\dfrac{12{,}903}{20{,}000}, \\dfrac{12{,}920}{20{,}000}, \\dfrac{13{,}312}{20{,}000}, \\dfrac{13{,}489}{20{,}000}, \\dfrac{13{,}999}{20{,}000}, \\dfrac{14{,}562}{20{,}000}, \\dfrac{14{,}765}{20{,}000}, \\text{ and } \\dfrac{14{,}930}{20{,}000}", "__seed__": "0358"}}, {"seed": 359, "data": {"p1_how_many": "12", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}019}{15{,}000}, \\dfrac{5{,}022}{15{,}000}, \\dfrac{5{,}109}{15{,}000}, \\dfrac{5{,}114}{15{,}000}, \\dfrac{5{,}159}{15{,}000}, \\dfrac{5{,}570}{15{,}000}, \\dfrac{5{,}599}{15{,}000}, \\dfrac{5{,}686}{15{,}000}, \\dfrac{5{,}763}{15{,}000}, \\dfrac{5{,}765}{15{,}000}, \\dfrac{5{,}812}{15{,}000}, \\text{ and } \\dfrac{5{,}905}{15{,}000}", "__seed__": "0359"}}, {"seed": 360, "data": {"p1_how_many": "10", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{8{,}605}{42{,}000}, \\dfrac{8{,}702}{42{,}000}, \\dfrac{8{,}926}{42{,}000}, \\dfrac{9{,}543}{42{,}000}, \\dfrac{10{,}628}{42{,}000}, \\dfrac{10{,}853}{42{,}000}, \\dfrac{11{,}227}{42{,}000}, \\dfrac{11{,}436}{42{,}000}, \\dfrac{11{,}611}{42{,}000}, \\dfrac{11{,}736}{42{,}000}, \\text{ and } \\dfrac{11{,}982}{42{,}000}", "__seed__": "0360"}}, {"seed": 361, "data": {"p1_how_many": "12", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}023}{12{,}000}, \\dfrac{8{,}138}{12{,}000}, \\dfrac{8{,}205}{12{,}000}, \\dfrac{8{,}393}{12{,}000}, \\dfrac{8{,}398}{12{,}000}, \\dfrac{8{,}423}{12{,}000}, \\dfrac{8{,}535}{12{,}000}, \\dfrac{8{,}573}{12{,}000}, \\dfrac{8{,}761}{12{,}000}, \\dfrac{8{,}770}{12{,}000}, \\dfrac{8{,}846}{12{,}000}, \\text{ and } \\dfrac{8{,}990}{12{,}000}", "__seed__": "0361"}}, {"seed": 362, "data": {"p1_how_many": "14", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.745, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735", "2.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}952}{63{,}000}, \\dfrac{10{,}052}{63{,}000}, \\dfrac{10{,}987}{63{,}000}, \\dfrac{11{,}495}{63{,}000}, \\dfrac{12{,}515}{63{,}000}, \\dfrac{12{,}762}{63{,}000}, \\dfrac{13{,}507}{63{,}000}, \\dfrac{13{,}562}{63{,}000}, \\text{ and } \\dfrac{13{,}601}{63{,}000}", "__seed__": "0362"}}, {"seed": 363, "data": {"p1_how_many": "14", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.025, 6.03, 6.035, 6.04, 6.045, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015", "6.0249999999999995", "6.035", "6.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}235}{7{,}700}, \\dfrac{4{,}512}{7{,}700}, \\dfrac{4{,}552}{7{,}700}, \\dfrac{4{,}649}{7{,}700}, \\dfrac{4{,}727}{7{,}700}, \\dfrac{4{,}748}{7{,}700}, \\dfrac{4{,}812}{7{,}700}, \\dfrac{5{,}091}{7{,}700}, \\dfrac{5{,}180}{7{,}700}, \\dfrac{5{,}423}{7{,}700}, \\dfrac{5{,}474}{7{,}700}, \\text{ and } \\dfrac{5{,}494}{7{,}700}", "__seed__": "0363"}}, {"seed": 364, "data": {"p1_how_many": "10", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}809}{6{,}300}, \\dfrac{2{,}837}{6{,}300}, \\dfrac{3{,}023}{6{,}300}, \\dfrac{3{,}224}{6{,}300}, \\dfrac{3{,}279}{6{,}300}, \\dfrac{3{,}338}{6{,}300}, \\dfrac{3{,}398}{6{,}300}, \\dfrac{3{,}422}{6{,}300}, \\dfrac{3{,}454}{6{,}300}, \\dfrac{3{,}546}{6{,}300}, \\text{ and } \\dfrac{3{,}596}{6{,}300}", "__seed__": "0364"}}, {"seed": 365, "data": {"p1_how_many": "14", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.635, 4.64, 4.645, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999", "4.635", "4.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}355}{7{,}700}, \\dfrac{4{,}697}{7{,}700}, \\dfrac{5{,}150}{7{,}700}, \\dfrac{5{,}432}{7{,}700}, \\dfrac{5{,}525}{7{,}700}, \\dfrac{5{,}786}{7{,}700}, \\dfrac{5{,}977}{7{,}700}, \\dfrac{6{,}017}{7{,}700}, \\dfrac{6{,}184}{7{,}700}, \\dfrac{6{,}253}{7{,}700}, \\text{ and } \\dfrac{6{,}276}{7{,}700}", "__seed__": "0365"}}, {"seed": 366, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}288}{56{,}000}, \\dfrac{35{,}717}{56{,}000}, \\dfrac{36{,}763}{56{,}000}, \\dfrac{37{,}706}{56{,}000}, \\dfrac{37{,}929}{56{,}000}, \\dfrac{38{,}855}{56{,}000}, \\dfrac{38{,}905}{56{,}000}, \\dfrac{39{,}016}{56{,}000}, \\dfrac{39{,}093}{56{,}000}, \\dfrac{39{,}412}{56{,}000}, \\dfrac{39{,}827}{56{,}000}, \\text{ and } \\dfrac{39{,}932}{56{,}000}", "__seed__": "0366"}}, {"seed": 367, "data": {"p1_how_many": "12", "p1_a": "2.04", "p1_b": "2.05", "p1_numbers": "2.0405, 2.041, 2.0415, 2.042, 2.0425, 2.043, 2.044, 2.045, 2.046, 2.047, 2.048, and 2.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.041", "2.042", "2.043", "2.044", "2.045", "2.046", "2.047", "2.048", "2.049"], "p1_2_xs": ["2.0405", "2.0415", "2.0425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}474}{63{,}000}, \\dfrac{10{,}011}{63{,}000}, \\dfrac{10{,}104}{63{,}000}, \\dfrac{11{,}362}{63{,}000}, \\dfrac{11{,}599}{63{,}000}, \\dfrac{12{,}510}{63{,}000}, \\dfrac{13{,}013}{63{,}000}, \\dfrac{13{,}465}{63{,}000}, \\dfrac{13{,}727}{63{,}000}, \\dfrac{13{,}743}{63{,}000}, \\text{ and } \\dfrac{13{,}955}{63{,}000}", "__seed__": "0367"}}, {"seed": 368, "data": {"p1_how_many": "11", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{421}{2{,}000}, \\dfrac{424}{2{,}000}, \\dfrac{429}{2{,}000}, \\dfrac{437}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{457}{2{,}000}, \\dfrac{460}{2{,}000}, \\dfrac{462}{2{,}000}, \\text{ and } \\dfrac{474}{2{,}000}", "__seed__": "0368"}}, {"seed": 369, "data": {"p1_how_many": "13", "p1_a": "8.96", "p1_b": "8.97", "p1_numbers": "8.9605, 8.961, 8.9615, 8.962, 8.9625, 8.963, 8.9635, 8.964, 8.965, 8.966, 8.967, 8.968, and 8.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.961", "8.962000000000002", "8.963000000000001", "8.964", "8.965000000000002", "8.966000000000001", "8.967", "8.968", "8.969000000000001"], "p1_2_xs": ["8.960500000000001", "8.961500000000001", "8.962500000000002", "8.963500000000002"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}120}{42{,}000}, \\dfrac{35{,}232}{42{,}000}, \\dfrac{35{,}257}{42{,}000}, \\dfrac{35{,}377}{42{,}000}, \\dfrac{35{,}396}{42{,}000}, \\dfrac{35{,}417}{42{,}000}, \\dfrac{35{,}429}{42{,}000}, \\dfrac{35{,}673}{42{,}000}, \\text{ and } \\dfrac{35{,}948}{42{,}000}", "__seed__": "0369"}}, {"seed": 370, "data": {"p1_how_many": "12", "p1_a": "4.91", "p1_b": "4.92", "p1_numbers": "4.9105, 4.911, 4.9115, 4.912, 4.9125, 4.913, 4.914, 4.915, 4.916, 4.917, 4.918, and 4.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.9110000000000005", "4.912", "4.913", "4.914", "4.915", "4.916", "4.917", "4.918", "4.9190000000000005"], "p1_2_xs": ["4.9105", "4.9115", "4.9125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}076}{35{,}000}, \\dfrac{14{,}182}{35{,}000}, \\dfrac{14{,}197}{35{,}000}, \\dfrac{14{,}255}{35{,}000}, \\dfrac{14{,}327}{35{,}000}, \\dfrac{14{,}507}{35{,}000}, \\text{ and } \\dfrac{14{,}729}{35{,}000}", "__seed__": "0370"}}, {"seed": 371, "data": {"p1_how_many": "11", "p1_a": "1.95", "p1_b": "1.96", "p1_numbers": "1.9505, 1.951, 1.9515, 1.952, 1.953, 1.954, 1.955, 1.956, 1.957, 1.958, and 1.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9509999999999998", "1.952", "1.9529999999999998", "1.954", "1.9549999999999998", "1.956", "1.9569999999999999", "1.958", "1.9589999999999999"], "p1_2_xs": ["1.9505", "1.9514999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{623}{4{,}200}, \\dfrac{631}{4{,}200}, \\dfrac{654}{4{,}200}, \\dfrac{662}{4{,}200}, \\dfrac{664}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{673}{4{,}200}, \\dfrac{689}{4{,}200}, \\dfrac{690}{4{,}200}, \\text{ and } \\dfrac{691}{4{,}200}", "__seed__": "0371"}}, {"seed": 372, "data": {"p1_how_many": "13", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.205, 9.21, 9.215, 9.22, 9.225, 9.23, 9.235, 9.24, 9.25, 9.26, 9.27, 9.28, and 9.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.209999999999999", "9.219999999999999", "9.229999999999999", "9.239999999999998", "9.25", "9.26", "9.27", "9.28", "9.29"], "p1_2_xs": ["9.205", "9.215", "9.225", "9.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}506}{42{,}000}, \\dfrac{30{,}521}{42{,}000}, \\dfrac{30{,}922}{42{,}000}, \\dfrac{30{,}951}{42{,}000}, \\dfrac{31{,}011}{42{,}000}, \\dfrac{32{,}730}{42{,}000}, \\dfrac{33{,}209}{42{,}000}, \\dfrac{33{,}535}{42{,}000}, \\dfrac{33{,}616}{42{,}000}, \\dfrac{33{,}956}{42{,}000}, \\dfrac{34{,}192}{42{,}000}, \\text{ and } \\dfrac{34{,}193}{42{,}000}", "__seed__": "0372"}}, {"seed": 373, "data": {"p1_how_many": "14", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.6005, 2.601, 2.6015, 2.602, 2.6025, 2.603, 2.6035, 2.604, 2.6045, 2.605, 2.606, 2.607, 2.608, and 2.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.601", "2.602", "2.603", "2.604", "2.605", "2.606", "2.607", "2.608", "2.609"], "p1_2_xs": ["2.6005000000000003", "2.6015", "2.6025", "2.6035000000000004", "2.6045000000000003"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{327}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{343}{1{,}200}, \\dfrac{349}{1{,}200}, \\dfrac{352}{1{,}200}, \\dfrac{361}{1{,}200}, \\dfrac{383}{1{,}200}, \\dfrac{386}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0373"}}, {"seed": 374, "data": {"p1_how_many": "10", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{783}{4{,}200}, \\dfrac{791}{4{,}200}, \\dfrac{803}{4{,}200}, \\dfrac{820}{4{,}200}, \\dfrac{845}{4{,}200}, \\dfrac{861}{4{,}200}, \\dfrac{876}{4{,}200}, \\dfrac{998}{4{,}200}, \\dfrac{1{,}002}{4{,}200}, \\dfrac{1{,}047}{4{,}200}, \\dfrac{1{,}142}{4{,}200}, \\text{ and } \\dfrac{1{,}193}{4{,}200}", "__seed__": "0374"}}, {"seed": 375, "data": {"p1_how_many": "11", "p1_a": "1.02", "p1_b": "1.03", "p1_numbers": "1.0205, 1.021, 1.0215, 1.022, 1.023, 1.024, 1.025, 1.026, 1.027, 1.028, and 1.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.021", "1.022", "1.023", "1.024", "1.025", "1.026", "1.027", "1.028", "1.029"], "p1_2_xs": ["1.0205", "1.0214999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}117}{15{,}000}, \\dfrac{6{,}454}{15{,}000}, \\dfrac{7{,}631}{15{,}000}, \\dfrac{7{,}741}{15{,}000}, \\dfrac{8{,}109}{15{,}000}, \\dfrac{8{,}387}{15{,}000}, \\dfrac{8{,}626}{15{,}000}, \\dfrac{8{,}691}{15{,}000}, \\dfrac{8{,}718}{15{,}000}, \\text{ and } \\dfrac{9{,}704}{15{,}000}", "__seed__": "0375"}}, {"seed": 376, "data": {"p1_how_many": "11", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{505}{2{,}000}, \\dfrac{542}{2{,}000}, \\dfrac{573}{2{,}000}, \\dfrac{579}{2{,}000}, \\dfrac{585}{2{,}000}, \\dfrac{604}{2{,}000}, \\dfrac{607}{2{,}000}, \\dfrac{609}{2{,}000}, \\dfrac{655}{2{,}000}, \\dfrac{683}{2{,}000}, \\dfrac{689}{2{,}000}, \\text{ and } \\dfrac{779}{2{,}000}", "__seed__": "0376"}}, {"seed": 377, "data": {"p1_how_many": "13", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.5005, 8.501, 8.5015, 8.502, 8.5025, 8.503, 8.5035, 8.504, 8.505, 8.506, 8.507, 8.508, and 8.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.501", "8.502", "8.503", "8.504", "8.505", "8.506", "8.507", "8.508", "8.509"], "p1_2_xs": ["8.5005", "8.5015", "8.502500000000001", "8.5035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}031}{3{,}500}, \\dfrac{1{,}103}{3{,}500}, \\dfrac{1{,}125}{3{,}500}, \\dfrac{1{,}126}{3{,}500}, \\dfrac{1{,}182}{3{,}500}, \\dfrac{1{,}220}{3{,}500}, \\dfrac{1{,}270}{3{,}500}, \\dfrac{1{,}282}{3{,}500}, \\text{ and } \\dfrac{1{,}391}{3{,}500}", "__seed__": "0377"}}, {"seed": 378, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.6005, 5.601, 5.602, 5.603, 5.604, 5.605, 5.606, 5.607, 5.608, and 5.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.601", "5.601999999999999", "5.603", "5.603999999999999", "5.6049999999999995", "5.606", "5.606999999999999", "5.608", "5.609"], "p1_2_xs": ["5.600499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{7{,}062}{15{,}000}, \\dfrac{7{,}548}{15{,}000}, \\dfrac{8{,}753}{15{,}000}, \\dfrac{9{,}270}{15{,}000}, \\dfrac{9{,}327}{15{,}000}, \\dfrac{9{,}425}{15{,}000}, \\text{ and } \\dfrac{9{,}681}{15{,}000}", "__seed__": "0378"}}, {"seed": 379, "data": {"p1_how_many": "14", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.635, 3.64, 3.645, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625", "3.635", "3.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{743}{4{,}200}, \\dfrac{787}{4{,}200}, \\dfrac{796}{4{,}200}, \\dfrac{831}{4{,}200}, \\dfrac{884}{4{,}200}, \\dfrac{960}{4{,}200}, \\dfrac{969}{4{,}200}, \\dfrac{994}{4{,}200}, \\dfrac{1{,}131}{4{,}200}, \\text{ and } \\dfrac{1{,}140}{4{,}200}", "__seed__": "0379"}}, {"seed": 380, "data": {"p1_how_many": "10", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.7005, 5.701, 5.702, 5.703, 5.704, 5.705, 5.706, 5.707, 5.708, and 5.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7010000000000005", "5.702", "5.703", "5.704", "5.705", "5.706", "5.707", "5.708", "5.7090000000000005"], "p1_2_xs": ["5.7005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}204}{2{,}000}, \\dfrac{1{,}236}{2{,}000}, \\dfrac{1{,}301}{2{,}000}, \\dfrac{1{,}347}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\dfrac{1{,}445}{2{,}000}, \\text{ and } \\dfrac{1{,}465}{2{,}000}", "__seed__": "0380"}}, {"seed": 381, "data": {"p1_how_many": "12", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{305}{420}, \\dfrac{309}{420}, \\dfrac{312}{420}, \\dfrac{315}{420}, \\dfrac{328}{420}, \\dfrac{329}{420}, \\text{ and } \\dfrac{341}{420}", "__seed__": "0381"}}, {"seed": 382, "data": {"p1_how_many": "12", "p1_a": "8.33", "p1_b": "8.34", "p1_numbers": "8.3305, 8.331, 8.3315, 8.332, 8.3325, 8.333, 8.334, 8.335, 8.336, 8.337, 8.338, and 8.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.331", "8.332", "8.333", "8.334", "8.335", "8.336", "8.337", "8.338", "8.339"], "p1_2_xs": ["8.3305", "8.3315", "8.332500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{516}{1{,}500}, \\dfrac{521}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{531}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{551}{1{,}500}, \\text{ and } \\dfrac{577}{1{,}500}", "__seed__": "0382"}}, {"seed": 383, "data": {"p1_how_many": "14", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.025, 3.03, 3.035, 3.04, 3.045, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997", "3.025", "3.0349999999999997", "3.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}606}{5{,}600}, \\dfrac{1{,}635}{5{,}600}, \\dfrac{1{,}775}{5{,}600}, \\dfrac{1{,}786}{5{,}600}, \\dfrac{1{,}869}{5{,}600}, \\dfrac{1{,}904}{5{,}600}, \\dfrac{1{,}994}{5{,}600}, \\text{ and } \\dfrac{2{,}014}{5{,}600}", "__seed__": "0383"}}, {"seed": 384, "data": {"p1_how_many": "10", "p1_a": "7.37", "p1_b": "7.38", "p1_numbers": "7.3705, 7.371, 7.372, 7.373, 7.374, 7.375, 7.376, 7.377, 7.378, and 7.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.371", "7.372", "7.373", "7.374", "7.375", "7.376", "7.377", "7.378", "7.3790000000000004"], "p1_2_xs": ["7.3705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}012}{15{,}000}, \\dfrac{5{,}068}{15{,}000}, \\dfrac{5{,}131}{15{,}000}, \\dfrac{5{,}312}{15{,}000}, \\dfrac{5{,}426}{15{,}000}, \\dfrac{5{,}623}{15{,}000}, \\text{ and } \\dfrac{5{,}823}{15{,}000}", "__seed__": "0384"}}, {"seed": 385, "data": {"p1_how_many": "11", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.7005, 8.701, 8.7015, 8.702, 8.703, 8.704, 8.705, 8.706, 8.707, 8.708, and 8.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.700999999999999", "8.702", "8.703", "8.703999999999999", "8.705", "8.706", "8.706999999999999", "8.707999999999998", "8.709"], "p1_2_xs": ["8.7005", "8.7015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0385"}}, {"seed": 386, "data": {"p1_how_many": "12", "p1_a": "9.12", "p1_b": "9.13", "p1_numbers": "9.1205, 9.121, 9.1215, 9.122, 9.1225, 9.123, 9.124, 9.125, 9.126, 9.127, 9.128, and 9.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.120999999999999", "9.122", "9.123", "9.123999999999999", "9.125", "9.126", "9.126999999999999", "9.127999999999998", "9.129"], "p1_2_xs": ["9.1205", "9.1215", "9.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{64}{150}, \\dfrac{67}{150}, \\dfrac{70}{150}, \\dfrac{72}{150}, \\dfrac{74}{150}, \\dfrac{81}{150}, \\dfrac{85}{150}, \\dfrac{87}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0386"}}, {"seed": 387, "data": {"p1_how_many": "13", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{801}{1{,}200}, \\dfrac{826}{1{,}200}, \\dfrac{827}{1{,}200}, \\dfrac{829}{1{,}200}, \\dfrac{846}{1{,}200}, \\dfrac{848}{1{,}200}, \\dfrac{865}{1{,}200}, \\dfrac{869}{1{,}200}, \\dfrac{871}{1{,}200}, \\dfrac{878}{1{,}200}, \\dfrac{880}{1{,}200}, \\text{ and } \\dfrac{882}{1{,}200}", "__seed__": 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2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{514}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{557}{1{,}500}, \\dfrac{559}{1{,}500}, \\dfrac{570}{1{,}500}, \\dfrac{572}{1{,}500}, \\text{ and } \\dfrac{599}{1{,}500}", "__seed__": "0390"}}, {"seed": 391, "data": {"p1_how_many": "13", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}502}{2{,}000}, \\dfrac{1{,}512}{2{,}000}, \\dfrac{1{,}525}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}532}{2{,}000}, \\dfrac{1{,}540}{2{,}000}, \\dfrac{1{,}550}{2{,}000}, \\dfrac{1{,}561}{2{,}000}, \\text{ and } \\dfrac{1{,}573}{2{,}000}", "__seed__": "0391"}}, {"seed": 392, "data": {"p1_how_many": "13", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.735, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725", "9.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{162}{350}, \\dfrac{163}{350}, \\dfrac{167}{350}, \\dfrac{185}{350}, \\dfrac{187}{350}, \\dfrac{197}{350}, \\text{ and } \\dfrac{199}{350}", "__seed__": "0392"}}, {"seed": 393, "data": {"p1_how_many": "12", "p1_a": "3.31", "p1_b": "3.32", "p1_numbers": "3.3105, 3.311, 3.3115, 3.312, 3.3125, 3.313, 3.314, 3.315, 3.316, 3.317, 3.318, and 3.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.311", "3.312", "3.313", "3.314", "3.315", "3.316", "3.317", "3.318", "3.319"], "p1_2_xs": ["3.3105", "3.3115", "3.3125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}022}{12{,}000}, \\dfrac{3{,}031}{12{,}000}, \\dfrac{3{,}108}{12{,}000}, \\dfrac{3{,}259}{12{,}000}, \\dfrac{3{,}354}{12{,}000}, \\dfrac{3{,}384}{12{,}000}, \\dfrac{3{,}446}{12{,}000}, \\dfrac{3{,}552}{12{,}000}, \\dfrac{3{,}896}{12{,}000}, \\text{ and } \\dfrac{3{,}947}{12{,}000}", "__seed__": "0393"}}, {"seed": 394, "data": {"p1_how_many": "14", "p1_a": "4.51", "p1_b": "4.52", "p1_numbers": "4.5105, 4.511, 4.5115, 4.512, 4.5125, 4.513, 4.5135, 4.514, 4.5145, 4.515, 4.516, 4.517, 4.518, and 4.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.511", "4.512", "4.513", "4.513999999999999", "4.515", "4.516", "4.5169999999999995", "4.518", "4.519"], "p1_2_xs": ["4.5104999999999995", "4.5115", "4.512499999999999", "4.5135", "4.514499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{16{,}619}{35{,}000}, \\dfrac{18{,}247}{35{,}000}, \\dfrac{18{,}586}{35{,}000}, \\dfrac{19{,}184}{35{,}000}, \\dfrac{19{,}860}{35{,}000}, \\dfrac{20{,}529}{35{,}000}, \\text{ and } \\dfrac{20{,}550}{35{,}000}", "__seed__": "0394"}}, {"seed": 395, "data": {"p1_how_many": "11", "p1_a": "7.71", "p1_b": "7.72", "p1_numbers": "7.7105, 7.711, 7.7115, 7.712, 7.713, 7.714, 7.715, 7.716, 7.717, 7.718, and 7.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.711", "7.712", "7.713", "7.7139999999999995", "7.715", "7.716", "7.717", "7.718", "7.719"], "p1_2_xs": ["7.7105", "7.7115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{721}{4{,}200}, \\dfrac{746}{4{,}200}, \\dfrac{766}{4{,}200}, \\dfrac{806}{4{,}200}, \\dfrac{882}{4{,}200}, \\dfrac{928}{4{,}200}, \\dfrac{1{,}054}{4{,}200}, \\dfrac{1{,}066}{4{,}200}, \\dfrac{1{,}078}{4{,}200}, \\dfrac{1{,}092}{4{,}200}, \\text{ and } \\dfrac{1{,}164}{4{,}200}", "__seed__": "0395"}}, {"seed": 396, "data": {"p1_how_many": "14", "p1_a": "2.44", "p1_b": "2.45", "p1_numbers": "2.4405, 2.441, 2.4415, 2.442, 2.4425, 2.443, 2.4435, 2.444, 2.4445, 2.445, 2.446, 2.447, 2.448, and 2.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.441", "2.4419999999999997", "2.443", "2.444", "2.445", "2.4459999999999997", "2.447", "2.448", "2.449"], "p1_2_xs": ["2.4405", "2.4415", "2.4425", "2.4435000000000002", "2.4445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{81}{420}, \\dfrac{83}{420}, \\dfrac{85}{420}, \\dfrac{86}{420}, \\dfrac{89}{420}, \\dfrac{96}{420}, \\dfrac{97}{420}, \\dfrac{115}{420}, \\text{ and } \\dfrac{117}{420}", "__seed__": "0396"}}, {"seed": 397, "data": {"p1_how_many": "12", "p1_a": "4.0", "p1_b": "4.1", "p1_numbers": "4.005, 4.01, 4.015, 4.02, 4.025, 4.03, 4.04, 4.05, 4.06, 4.07, 4.08, and 4.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.01", "4.02", "4.03", "4.04", "4.05", "4.06", "4.07", "4.08", "4.09"], "p1_2_xs": ["4.005", "4.015", "4.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{303}{420}, \\dfrac{308}{420}, \\dfrac{318}{420}, \\dfrac{322}{420}, \\dfrac{324}{420}, \\dfrac{337}{420}, \\dfrac{340}{420}, \\dfrac{341}{420}, \\text{ and } \\dfrac{349}{420}", "__seed__": "0397"}}, {"seed": 398, "data": {"p1_how_many": "10", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}510}{2{,}000}, \\dfrac{1{,}518}{2{,}000}, \\dfrac{1{,}524}{2{,}000}, \\dfrac{1{,}534}{2{,}000}, \\dfrac{1{,}541}{2{,}000}, \\dfrac{1{,}547}{2{,}000}, \\dfrac{1{,}570}{2{,}000}, \\dfrac{1{,}582}{2{,}000}, \\dfrac{1{,}583}{2{,}000}, \\dfrac{1{,}584}{2{,}000}, \\dfrac{1{,}592}{2{,}000}, \\text{ and } \\dfrac{1{,}594}{2{,}000}", "__seed__": "0398"}}, {"seed": 399, "data": {"p1_how_many": "14", "p1_a": "3.06", "p1_b": "3.07", "p1_numbers": "3.0605, 3.061, 3.0615, 3.062, 3.0625, 3.063, 3.0635, 3.064, 3.0645, 3.065, 3.066, 3.067, 3.068, and 3.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.061", "3.062", "3.063", "3.064", "3.065", "3.066", "3.067", "3.068", "3.069"], "p1_2_xs": ["3.0605", "3.0615", "3.0625", "3.0635000000000003", "3.0645000000000002"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{312}{420}, \\dfrac{315}{420}, \\dfrac{319}{420}, \\dfrac{324}{420}, \\dfrac{327}{420}, \\dfrac{339}{420}, \\text{ and } \\dfrac{344}{420}", "__seed__": "0399"}}, {"seed": 400, "data": {"p1_how_many": "10", "p1_a": "9.87", "p1_b": "9.88", "p1_numbers": "9.8705, 9.871, 9.872, 9.873, 9.874, 9.875, 9.876, 9.877, 9.878, and 9.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.870999999999999", "9.872", "9.873", "9.873999999999999", "9.875", "9.876", "9.876999999999999", "9.877999999999998", "9.879"], "p1_2_xs": ["9.8705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}085}{35{,}000}, 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\\dfrac{926}{1{,}500}, \\text{ and } \\dfrac{967}{1{,}500}", "__seed__": "0401"}}, {"seed": 402, "data": {"p1_how_many": "14", "p1_a": "4.24", "p1_b": "4.25", "p1_numbers": "4.2405, 4.241, 4.2415, 4.242, 4.2425, 4.243, 4.2435, 4.244, 4.2445, 4.245, 4.246, 4.247, 4.248, and 4.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.2410000000000005", "4.242", "4.243", "4.244", "4.245", "4.246", "4.247", "4.248", "4.2490000000000006"], "p1_2_xs": ["4.2405", "4.2415", "4.2425", "4.2435", "4.2444999999999995"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{802}{1{,}200}, \\dfrac{804}{1{,}200}, \\dfrac{807}{1{,}200}, \\dfrac{841}{1{,}200}, \\dfrac{855}{1{,}200}, \\dfrac{869}{1{,}200}, \\dfrac{870}{1{,}200}, \\dfrac{875}{1{,}200}, \\dfrac{879}{1{,}200}, \\dfrac{896}{1{,}200}, \\text{ and } \\dfrac{899}{1{,}200}", "__seed__": "0402"}}, {"seed": 403, "data": {"p1_how_many": "13", "p1_a": "6.15", "p1_b": "6.16", "p1_numbers": "6.1505, 6.151, 6.1515, 6.152, 6.1525, 6.153, 6.1535, 6.154, 6.155, 6.156, 6.157, 6.158, and 6.159", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.151000000000001", "6.152", "6.1530000000000005", "6.154", "6.155", "6.156000000000001", "6.157", "6.158", "6.159000000000001"], "p1_2_xs": ["6.1505", "6.1515", "6.1525", "6.1535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}646}{42{,}000}, \\dfrac{8{,}020}{42{,}000}, \\dfrac{8{,}455}{42{,}000}, \\dfrac{8{,}767}{42{,}000}, \\dfrac{9{,}119}{42{,}000}, \\dfrac{9{,}961}{42{,}000}, \\dfrac{11{,}103}{42{,}000}, \\dfrac{11{,}121}{42{,}000}, \\text{ and } \\dfrac{11{,}865}{42{,}000}", "__seed__": "0403"}}, {"seed": 404, "data": {"p1_how_many": "12", 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"p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}015}{56{,}000}, \\dfrac{32{,}386}{56{,}000}, \\dfrac{32{,}502}{56{,}000}, \\dfrac{33{,}170}{56{,}000}, \\dfrac{33{,}285}{56{,}000}, \\dfrac{33{,}701}{56{,}000}, \\dfrac{34{,}384}{56{,}000}, \\text{ and } \\dfrac{34{,}851}{56{,}000}", "__seed__": "0405"}}, {"seed": 406, "data": {"p1_how_many": "11", "p1_a": "7.16", "p1_b": "7.17", "p1_numbers": "7.1605, 7.161, 7.1615, 7.162, 7.163, 7.164, 7.165, 7.166, 7.167, 7.168, and 7.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.1610000000000005", "7.162", "7.163", "7.164", "7.165", "7.166", "7.167", "7.168", "7.1690000000000005"], "p1_2_xs": ["7.1605", "7.1615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{68}{150}, \\dfrac{84}{150}, \\dfrac{86}{150}, \\dfrac{90}{150}, \\dfrac{92}{150}, \\dfrac{96}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0406"}}, {"seed": 407, "data": {"p1_how_many": "13", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{127}{200}, \\dfrac{129}{200}, \\dfrac{135}{200}, \\dfrac{136}{200}, \\dfrac{139}{200}, \\dfrac{141}{200}, \\dfrac{142}{200}, \\text{ and } \\dfrac{145}{200}", "__seed__": "0407"}}, {"seed": 408, "data": {"p1_how_many": "11", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}541}{5{,}600}, \\dfrac{3{,}552}{5{,}600}, \\dfrac{3{,}581}{5{,}600}, \\dfrac{3{,}611}{5{,}600}, \\dfrac{3{,}620}{5{,}600}, \\dfrac{3{,}635}{5{,}600}, \\dfrac{3{,}758}{5{,}600}, \\dfrac{3{,}787}{5{,}600}, \\dfrac{3{,}839}{5{,}600}, \\text{ and } \\dfrac{3{,}890}{5{,}600}", "__seed__": "0408"}}, {"seed": 409, "data": {"p1_how_many": "14", "p1_a": "1.42", "p1_b": "1.43", "p1_numbers": "1.4205, 1.421, 1.4215, 1.422, 1.4225, 1.423, 1.4235, 1.424, 1.4245, 1.425, 1.426, 1.427, 1.428, and 1.429", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4209999999999998", "1.422", "1.4229999999999998", "1.424", "1.4249999999999998", "1.426", "1.4269999999999998", "1.428", "1.4289999999999998"], "p1_2_xs": ["1.4204999999999999", "1.4214999999999998", "1.4224999999999999", "1.4234999999999998", "1.4244999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}506}{4{,}200}, \\dfrac{3{,}528}{4{,}200}, \\dfrac{3{,}542}{4{,}200}, \\dfrac{3{,}544}{4{,}200}, \\dfrac{3{,}545}{4{,}200}, \\dfrac{3{,}548}{4{,}200}, \\dfrac{3{,}554}{4{,}200}, \\dfrac{3{,}569}{4{,}200}, \\dfrac{3{,}574}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\dfrac{3{,}587}{4{,}200}, \\text{ and } \\dfrac{3{,}588}{4{,}200}", "__seed__": "0409"}}, {"seed": 410, "data": {"p1_how_many": "14", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.125, 9.13, 9.135, 9.14, 9.145, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125", "9.135", "9.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}286}{56{,}000}, \\dfrac{16{,}728}{56{,}000}, \\dfrac{17{,}082}{56{,}000}, \\dfrac{17{,}272}{56{,}000}, \\dfrac{17{,}364}{56{,}000}, \\dfrac{17{,}800}{56{,}000}, \\dfrac{18{,}047}{56{,}000}, \\dfrac{18{,}117}{56{,}000}, \\dfrac{18{,}143}{56{,}000}, \\dfrac{20{,}275}{56{,}000}, \\dfrac{20{,}307}{56{,}000}, \\text{ and } \\dfrac{20{,}387}{56{,}000}", "__seed__": "0410"}}, {"seed": 411, "data": {"p1_how_many": "10", "p1_a": "5.02", "p1_b": "5.03", "p1_numbers": "5.0205, 5.021, 5.022, 5.023, 5.024, 5.025, 5.026, 5.027, 5.028, and 5.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.021", "5.021999999999999", "5.023", "5.023999999999999", "5.0249999999999995", "5.026", "5.026999999999999", "5.028", "5.029"], "p1_2_xs": ["5.020499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{411}{2{,}000}, \\dfrac{415}{2{,}000}, \\dfrac{424}{2{,}000}, \\dfrac{439}{2{,}000}, \\dfrac{440}{2{,}000}, \\dfrac{447}{2{,}000}, \\dfrac{451}{2{,}000}, \\dfrac{459}{2{,}000}, \\dfrac{476}{2{,}000}, \\text{ and } \\dfrac{480}{2{,}000}", "__seed__": "0411"}}, {"seed": 412, "data": {"p1_how_many": "10", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}889}{6{,}300}, \\dfrac{2{,}904}{6{,}300}, \\dfrac{3{,}053}{6{,}300}, \\dfrac{3{,}110}{6{,}300}, \\dfrac{3{,}213}{6{,}300}, \\dfrac{3{,}366}{6{,}300}, \\dfrac{3{,}426}{6{,}300}, \\dfrac{3{,}451}{6{,}300}, \\text{ and } \\dfrac{3{,}470}{6{,}300}", "__seed__": "0412"}}, {"seed": 413, "data": {"p1_how_many": "14", "p1_a": "6.25", "p1_b": "6.26", "p1_numbers": "6.2505, 6.251, 6.2515, 6.252, 6.2525, 6.253, 6.2535, 6.254, 6.2545, 6.255, 6.256, 6.257, 6.258, and 6.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.251", "6.252", "6.253", "6.254", "6.255", "6.256", "6.257", "6.258", "6.259"], "p1_2_xs": ["6.2505", "6.2515", "6.2524999999999995", "6.2535", "6.254499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}632}{5{,}600}, \\dfrac{1{,}716}{5{,}600}, \\dfrac{1{,}849}{5{,}600}, \\dfrac{1{,}891}{5{,}600}, \\dfrac{1{,}948}{5{,}600}, \\dfrac{1{,}954}{5{,}600}, \\dfrac{1{,}977}{5{,}600}, \\text{ and } \\dfrac{2{,}075}{5{,}600}", "__seed__": "0413"}}, {"seed": 414, "data": {"p1_how_many": "11", "p1_a": "5.05", "p1_b": "5.06", "p1_numbers": "5.0505, 5.051, 5.0515, 5.052, 5.053, 5.054, 5.055, 5.056, 5.057, 5.058, and 5.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.051", "5.052", "5.053", "5.053999999999999", "5.055", "5.056", "5.0569999999999995", "5.058", "5.059"], "p1_2_xs": ["5.0504999999999995", "5.0515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}208}{2{,}000}, \\dfrac{1{,}209}{2{,}000}, \\dfrac{1{,}217}{2{,}000}, \\dfrac{1{,}252}{2{,}000}, \\dfrac{1{,}253}{2{,}000}, \\dfrac{1{,}278}{2{,}000}, \\dfrac{1{,}288}{2{,}000}, \\dfrac{1{,}301}{2{,}000}, \\dfrac{1{,}337}{2{,}000}, \\dfrac{1{,}389}{2{,}000}, \\dfrac{1{,}413}{2{,}000}, \\text{ and } \\dfrac{1{,}444}{2{,}000}", "__seed__": "0414"}}, {"seed": 415, "data": {"p1_how_many": "13", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}108}{30{,}000}, \\dfrac{5{,}297}{30{,}000}, \\dfrac{5{,}313}{30{,}000}, \\dfrac{5{,}374}{30{,}000}, \\dfrac{5{,}483}{30{,}000}, \\dfrac{5{,}553}{30{,}000}, \\dfrac{5{,}563}{30{,}000}, \\dfrac{5{,}587}{30{,}000}, \\dfrac{5{,}651}{30{,}000}, \\text{ and } \\dfrac{5{,}668}{30{,}000}", "__seed__": "0415"}}, {"seed": 416, "data": {"p1_how_many": "14", "p1_a": "5.72", "p1_b": "5.73", "p1_numbers": "5.7205, 5.721, 5.7215, 5.722, 5.7225, 5.723, 5.7235, 5.724, 5.7245, 5.725, 5.726, 5.727, 5.728, and 5.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.721", "5.7219999999999995", "5.723", "5.723999999999999", "5.725", "5.726", "5.726999999999999", "5.728", "5.729"], "p1_2_xs": ["5.7204999999999995", "5.7215", "5.722499999999999", "5.7235", "5.724499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}134}{42{,}000}, \\dfrac{35{,}328}{42{,}000}, \\dfrac{35{,}341}{42{,}000}, \\dfrac{35{,}414}{42{,}000}, \\dfrac{35{,}561}{42{,}000}, \\dfrac{35{,}721}{42{,}000}, \\text{ and } \\dfrac{35{,}866}{42{,}000}", "__seed__": "0416"}}, {"seed": 417, "data": {"p1_how_many": "11", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.015, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{736}{3{,}500}, \\dfrac{761}{3{,}500}, \\dfrac{768}{3{,}500}, \\dfrac{808}{3{,}500}, \\dfrac{822}{3{,}500}, \\dfrac{848}{3{,}500}, \\dfrac{872}{3{,}500}, \\dfrac{876}{3{,}500}, \\text{ and } \\dfrac{959}{3{,}500}", "__seed__": "0417"}}, {"seed": 418, "data": {"p1_how_many": "12", "p1_a": "9.76", "p1_b": "9.77", "p1_numbers": "9.7605, 9.761, 9.7615, 9.762, 9.7625, 9.763, 9.764, 9.765, 9.766, 9.767, 9.768, and 9.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.761", "9.762", "9.763", "9.764", "9.765", "9.766", "9.767", "9.767999999999999", "9.769"], "p1_2_xs": ["9.7605", "9.7615", "9.762500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}457}{56{,}000}, \\dfrac{18{,}198}{56{,}000}, \\dfrac{18{,}692}{56{,}000}, \\dfrac{19{,}228}{56{,}000}, \\dfrac{19{,}467}{56{,}000}, \\dfrac{19{,}519}{56{,}000}, \\dfrac{19{,}617}{56{,}000}, \\dfrac{20{,}106}{56{,}000}, \\dfrac{20{,}772}{56{,}000}, \\dfrac{20{,}829}{56{,}000}, \\dfrac{20{,}878}{56{,}000}, \\text{ and } \\dfrac{20{,}900}{56{,}000}", "__seed__": "0418"}}, {"seed": 419, "data": {"p1_how_many": "11", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}862}{35{,}000}, \\dfrac{16{,}238}{35{,}000}, \\dfrac{16{,}292}{35{,}000}, \\dfrac{17{,}024}{35{,}000}, \\dfrac{17{,}159}{35{,}000}, \\dfrac{17{,}190}{35{,}000}, \\dfrac{18{,}106}{35{,}000}, \\dfrac{19{,}544}{35{,}000}, \\dfrac{20{,}117}{35{,}000}, \\text{ and } \\dfrac{20{,}636}{35{,}000}", "__seed__": "0419"}}, {"seed": 420, "data": {"p1_how_many": "14", "p1_a": "6.82", "p1_b": "6.83", "p1_numbers": "6.8205, 6.821, 6.8215, 6.822, 6.8225, 6.823, 6.8235, 6.824, 6.8245, 6.825, 6.826, 6.827, 6.828, and 6.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.821000000000001", "6.822", "6.823", "6.824", "6.825", "6.8260000000000005", "6.827", "6.828", "6.829000000000001"], "p1_2_xs": ["6.8205", "6.8215", "6.8225", "6.8235", "6.8245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}271}{42{,}000}, \\dfrac{31{,}067}{42{,}000}, \\dfrac{31{,}299}{42{,}000}, \\dfrac{31{,}470}{42{,}000}, \\dfrac{31{,}897}{42{,}000}, \\dfrac{32{,}338}{42{,}000}, \\dfrac{32{,}617}{42{,}000}, \\dfrac{32{,}685}{42{,}000}, \\text{ and } \\dfrac{33{,}992}{42{,}000}", "__seed__": "0420"}}, {"seed": 421, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", "2.4349999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{6{,}017}{20{,}000}, \\dfrac{6{,}050}{20{,}000}, \\dfrac{6{,}171}{20{,}000}, \\dfrac{6{,}218}{20{,}000}, \\dfrac{6{,}432}{20{,}000}, \\dfrac{6{,}796}{20{,}000}, \\dfrac{6{,}885}{20{,}000}, \\dfrac{7{,}460}{20{,}000}, \\text{ and } \\dfrac{7{,}910}{20{,}000}", "__seed__": "0421"}}, {"seed": 422, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", "2.4349999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, \\dfrac{243}{300}, \\dfrac{244}{300}, \\dfrac{245}{300}, \\dfrac{246}{300}, \\dfrac{247}{300}, \\text{ and } \\dfrac{249}{300}", "__seed__": "0422"}}, {"seed": 423, "data": {"p1_how_many": "12", "p1_a": "6.26", "p1_b": "6.27", "p1_numbers": "6.2605, 6.261, 6.2615, 6.262, 6.2625, 6.263, 6.264, 6.265, 6.266, 6.267, 6.268, and 6.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.261", "6.262", "6.263", "6.263999999999999", "6.265", "6.266", "6.2669999999999995", "6.268", "6.269"], "p1_2_xs": ["6.2604999999999995", "6.2615", "6.262499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}510}{4{,}200}, \\dfrac{3{,}511}{4{,}200}, \\dfrac{3{,}526}{4{,}200}, \\dfrac{3{,}531}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}540}{4{,}200}, \\dfrac{3{,}549}{4{,}200}, \\dfrac{3{,}550}{4{,}200}, \\dfrac{3{,}563}{4{,}200}, \\dfrac{3{,}566}{4{,}200}, \\dfrac{3{,}568}{4{,}200}, \\text{ and } \\dfrac{3{,}572}{4{,}200}", "__seed__": "0423"}}, {"seed": 424, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0424"}}, {"seed": 425, "data": {"p1_how_many": "12", "p1_a": "8.82", "p1_b": "8.83", "p1_numbers": "8.8205, 8.821, 8.8215, 8.822, 8.8225, 8.823, 8.824, 8.825, 8.826, 8.827, 8.828, and 8.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.821", "8.822000000000001", "8.823", "8.824", "8.825000000000001", "8.826", "8.827", "8.828", "8.829"], "p1_2_xs": ["8.820500000000001", "8.8215", "8.822500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{534}{2{,}000}, \\dfrac{566}{2{,}000}, \\dfrac{673}{2{,}000}, \\dfrac{695}{2{,}000}, \\dfrac{704}{2{,}000}, \\dfrac{747}{2{,}000}, \\dfrac{783}{2{,}000}, \\text{ and } \\dfrac{790}{2{,}000}", "__seed__": "0425"}}, {"seed": 426, "data": {"p1_how_many": "11", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{205}{350}, \\dfrac{215}{350}, \\dfrac{218}{350}, \\dfrac{221}{350}, \\dfrac{225}{350}, \\dfrac{229}{350}, \\text{ and } \\dfrac{260}{350}", "__seed__": "0426"}}, {"seed": 427, "data": {"p1_how_many": "14", "p1_a": "6.33", "p1_b": "6.34", "p1_numbers": "6.3305, 6.331, 6.3315, 6.332, 6.3325, 6.333, 6.3335, 6.334, 6.3345, 6.335, 6.336, 6.337, 6.338, and 6.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.331", "6.332", "6.333", "6.334", "6.335", "6.336", "6.337", "6.338", "6.339"], "p1_2_xs": ["6.3305", "6.3315", "6.3325", "6.3335", "6.334499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}563}{42{,}000}, \\dfrac{30{,}646}{42{,}000}, \\dfrac{30{,}777}{42{,}000}, \\dfrac{31{,}489}{42{,}000}, \\dfrac{32{,}615}{42{,}000}, \\dfrac{32{,}739}{42{,}000}, \\dfrac{33{,}281}{42{,}000}, \\dfrac{33{,}927}{42{,}000}, \\dfrac{34{,}215}{42{,}000}, \\text{ and } \\dfrac{34{,}635}{42{,}000}", "__seed__": "0427"}}, {"seed": 428, "data": {"p1_how_many": "12", "p1_a": "9.1", "p1_b": "9.2", "p1_numbers": "9.105, 9.11, 9.115, 9.12, 9.125, 9.13, 9.14, 9.15, 9.16, 9.17, 9.18, and 9.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}058}{15{,}000}, \\dfrac{5{,}121}{15{,}000}, \\dfrac{5{,}312}{15{,}000}, \\dfrac{5{,}330}{15{,}000}, \\dfrac{5{,}339}{15{,}000}, \\dfrac{5{,}378}{15{,}000}, \\dfrac{5{,}383}{15{,}000}, \\dfrac{5{,}428}{15{,}000}, \\dfrac{5{,}435}{15{,}000}, \\dfrac{5{,}684}{15{,}000}, \\dfrac{5{,}755}{15{,}000}, \\text{ and } \\dfrac{5{,}829}{15{,}000}", "__seed__": "0428"}}, {"seed": 429, "data": {"p1_how_many": "14", "p1_a": "2.55", "p1_b": "2.56", "p1_numbers": "2.5505, 2.551, 2.5515, 2.552, 2.5525, 2.553, 2.5535, 2.554, 2.5545, 2.555, 2.556, 2.557, 2.558, and 2.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5509999999999997", "2.5519999999999996", "2.553", "2.554", "2.5549999999999997", "2.5559999999999996", "2.557", "2.558", "2.5589999999999997"], "p1_2_xs": ["2.5505", "2.5515", "2.5524999999999998", "2.5535", "2.5545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}233}{2{,}000}, \\dfrac{1{,}235}{2{,}000}, \\dfrac{1{,}251}{2{,}000}, \\dfrac{1{,}311}{2{,}000}, \\dfrac{1{,}408}{2{,}000}, \\dfrac{1{,}440}{2{,}000}, \\dfrac{1{,}464}{2{,}000}, \\text{ and } \\dfrac{1{,}475}{2{,}000}", "__seed__": "0429"}}, {"seed": 430, "data": {"p1_how_many": "12", "p1_a": "6.95", "p1_b": "6.96", "p1_numbers": "6.9505, 6.951, 6.9515, 6.952, 6.9525, 6.953, 6.954, 6.955, 6.956, 6.957, 6.958, and 6.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.9510000000000005", "6.952", "6.953", "6.954", "6.955", "6.956", "6.957", "6.958", "6.9590000000000005"], "p1_2_xs": ["6.9505", "6.9515", "6.9525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}306}{7{,}700}, \\dfrac{4{,}658}{7{,}700}, \\dfrac{4{,}801}{7{,}700}, \\dfrac{4{,}863}{7{,}700}, \\dfrac{4{,}886}{7{,}700}, \\dfrac{4{,}987}{7{,}700}, \\dfrac{5{,}144}{7{,}700}, \\dfrac{5{,}652}{7{,}700}, \\dfrac{6{,}029}{7{,}700}, \\dfrac{6{,}103}{7{,}700}, \\text{ and } \\dfrac{6{,}120}{7{,}700}", "__seed__": "0430"}}, {"seed": 431, "data": {"p1_how_many": "12", "p1_a": "9.35", "p1_b": "9.36", "p1_numbers": "9.3505, 9.351, 9.3515, 9.352, 9.3525, 9.353, 9.354, 9.355, 9.356, 9.357, 9.358, and 9.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.350999999999999", "9.352", "9.353", "9.354", "9.355", "9.356", "9.357", "9.357999999999999", "9.359"], "p1_2_xs": ["9.3505", "9.3515", "9.352500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}016}{30{,}000}, \\dfrac{5{,}055}{30{,}000}, \\dfrac{5{,}309}{30{,}000}, \\dfrac{5{,}322}{30{,}000}, \\dfrac{5{,}529}{30{,}000}, \\dfrac{5{,}530}{30{,}000}, \\dfrac{5{,}669}{30{,}000}, \\dfrac{5{,}686}{30{,}000}, \\dfrac{5{,}732}{30{,}000}, \\dfrac{5{,}787}{30{,}000}, \\dfrac{5{,}847}{30{,}000}, \\text{ and } \\dfrac{5{,}904}{30{,}000}", "__seed__": "0431"}}, {"seed": 432, "data": {"p1_how_many": "14", "p1_a": "1.85", "p1_b": "1.86", "p1_numbers": "1.8505, 1.851, 1.8515, 1.852, 1.8525, 1.853, 1.8535, 1.854, 1.8545, 1.855, 1.856, 1.857, 1.858, and 1.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.851", "1.852", "1.853", "1.854", "1.855", "1.856", "1.857", "1.858", "1.859"], "p1_2_xs": ["1.8505", "1.8515", "1.8525", "1.8535", "1.8545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}133}{30{,}000}, \\dfrac{24{,}148}{30{,}000}, \\dfrac{24{,}177}{30{,}000}, \\dfrac{24{,}322}{30{,}000}, \\dfrac{24{,}350}{30{,}000}, \\dfrac{24{,}371}{30{,}000}, \\dfrac{24{,}497}{30{,}000}, \\dfrac{24{,}502}{30{,}000}, \\dfrac{24{,}848}{30{,}000}, \\text{ and } \\dfrac{24{,}932}{30{,}000}", "__seed__": "0432"}}, {"seed": 433, "data": {"p1_how_many": "12", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.125, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999", "5.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{151}{350}, \\dfrac{157}{350}, \\dfrac{158}{350}, \\dfrac{159}{350}, \\dfrac{178}{350}, \\dfrac{179}{350}, \\dfrac{199}{350}, \\dfrac{202}{350}, \\text{ and } \\dfrac{205}{350}", "__seed__": "0433"}}, {"seed": 434, "data": {"p1_how_many": "10", "p1_a": "2.14", "p1_b": "2.15", "p1_numbers": "2.1405, 2.141, 2.142, 2.143, 2.144, 2.145, 2.146, 2.147, 2.148, and 2.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.141", "2.142", "2.1430000000000002", "2.144", "2.145", "2.146", "2.1470000000000002", "2.148", "2.149"], "p1_2_xs": ["2.1405000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}851}{6{,}300}, \\dfrac{2{,}903}{6{,}300}, \\dfrac{2{,}962}{6{,}300}, \\dfrac{3{,}129}{6{,}300}, \\dfrac{3{,}248}{6{,}300}, \\dfrac{3{,}270}{6{,}300}, \\dfrac{3{,}450}{6{,}300}, \\text{ and } \\dfrac{3{,}510}{6{,}300}", "__seed__": "0434"}}, {"seed": 435, "data": {"p1_how_many": "11", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}045}{35{,}000}, \\dfrac{7{,}172}{35{,}000}, \\dfrac{7{,}520}{35{,}000}, \\dfrac{8{,}103}{35{,}000}, \\dfrac{8{,}664}{35{,}000}, \\dfrac{8{,}873}{35{,}000}, \\dfrac{9{,}327}{35{,}000}, \\text{ and } \\dfrac{9{,}407}{35{,}000}", "__seed__": "0435"}}, {"seed": 436, "data": {"p1_how_many": "12", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}077}{4{,}200}, \\dfrac{3{,}166}{4{,}200}, \\dfrac{3{,}227}{4{,}200}, \\dfrac{3{,}336}{4{,}200}, \\dfrac{3{,}393}{4{,}200}, \\dfrac{3{,}397}{4{,}200}, \\dfrac{3{,}430}{4{,}200}, \\text{ and } \\dfrac{3{,}432}{4{,}200}", "__seed__": "0436"}}, {"seed": 437, "data": {"p1_how_many": "14", "p1_a": "8.73", "p1_b": "8.74", "p1_numbers": "8.7305, 8.731, 8.7315, 8.732, 8.7325, 8.733, 8.7335, 8.734, 8.7345, 8.735, 8.736, 8.737, 8.738, and 8.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.731", "8.732000000000001", "8.733", "8.734", "8.735000000000001", "8.736", "8.737", "8.738", "8.739"], "p1_2_xs": ["8.730500000000001", "8.7315", "8.732500000000002", "8.733500000000001", "8.7345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}406}{6{,}300}, \\dfrac{1{,}415}{6{,}300}, \\dfrac{1{,}438}{6{,}300}, \\dfrac{1{,}520}{6{,}300}, \\dfrac{1{,}544}{6{,}300}, \\dfrac{1{,}563}{6{,}300}, \\dfrac{1{,}568}{6{,}300}, \\dfrac{1{,}640}{6{,}300}, \\dfrac{1{,}682}{6{,}300}, \\dfrac{1{,}697}{6{,}300}, \\text{ and } \\dfrac{1{,}767}{6{,}300}", "__seed__": "0437"}}, {"seed": 438, "data": {"p1_how_many": "11", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{806}{1{,}200}, \\dfrac{821}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{838}{1{,}200}, \\dfrac{845}{1{,}200}, \\dfrac{853}{1{,}200}, \\dfrac{854}{1{,}200}, \\dfrac{855}{1{,}200}, \\dfrac{868}{1{,}200}, \\dfrac{896}{1{,}200}, \\dfrac{897}{1{,}200}, \\text{ and } \\dfrac{898}{1{,}200}", "__seed__": "0438"}}, {"seed": 439, "data": {"p1_how_many": "12", "p1_a": "8.02", "p1_b": "8.03", "p1_numbers": "8.0205, 8.021, 8.0215, 8.022, 8.0225, 8.023, 8.024, 8.025, 8.026, 8.027, 8.028, and 8.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.020999999999999", "8.022", "8.023", "8.024", "8.025", "8.026", "8.027", "8.027999999999999", "8.029"], "p1_2_xs": ["8.0205", "8.0215", "8.0225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}701}{6{,}300}, \\dfrac{2{,}720}{6{,}300}, \\dfrac{2{,}738}{6{,}300}, \\dfrac{2{,}761}{6{,}300}, \\dfrac{2{,}762}{6{,}300}, \\dfrac{2{,}765}{6{,}300}, \\dfrac{2{,}782}{6{,}300}, \\dfrac{2{,}783}{6{,}300}, \\dfrac{2{,}789}{6{,}300}, \\dfrac{2{,}790}{6{,}300}, \\text{ and } \\dfrac{2{,}793}{6{,}300}", "__seed__": "0439"}}, {"seed": 440, "data": {"p1_how_many": "10", "p1_a": "7.2", "p1_b": "7.3", "p1_numbers": "7.205, 7.21, 7.22, 7.23, 7.24, 7.25, 7.26, 7.27, 7.28, and 7.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.21", "7.22", "7.23", "7.24", "7.25", "7.26", "7.2700000000000005", "7.28", "7.29"], "p1_2_xs": ["7.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}033}{3{,}500}, \\dfrac{2{,}081}{3{,}500}, \\dfrac{2{,}148}{3{,}500}, \\dfrac{2{,}213}{3{,}500}, \\dfrac{2{,}416}{3{,}500}, \\dfrac{2{,}425}{3{,}500}, \\dfrac{2{,}467}{3{,}500}, \\dfrac{2{,}513}{3{,}500}, \\dfrac{2{,}652}{3{,}500}, \\dfrac{2{,}653}{3{,}500}, \\text{ and } \\dfrac{2{,}683}{3{,}500}", "__seed__": "0440"}}, {"seed": 441, "data": {"p1_how_many": "11", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{17{,}506}{35{,}000}, \\dfrac{17{,}643}{35{,}000}, \\dfrac{18{,}243}{35{,}000}, \\dfrac{19{,}130}{35{,}000}, \\dfrac{19{,}441}{35{,}000}, \\dfrac{19{,}564}{35{,}000}, \\dfrac{19{,}794}{35{,}000}, \\text{ and } \\dfrac{20{,}232}{35{,}000}", "__seed__": "0441"}}, {"seed": 442, "data": {"p1_how_many": "13", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.535, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995", "6.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{271}{630}, \\dfrac{272}{630}, \\dfrac{273}{630}, \\dfrac{275}{630}, \\dfrac{276}{630}, \\dfrac{277}{630}, \\text{ and } \\dfrac{279}{630}", "__seed__": "0442"}}, {"seed": 443, "data": {"p1_how_many": "12", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.625, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}229}{56{,}000}, \\dfrac{48{,}339}{56{,}000}, \\dfrac{48{,}501}{56{,}000}, \\dfrac{48{,}548}{56{,}000}, \\dfrac{48{,}643}{56{,}000}, \\dfrac{48{,}729}{56{,}000}, \\dfrac{48{,}744}{56{,}000}, \\dfrac{48{,}769}{56{,}000}, \\text{ and } \\dfrac{48{,}854}{56{,}000}", "__seed__": "0443"}}, {"seed": 444, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0444"}}, {"seed": 445, "data": {"p1_how_many": "14", "p1_a": "1.83", "p1_b": "1.84", "p1_numbers": "1.8305, 1.831, 1.8315, 1.832, 1.8325, 1.833, 1.8335, 1.834, 1.8345, 1.835, 1.836, 1.837, 1.838, and 1.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.831", "1.832", "1.833", "1.834", "1.835", "1.836", "1.837", "1.838", "1.839"], "p1_2_xs": ["1.8305", "1.8315", "1.8325", "1.8335", "1.8345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number 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"\\dfrac{4{,}492}{7{,}700}, \\dfrac{4{,}537}{7{,}700}, \\dfrac{4{,}601}{7{,}700}, \\dfrac{4{,}883}{7{,}700}, \\dfrac{4{,}979}{7{,}700}, \\dfrac{5{,}187}{7{,}700}, \\dfrac{5{,}626}{7{,}700}, \\dfrac{5{,}710}{7{,}700}, \\dfrac{6{,}223}{7{,}700}, \\dfrac{6{,}366}{7{,}700}, \\dfrac{6{,}454}{7{,}700}, \\text{ and } \\dfrac{6{,}483}{7{,}700}", "__seed__": "0446"}}, {"seed": 447, "data": {"p1_how_many": "12", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{21{,}201}{35{,}000}, \\dfrac{21{,}919}{35{,}000}, \\dfrac{23{,}160}{35{,}000}, \\dfrac{23{,}939}{35{,}000}, \\dfrac{24{,}265}{35{,}000}, \\dfrac{25{,}519}{35{,}000}, \\text{ and } \\dfrac{27{,}088}{35{,}000}", "__seed__": "0447"}}, {"seed": 448, "data": {"p1_how_many": "10", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.02, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}702}{42{,}000}, \\dfrac{30{,}727}{42{,}000}, \\dfrac{31{,}440}{42{,}000}, \\dfrac{31{,}961}{42{,}000}, \\dfrac{32{,}003}{42{,}000}, \\dfrac{32{,}196}{42{,}000}, \\dfrac{32{,}214}{42{,}000}, \\dfrac{33{,}414}{42{,}000}, \\text{ and } \\dfrac{34{,}845}{42{,}000}", "__seed__": "0448"}}, {"seed": 449, "data": {"p1_how_many": "10", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}213}{20{,}000}, \\dfrac{4{,}354}{20{,}000}, \\dfrac{4{,}439}{20{,}000}, \\dfrac{4{,}667}{20{,}000}, \\dfrac{4{,}721}{20{,}000}, \\dfrac{4{,}804}{20{,}000}, \\dfrac{4{,}836}{20{,}000}, \\dfrac{4{,}878}{20{,}000}, \\dfrac{4{,}886}{20{,}000}, \\text{ and } \\dfrac{4{,}967}{20{,}000}", "__seed__": "0449"}}, {"seed": 450, "data": {"p1_how_many": "14", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.545, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535", "7.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{200}, \\dfrac{58}{200}, \\dfrac{60}{200}, \\dfrac{63}{200}, \\dfrac{65}{200}, \\dfrac{72}{200}, \\dfrac{75}{200}, \\text{ and } \\dfrac{79}{200}", "__seed__": "0450"}}, {"seed": 451, "data": {"p1_how_many": "10", "p1_a": "9.93", "p1_b": "9.94", "p1_numbers": "9.9305, 9.931, 9.932, 9.933, 9.934, 9.935, 9.936, 9.937, 9.938, and 9.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.931", "9.932", "9.933", "9.934", "9.935", "9.936", "9.937", "9.937999999999999", "9.939"], "p1_2_xs": ["9.9305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}218}{2{,}000}, \\dfrac{1{,}226}{2{,}000}, \\dfrac{1{,}245}{2{,}000}, \\dfrac{1{,}274}{2{,}000}, \\dfrac{1{,}295}{2{,}000}, \\dfrac{1{,}303}{2{,}000}, \\dfrac{1{,}316}{2{,}000}, \\dfrac{1{,}321}{2{,}000}, \\dfrac{1{,}388}{2{,}000}, \\dfrac{1{,}428}{2{,}000}, \\dfrac{1{,}434}{2{,}000}, \\text{ and } \\dfrac{1{,}446}{2{,}000}", "__seed__": "0451"}}, {"seed": 452, "data": {"p1_how_many": "10", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.02, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}807}{5{,}600}, \\dfrac{4{,}818}{5{,}600}, \\dfrac{4{,}819}{5{,}600}, \\dfrac{4{,}825}{5{,}600}, \\dfrac{4{,}839}{5{,}600}, \\dfrac{4{,}847}{5{,}600}, \\dfrac{4{,}855}{5{,}600}, \\dfrac{4{,}863}{5{,}600}, \\dfrac{4{,}880}{5{,}600}, \\text{ and } \\dfrac{4{,}887}{5{,}600}", "__seed__": "0452"}}, {"seed": 453, "data": {"p1_how_many": "11", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.73, 9.74, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}375}{15{,}000}, \\dfrac{5{,}504}{15{,}000}, \\dfrac{5{,}545}{15{,}000}, \\dfrac{5{,}619}{15{,}000}, \\dfrac{5{,}758}{15{,}000}, \\dfrac{5{,}806}{15{,}000}, \\dfrac{5{,}846}{15{,}000}, \\dfrac{5{,}914}{15{,}000}, \\dfrac{5{,}975}{15{,}000}, \\text{ and } \\dfrac{5{,}992}{15{,}000}", "__seed__": "0453"}}, {"seed": 454, "data": {"p1_how_many": "11", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.005, 5.01, 5.015, 5.02, 5.03, 5.04, 5.05, 5.06, 5.07, 5.08, and 5.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005", "5.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}213}{35{,}000}, \\dfrac{15{,}311}{35{,}000}, \\dfrac{15{,}670}{35{,}000}, \\dfrac{16{,}424}{35{,}000}, \\dfrac{18{,}356}{35{,}000}, \\dfrac{18{,}360}{35{,}000}, \\dfrac{18{,}633}{35{,}000}, \\dfrac{19{,}073}{35{,}000}, \\text{ and } \\dfrac{19{,}718}{35{,}000}", "__seed__": "0454"}}, {"seed": 455, "data": {"p1_how_many": "11", "p1_a": "4.27", "p1_b": "4.28", "p1_numbers": "4.2705, 4.271, 4.2715, 4.272, 4.273, 4.274, 4.275, 4.276, 4.277, 4.278, and 4.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.271", "4.271999999999999", "4.273", "4.273999999999999", "4.2749999999999995", "4.276", "4.276999999999999", "4.278", "4.279"], "p1_2_xs": ["4.270499999999999", "4.2715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}154}{42{,}000}, \\dfrac{30{,}495}{42{,}000}, \\dfrac{30{,}523}{42{,}000}, \\dfrac{32{,}051}{42{,}000}, \\dfrac{33{,}036}{42{,}000}, \\dfrac{33{,}098}{42{,}000}, \\dfrac{33{,}318}{42{,}000}, \\dfrac{33{,}337}{42{,}000}, \\text{ and } \\dfrac{33{,}447}{42{,}000}", "__seed__": "0455"}}, {"seed": 456, "data": {"p1_how_many": "11", "p1_a": "8.77", "p1_b": "8.78", "p1_numbers": "8.7705, 8.771, 8.7715, 8.772, 8.773, 8.774, 8.775, 8.776, 8.777, 8.778, and 8.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.770999999999999", "8.772", "8.773", "8.774", "8.775", "8.776", "8.777", "8.777999999999999", "8.779"], "p1_2_xs": ["8.7705", "8.7715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}075}{42{,}000}, \\dfrac{7{,}579}{42{,}000}, \\dfrac{9{,}538}{42{,}000}, \\dfrac{9{,}646}{42{,}000}, \\dfrac{9{,}804}{42{,}000}, \\dfrac{10{,}397}{42{,}000}, \\dfrac{11{,}563}{42{,}000}, \\text{ and } \\dfrac{11{,}959}{42{,}000}", "__seed__": "0456"}}, {"seed": 457, "data": {"p1_how_many": "12", "p1_a": "4.2", "p1_b": "4.3", "p1_numbers": "4.205, 4.21, 4.215, 4.22, 4.225, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.21", "4.22", "4.23", "4.24", "4.25", "4.26", "4.2700000000000005", "4.28", "4.29"], "p1_2_xs": ["4.205", "4.215", "4.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}086}{20{,}000}, \\dfrac{4{,}140}{20{,}000}, \\dfrac{4{,}247}{20{,}000}, \\dfrac{4{,}362}{20{,}000}, \\dfrac{4{,}655}{20{,}000}, \\dfrac{4{,}679}{20{,}000}, \\dfrac{4{,}966}{20{,}000}, \\dfrac{4{,}988}{20{,}000}, \\text{ and } \\dfrac{4{,}996}{20{,}000}", "__seed__": "0457"}}, {"seed": 458, "data": {"p1_how_many": "13", "p1_a": "9.67", "p1_b": "9.68", "p1_numbers": "9.6705, 9.671, 9.6715, 9.672, 9.6725, 9.673, 9.6735, 9.674, 9.675, 9.676, 9.677, 9.678, and 9.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.671", "9.672", "9.673", "9.674", "9.675", "9.676", "9.677", "9.677999999999999", "9.679"], "p1_2_xs": ["9.6705", "9.6715", "9.672500000000001", "9.6735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}369}{7{,}700}, \\dfrac{4{,}508}{7{,}700}, \\dfrac{4{,}644}{7{,}700}, \\dfrac{4{,}789}{7{,}700}, \\dfrac{4{,}895}{7{,}700}, \\dfrac{4{,}942}{7{,}700}, \\dfrac{5{,}472}{7{,}700}, \\text{ and } \\dfrac{5{,}487}{7{,}700}", "__seed__": "0458"}}, {"seed": 459, "data": {"p1_how_many": "14", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.345, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335", "5.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}471}{42{,}000}, \\dfrac{7{,}886}{42{,}000}, \\dfrac{8{,}262}{42{,}000}, \\dfrac{9{,}648}{42{,}000}, \\dfrac{10{,}353}{42{,}000}, \\dfrac{10{,}711}{42{,}000}, \\dfrac{10{,}833}{42{,}000}, \\text{ and } \\dfrac{11{,}609}{42{,}000}", "__seed__": "0459"}}, {"seed": 460, "data": {"p1_how_many": "11", "p1_a": "8.32", "p1_b": "8.33", "p1_numbers": "8.3205, 8.321, 8.3215, 8.322, 8.323, 8.324, 8.325, 8.326, 8.327, 8.328, and 8.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.321", "8.322000000000001", "8.323", "8.324", "8.325000000000001", "8.326", "8.327", "8.328", "8.329"], "p1_2_xs": ["8.320500000000001", "8.3215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}007}{3{,}500}, \\dfrac{2{,}052}{3{,}500}, \\dfrac{2{,}089}{3{,}500}, \\dfrac{2{,}144}{3{,}500}, \\dfrac{2{,}192}{3{,}500}, \\dfrac{2{,}204}{3{,}500}, \\dfrac{2{,}284}{3{,}500}, \\dfrac{2{,}320}{3{,}500}, \\dfrac{2{,}397}{3{,}500}, \\dfrac{2{,}487}{3{,}500}, \\dfrac{2{,}625}{3{,}500}, \\text{ and } \\dfrac{2{,}762}{3{,}500}", "__seed__": "0460"}}, {"seed": 461, "data": {"p1_how_many": "10", "p1_a": "3.56", "p1_b": "3.57", "p1_numbers": "3.5605, 3.561, 3.562, 3.563, 3.564, 3.565, 3.566, 3.567, 3.568, and 3.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.561", "3.562", "3.563", "3.564", "3.565", "3.566", "3.567", "3.568", "3.569"], "p1_2_xs": ["3.5605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}084}{63{,}000}, \\dfrac{14{,}368}{63{,}000}, \\dfrac{14{,}822}{63{,}000}, \\dfrac{15{,}111}{63{,}000}, \\dfrac{15{,}179}{63{,}000}, \\dfrac{15{,}400}{63{,}000}, \\dfrac{15{,}413}{63{,}000}, \\dfrac{15{,}819}{63{,}000}, \\dfrac{17{,}345}{63{,}000}, \\dfrac{17{,}655}{63{,}000}, \\text{ and } \\dfrac{17{,}818}{63{,}000}", "__seed__": "0461"}}, {"seed": 462, "data": {"p1_how_many": "14", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.145, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135", "4.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}052}{56{,}000}, \\dfrac{48{,}151}{56{,}000}, \\dfrac{48{,}328}{56{,}000}, \\dfrac{48{,}341}{56{,}000}, \\dfrac{48{,}486}{56{,}000}, \\dfrac{48{,}516}{56{,}000}, \\dfrac{48{,}598}{56{,}000}, \\dfrac{48{,}803}{56{,}000}, \\dfrac{48{,}904}{56{,}000}, \\text{ and } \\dfrac{48{,}906}{56{,}000}", "__seed__": "0462"}}, {"seed": 463, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}712}{6{,}300}, \\dfrac{2{,}713}{6{,}300}, \\dfrac{2{,}715}{6{,}300}, \\dfrac{2{,}725}{6{,}300}, \\dfrac{2{,}729}{6{,}300}, \\dfrac{2{,}754}{6{,}300}, \\dfrac{2{,}762}{6{,}300}, \\dfrac{2{,}770}{6{,}300}, \\dfrac{2{,}782}{6{,}300}, \\text{ and } \\dfrac{2{,}790}{6{,}300}", "__seed__": "0463"}}, {"seed": 464, "data": {"p1_how_many": "14", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.735, 6.74, 6.745, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725", "6.735", "6.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}402}{3{,}500}, \\dfrac{1{,}414}{3{,}500}, \\dfrac{1{,}436}{3{,}500}, \\dfrac{1{,}447}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}480}{3{,}500}, \\text{ and } \\dfrac{1{,}493}{3{,}500}", "__seed__": "0464"}}, {"seed": 465, "data": {"p1_how_many": "10", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.5005, 4.501, 4.502, 4.503, 4.504, 4.505, 4.506, 4.507, 4.508, and 4.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.501", "4.502", "4.503", "4.504", "4.505", "4.506", "4.507", "4.508", "4.509"], "p1_2_xs": ["4.5005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}167}{30{,}000}, \\dfrac{24{,}326}{30{,}000}, \\dfrac{24{,}363}{30{,}000}, \\dfrac{24{,}410}{30{,}000}, \\dfrac{24{,}417}{30{,}000}, \\dfrac{24{,}450}{30{,}000}, \\dfrac{24{,}547}{30{,}000}, \\dfrac{24{,}690}{30{,}000}, \\dfrac{24{,}860}{30{,}000}, \\dfrac{24{,}862}{30{,}000}, \\text{ and } \\dfrac{24{,}966}{30{,}000}", "__seed__": "0465"}}, {"seed": 466, "data": {"p1_how_many": "10", "p1_a": "3.14", "p1_b": "3.15", "p1_numbers": "3.1405, 3.141, 3.142, 3.143, 3.144, 3.145, 3.146, 3.147, 3.148, and 3.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.141", "3.142", "3.1430000000000002", "3.144", "3.145", "3.146", "3.1470000000000002", "3.148", "3.149"], "p1_2_xs": ["3.1405000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{43{,}510}{77{,}000}, \\dfrac{47{,}026}{77{,}000}, \\dfrac{47{,}537}{77{,}000}, \\dfrac{51{,}915}{77{,}000}, \\dfrac{51{,}917}{77{,}000}, \\dfrac{52{,}676}{77{,}000}, \\dfrac{53{,}168}{77{,}000}, \\dfrac{56{,}479}{77{,}000}, \\dfrac{56{,}820}{77{,}000}, \\dfrac{60{,}894}{77{,}000}, \\dfrac{61{,}024}{77{,}000}, \\text{ and } \\dfrac{63{,}989}{77{,}000}", "__seed__": "0466"}}, {"seed": 467, "data": {"p1_how_many": "13", "p1_a": "1.44", "p1_b": "1.45", "p1_numbers": "1.4405, 1.441, 1.4415, 1.442, 1.4425, 1.443, 1.4435, 1.444, 1.445, 1.446, 1.447, 1.448, and 1.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4409999999999998", "1.442", "1.4429999999999998", "1.444", "1.4449999999999998", "1.446", "1.4469999999999998", "1.448", "1.4489999999999998"], "p1_2_xs": ["1.4405", "1.4414999999999998", "1.4425", "1.4434999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{504}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{516}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{535}{1{,}500}, \\dfrac{539}{1{,}500}, \\dfrac{545}{1{,}500}, \\text{ and } \\dfrac{558}{1{,}500}", "__seed__": "0467"}}, {"seed": 468, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{74}{350}, \\dfrac{75}{350}, \\dfrac{76}{350}, \\dfrac{77}{350}, \\dfrac{78}{350}, \\dfrac{80}{350}, \\dfrac{86}{350}, \\dfrac{90}{350}, \\text{ and } \\dfrac{98}{350}", "__seed__": "0468"}}, {"seed": 469, "data": {"p1_how_many": "12", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{32}{120}, \\dfrac{33}{120}, \\dfrac{34}{120}, \\dfrac{35}{120}, \\dfrac{36}{120}, \\dfrac{37}{120}, \\dfrac{38}{120}, \\text{ and } \\dfrac{39}{120}", "__seed__": "0469"}}, {"seed": 470, "data": {"p1_how_many": "13", "p1_a": "7.45", "p1_b": "7.46", "p1_numbers": "7.4505, 7.451, 7.4515, 7.452, 7.4525, 7.453, 7.4535, 7.454, 7.455, 7.456, 7.457, 7.458, and 7.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.4510000000000005", "7.452", "7.453", "7.454", "7.455", "7.456", "7.457", "7.458", "7.4590000000000005"], "p1_2_xs": ["7.4505", "7.4515", "7.4525", "7.4535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}324}{35{,}000}, \\dfrac{7{,}569}{35{,}000}, \\dfrac{7{,}972}{35{,}000}, \\dfrac{7{,}985}{35{,}000}, \\dfrac{9{,}025}{35{,}000}, \\dfrac{9{,}360}{35{,}000}, \\dfrac{9{,}580}{35{,}000}, \\dfrac{9{,}671}{35{,}000}, \\text{ and } \\dfrac{9{,}989}{35{,}000}", "__seed__": "0470"}}, {"seed": 471, "data": {"p1_how_many": "12", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.625, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999", "6.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}140}{12{,}000}, \\dfrac{8{,}194}{12{,}000}, \\dfrac{8{,}307}{12{,}000}, \\dfrac{8{,}354}{12{,}000}, \\dfrac{8{,}684}{12{,}000}, \\dfrac{8{,}699}{12{,}000}, \\text{ and } \\dfrac{8{,}834}{12{,}000}", "__seed__": "0471"}}, {"seed": 472, "data": {"p1_how_many": "13", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.425, 5.43, 5.435, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415", "5.425", "5.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}610}{56{,}000}, \\dfrac{21{,}678}{56{,}000}, \\dfrac{22{,}078}{56{,}000}, \\dfrac{22{,}169}{56{,}000}, \\dfrac{22{,}617}{56{,}000}, \\dfrac{22{,}820}{56{,}000}, \\dfrac{23{,}102}{56{,}000}, \\text{ and } \\dfrac{23{,}619}{56{,}000}", "__seed__": "0472"}}, {"seed": 473, "data": {"p1_how_many": "14", "p1_a": "3.53", "p1_b": "3.54", "p1_numbers": "3.5305, 3.531, 3.5315, 3.532, 3.5325, 3.533, 3.5335, 3.534, 3.5345, 3.535, 3.536, 3.537, 3.538, and 3.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.5309999999999997", "3.5319999999999996", "3.533", "3.534", "3.5349999999999997", "3.5359999999999996", "3.537", "3.538", "3.5389999999999997"], "p1_2_xs": ["3.5305", "3.5315", "3.5324999999999998", "3.5335", "3.5345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}425}{3{,}500}, \\dfrac{1{,}431}{3{,}500}, \\dfrac{1{,}447}{3{,}500}, \\dfrac{1{,}454}{3{,}500}, \\dfrac{1{,}460}{3{,}500}, \\dfrac{1{,}480}{3{,}500}, \\text{ and } \\dfrac{1{,}485}{3{,}500}", "__seed__": "0473"}}, {"seed": 474, "data": {"p1_how_many": "12", "p1_a": "2.84", "p1_b": "2.85", "p1_numbers": "2.8405, 2.841, 2.8415, 2.842, 2.8425, 2.843, 2.844, 2.845, 2.846, 2.847, 2.848, and 2.849", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.8409999999999997", "2.8419999999999996", "2.843", "2.844", "2.8449999999999998", "2.8459999999999996", "2.847", "2.848", "2.8489999999999998"], "p1_2_xs": ["2.8405", "2.8415", "2.8425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{313}{1{,}200}, \\dfrac{341}{1{,}200}, \\dfrac{353}{1{,}200}, \\dfrac{363}{1{,}200}, \\dfrac{377}{1{,}200}, \\dfrac{393}{1{,}200}, \\text{ and } \\dfrac{397}{1{,}200}", "__seed__": "0474"}}, {"seed": 475, "data": {"p1_how_many": "14", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.745, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725", "7.735", "7.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}222}{42{,}000}, \\dfrac{35{,}229}{42{,}000}, \\dfrac{35{,}264}{42{,}000}, \\dfrac{35{,}296}{42{,}000}, \\dfrac{35{,}302}{42{,}000}, \\dfrac{35{,}536}{42{,}000}, \\dfrac{35{,}839}{42{,}000}, \\text{ and } \\dfrac{35{,}873}{42{,}000}", "__seed__": "0475"}}, {"seed": 476, "data": {"p1_how_many": "13", "p1_a": "6.82", "p1_b": "6.83", "p1_numbers": "6.8205, 6.821, 6.8215, 6.822, 6.8225, 6.823, 6.8235, 6.824, 6.825, 6.826, 6.827, 6.828, and 6.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.821000000000001", "6.822", "6.823", "6.824", "6.825", "6.8260000000000005", "6.827", "6.828", "6.829000000000001"], "p1_2_xs": ["6.8205", "6.8215", "6.8225", "6.8235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}317}{56{,}000}, \\dfrac{35{,}387}{56{,}000}, \\dfrac{36{,}302}{56{,}000}, \\dfrac{36{,}466}{56{,}000}, \\dfrac{36{,}516}{56{,}000}, \\dfrac{37{,}080}{56{,}000}, \\dfrac{37{,}307}{56{,}000}, \\dfrac{38{,}020}{56{,}000}, \\dfrac{39{,}479}{56{,}000}, \\text{ and } \\dfrac{39{,}757}{56{,}000}", "__seed__": "0476"}}, {"seed": 477, "data": {"p1_how_many": "10", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}179}{15{,}000}, \\dfrac{6{,}256}{15{,}000}, \\dfrac{6{,}364}{15{,}000}, \\dfrac{6{,}393}{15{,}000}, \\dfrac{7{,}082}{15{,}000}, \\dfrac{8{,}386}{15{,}000}, \\dfrac{8{,}776}{15{,}000}, \\dfrac{8{,}823}{15{,}000}, \\dfrac{9{,}324}{15{,}000}, \\text{ and } \\dfrac{9{,}718}{15{,}000}", "__seed__": "0477"}}, {"seed": 478, "data": {"p1_how_many": "14", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.345, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335", "6.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0478"}}, {"seed": 479, "data": {"p1_how_many": "13", "p1_a": "2.43", "p1_b": "2.44", "p1_numbers": "2.4305, 2.431, 2.4315, 2.432, 2.4325, 2.433, 2.4335, 2.434, 2.435, 2.436, 2.437, 2.438, and 2.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.431", "2.432", "2.4330000000000003", "2.434", "2.435", "2.436", "2.4370000000000003", "2.438", "2.439"], "p1_2_xs": ["2.4305000000000003", "2.4315", "2.4325", "2.4335000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{548}{1{,}500}, \\dfrac{558}{1{,}500}, \\dfrac{560}{1{,}500}, \\dfrac{570}{1{,}500}, \\dfrac{579}{1{,}500}, \\text{ and } \\dfrac{595}{1{,}500}", "__seed__": "0479"}}, {"seed": 480, "data": {"p1_how_many": "11", "p1_a": "5.35", "p1_b": "5.36", "p1_numbers": "5.3505, 5.351, 5.3515, 5.352, 5.353, 5.354, 5.355, 5.356, 5.357, 5.358, and 5.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.351", "5.351999999999999", "5.353", "5.353999999999999", "5.3549999999999995", "5.356", "5.356999999999999", "5.358", "5.359"], "p1_2_xs": ["5.350499999999999", "5.3515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{13{,}029}{20{,}000}, \\dfrac{13{,}118}{20{,}000}, \\dfrac{13{,}157}{20{,}000}, \\dfrac{13{,}528}{20{,}000}, \\dfrac{13{,}713}{20{,}000}, \\dfrac{13{,}739}{20{,}000}, \\dfrac{13{,}941}{20{,}000}, \\dfrac{13{,}990}{20{,}000}, \\dfrac{14{,}236}{20{,}000}, \\dfrac{14{,}459}{20{,}000}, \\text{ and } \\dfrac{14{,}849}{20{,}000}", "__seed__": "0480"}}, {"seed": 481, "data": {"p1_how_many": "14", "p1_a": "5.36", "p1_b": "5.37", "p1_numbers": "5.3605, 5.361, 5.3615, 5.362, 5.3625, 5.363, 5.3635, 5.364, 5.3645, 5.365, 5.366, 5.367, 5.368, and 5.369", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.361000000000001", "5.362", "5.363", "5.364", "5.365", "5.3660000000000005", "5.367", "5.368", "5.369000000000001"], "p1_2_xs": ["5.3605", "5.3615", "5.3625", "5.3635", "5.3645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}326}{42{,}000}, \\dfrac{30{,}355}{42{,}000}, \\dfrac{30{,}685}{42{,}000}, \\dfrac{31{,}074}{42{,}000}, \\dfrac{32{,}090}{42{,}000}, \\dfrac{32{,}407}{42{,}000}, \\dfrac{32{,}708}{42{,}000}, \\dfrac{33{,}254}{42{,}000}, \\dfrac{34{,}082}{42{,}000}, \\dfrac{34{,}113}{42{,}000}, \\text{ and } \\dfrac{34{,}956}{42{,}000}", "__seed__": "0481"}}, {"seed": 482, "data": {"p1_how_many": "13", "p1_a": "6.73", "p1_b": "6.74", "p1_numbers": "6.7305, 6.731, 6.7315, 6.732, 6.7325, 6.733, 6.7335, 6.734, 6.735, 6.736, 6.737, 6.738, and 6.739", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.731000000000001", "6.732", "6.7330000000000005", "6.734", "6.735", "6.736000000000001", "6.737", "6.738", "6.739000000000001"], "p1_2_xs": ["6.7305", "6.7315000000000005", "6.7325", "6.7335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{728}{4{,}200}, \\dfrac{858}{4{,}200}, \\dfrac{879}{4{,}200}, \\dfrac{932}{4{,}200}, \\dfrac{952}{4{,}200}, \\dfrac{963}{4{,}200}, \\dfrac{1{,}034}{4{,}200}, \\dfrac{1{,}058}{4{,}200}, \\dfrac{1{,}073}{4{,}200}, \\dfrac{1{,}087}{4{,}200}, \\text{ and } \\dfrac{1{,}092}{4{,}200}", "__seed__": "0482"}}, {"seed": 483, "data": {"p1_how_many": "10", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}043}{35{,}000}, \\dfrac{14{,}325}{35{,}000}, \\dfrac{14{,}355}{35{,}000}, \\dfrac{14{,}365}{35{,}000}, \\dfrac{14{,}385}{35{,}000}, \\dfrac{14{,}489}{35{,}000}, \\dfrac{14{,}554}{35{,}000}, \\dfrac{14{,}560}{35{,}000}, \\dfrac{14{,}602}{35{,}000}, \\dfrac{14{,}788}{35{,}000}, \\dfrac{14{,}819}{35{,}000}, \\text{ and } \\dfrac{14{,}822}{35{,}000}", "__seed__": "0483"}}, {"seed": 484, "data": {"p1_how_many": "10", "p1_a": "5.0", "p1_b": "5.1", "p1_numbers": "5.005, 5.01, 5.02, 5.03, 5.04, 5.05, 5.06, 5.07, 5.08, and 5.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.01", "5.02", "5.03", "5.04", "5.05", "5.06", "5.07", "5.08", "5.09"], "p1_2_xs": ["5.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{271}{630}, \\dfrac{272}{630}, \\dfrac{273}{630}, \\dfrac{274}{630}, \\dfrac{275}{630}, \\dfrac{276}{630}, \\dfrac{277}{630}, \\text{ and } \\dfrac{278}{630}", "__seed__": "0484"}}, {"seed": 485, "data": {"p1_how_many": "12", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}477}{15{,}000}, \\dfrac{6{,}872}{15{,}000}, \\dfrac{7{,}019}{15{,}000}, \\dfrac{7{,}394}{15{,}000}, \\dfrac{7{,}671}{15{,}000}, \\dfrac{8{,}494}{15{,}000}, \\dfrac{8{,}742}{15{,}000}, \\dfrac{8{,}749}{15{,}000}, \\dfrac{8{,}822}{15{,}000}, \\dfrac{9{,}018}{15{,}000}, \\dfrac{9{,}422}{15{,}000}, \\text{ and } \\dfrac{9{,}983}{15{,}000}", "__seed__": "0485"}}, {"seed": 486, "data": {"p1_how_many": "10", "p1_a": "2.2", "p1_b": "2.3", "p1_numbers": "2.205, 2.21, 2.22, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, and 2.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.21", "2.22", "2.23", "2.24", "2.25", "2.2600000000000002", "2.27", "2.2800000000000002", "2.29"], "p1_2_xs": ["2.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}073}{63{,}000}, \\dfrac{14{,}114}{63{,}000}, \\dfrac{14{,}628}{63{,}000}, \\dfrac{15{,}070}{63{,}000}, \\dfrac{15{,}936}{63{,}000}, \\dfrac{16{,}095}{63{,}000}, \\dfrac{17{,}308}{63{,}000}, \\text{ and } \\dfrac{17{,}958}{63{,}000}", "__seed__": "0486"}}, {"seed": 487, "data": {"p1_how_many": "14", "p1_a": "1.91", "p1_b": "1.92", "p1_numbers": "1.9105, 1.911, 1.9115, 1.912, 1.9125, 1.913, 1.9135, 1.914, 1.9145, 1.915, 1.916, 1.917, 1.918, and 1.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9109999999999998", "1.912", "1.9129999999999998", "1.914", "1.9149999999999998", "1.916", "1.9169999999999998", "1.918", "1.9189999999999998"], "p1_2_xs": ["1.9104999999999999", "1.9114999999999998", "1.9124999999999999", "1.9134999999999998", "1.9144999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}115}{3{,}500}, \\dfrac{2{,}311}{3{,}500}, \\dfrac{2{,}489}{3{,}500}, \\dfrac{2{,}508}{3{,}500}, \\dfrac{2{,}518}{3{,}500}, \\dfrac{2{,}548}{3{,}500}, \\text{ and } \\dfrac{2{,}656}{3{,}500}", "__seed__": "0487"}}, {"seed": 488, "data": {"p1_how_many": "10", "p1_a": "9.74", "p1_b": "9.75", "p1_numbers": "9.7405, 9.741, 9.742, 9.743, 9.744, 9.745, 9.746, 9.747, 9.748, and 9.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.741", "9.742", "9.743", "9.744", "9.745000000000001", "9.746", "9.747", "9.748", "9.749"], "p1_2_xs": ["9.7405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}253}{7{,}700}, \\dfrac{4{,}311}{7{,}700}, \\dfrac{4{,}405}{7{,}700}, \\dfrac{4{,}414}{7{,}700}, \\dfrac{4{,}506}{7{,}700}, \\dfrac{4{,}735}{7{,}700}, \\dfrac{4{,}878}{7{,}700}, \\dfrac{5{,}116}{7{,}700}, \\dfrac{5{,}198}{7{,}700}, \\dfrac{5{,}224}{7{,}700}, \\text{ and } \\dfrac{5{,}284}{7{,}700}", "__seed__": "0488"}}, {"seed": 489, "data": {"p1_how_many": "13", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}626}{5{,}600}, \\dfrac{1{,}658}{5{,}600}, \\dfrac{1{,}712}{5{,}600}, \\dfrac{1{,}745}{5{,}600}, \\dfrac{1{,}798}{5{,}600}, \\dfrac{1{,}843}{5{,}600}, \\dfrac{1{,}933}{5{,}600}, \\dfrac{1{,}940}{5{,}600}, \\text{ and } \\dfrac{1{,}963}{5{,}600}", "__seed__": "0489"}}, {"seed": 490, "data": {"p1_how_many": "10", "p1_a": "2.55", "p1_b": "2.56", "p1_numbers": "2.5505, 2.551, 2.552, 2.553, 2.554, 2.555, 2.556, 2.557, 2.558, and 2.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5509999999999997", "2.5519999999999996", "2.553", "2.554", "2.5549999999999997", "2.5559999999999996", "2.557", "2.558", "2.5589999999999997"], "p1_2_xs": ["2.5505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}314}{20{,}000}, \\dfrac{5{,}501}{20{,}000}, \\dfrac{5{,}594}{20{,}000}, \\dfrac{5{,}642}{20{,}000}, \\dfrac{6{,}227}{20{,}000}, \\dfrac{6{,}604}{20{,}000}, \\dfrac{6{,}660}{20{,}000}, \\dfrac{7{,}183}{20{,}000}, \\dfrac{7{,}641}{20{,}000}, \\text{ and } \\dfrac{7{,}937}{20{,}000}", "__seed__": "0490"}}, {"seed": 491, "data": {"p1_how_many": "12", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}193}{35{,}000}, \\dfrac{14{,}255}{35{,}000}, \\dfrac{14{,}262}{35{,}000}, \\dfrac{14{,}650}{35{,}000}, \\dfrac{14{,}701}{35{,}000}, \\dfrac{14{,}742}{35{,}000}, \\dfrac{14{,}753}{35{,}000}, \\dfrac{14{,}795}{35{,}000}, \\dfrac{14{,}806}{35{,}000}, \\dfrac{14{,}976}{35{,}000}, \\text{ and } \\dfrac{14{,}979}{35{,}000}", "__seed__": "0491"}}, {"seed": 492, "data": {"p1_how_many": "11", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.015, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005", "8.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{7{,}028}{56{,}000}, \\dfrac{7{,}112}{56{,}000}, \\dfrac{7{,}164}{56{,}000}, \\dfrac{7{,}207}{56{,}000}, \\dfrac{7{,}224}{56{,}000}, \\dfrac{7{,}330}{56{,}000}, \\dfrac{7{,}402}{56{,}000}, \\dfrac{7{,}403}{56{,}000}, \\dfrac{7{,}460}{56{,}000}, \\dfrac{7{,}821}{56{,}000}, \\dfrac{7{,}937}{56{,}000}, \\text{ and } \\dfrac{7{,}951}{56{,}000}", "__seed__": "0492"}}, {"seed": 493, "data": {"p1_how_many": "12", "p1_a": "2.76", "p1_b": "2.77", "p1_numbers": "2.7605, 2.761, 2.7615, 2.762, 2.7625, 2.763, 2.764, 2.765, 2.766, 2.767, 2.768, and 2.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.7609999999999997", "2.7619999999999996", "2.763", "2.764", "2.7649999999999997", "2.7659999999999996", "2.767", "2.768", "2.7689999999999997"], "p1_2_xs": ["2.7605", "2.7615", "2.7624999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{435}{770}, \\dfrac{453}{770}, \\dfrac{463}{770}, 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\\dfrac{364}{1{,}200}, \\dfrac{374}{1{,}200}, \\dfrac{381}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0494"}}, {"seed": 495, "data": {"p1_how_many": "10", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}021}{15{,}000}, \\dfrac{6{,}546}{15{,}000}, \\dfrac{6{,}723}{15{,}000}, \\dfrac{6{,}843}{15{,}000}, \\dfrac{8{,}446}{15{,}000}, \\dfrac{8{,}594}{15{,}000}, \\dfrac{8{,}767}{15{,}000}, \\dfrac{9{,}189}{15{,}000}, \\text{ and } \\dfrac{9{,}947}{15{,}000}", "__seed__": "0495"}}, {"seed": 496, "data": {"p1_how_many": "10", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.5005, 8.501, 8.502, 8.503, 8.504, 8.505, 8.506, 8.507, 8.508, and 8.509", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.501", "8.502", "8.503", "8.504", "8.505", "8.506", "8.507", "8.508", "8.509"], "p1_2_xs": ["8.5005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}815}{5{,}600}, \\dfrac{4{,}821}{5{,}600}, \\dfrac{4{,}835}{5{,}600}, \\dfrac{4{,}841}{5{,}600}, \\dfrac{4{,}857}{5{,}600}, \\dfrac{4{,}862}{5{,}600}, \\dfrac{4{,}872}{5{,}600}, \\dfrac{4{,}886}{5{,}600}, \\text{ and } \\dfrac{4{,}891}{5{,}600}", "__seed__": "0496"}}, {"seed": 497, "data": {"p1_how_many": "10", "p1_a": "4.03", "p1_b": "4.04", "p1_numbers": "4.0305, 4.031, 4.032, 4.033, 4.034, 4.035, 4.036, 4.037, 4.038, and 4.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.031000000000001", "4.032", "4.033", "4.034", "4.035", "4.0360000000000005", "4.037", "4.038", "4.039000000000001"], "p1_2_xs": ["4.0305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}423}{3{,}500}, \\dfrac{1{,}454}{3{,}500}, \\dfrac{1{,}465}{3{,}500}, \\dfrac{1{,}469}{3{,}500}, \\dfrac{1{,}477}{3{,}500}, \\dfrac{1{,}489}{3{,}500}, \\dfrac{1{,}495}{3{,}500}, \\text{ and } \\dfrac{1{,}496}{3{,}500}", "__seed__": "0497"}}, {"seed": 498, "data": {"p1_how_many": "13", "p1_a": "2.05", "p1_b": "2.06", "p1_numbers": "2.0505, 2.051, 2.0515, 2.052, 2.0525, 2.053, 2.0535, 2.054, 2.055, 2.056, 2.057, 2.058, and 2.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.0509999999999997", "2.0519999999999996", "2.053", "2.054", "2.0549999999999997", "2.0559999999999996", "2.057", "2.058", "2.0589999999999997"], "p1_2_xs": ["2.0505", "2.0515", "2.0524999999999998", "2.0535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}097}{30{,}000}, \\dfrac{5{,}220}{30{,}000}, \\dfrac{5{,}465}{30{,}000}, \\dfrac{5{,}515}{30{,}000}, \\dfrac{5{,}540}{30{,}000}, \\dfrac{5{,}666}{30{,}000}, \\dfrac{5{,}742}{30{,}000}, \\dfrac{5{,}773}{30{,}000}, \\text{ and } \\dfrac{5{,}975}{30{,}000}", "__seed__": "0498"}}, {"seed": 499, "data": {"p1_how_many": "10", "p1_a": "8.95", "p1_b": "8.96", "p1_numbers": "8.9505, 8.951, 8.952, 8.953, 8.954, 8.955, 8.956, 8.957, 8.958, and 8.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.950999999999999", "8.952", "8.953", "8.953999999999999", "8.955", "8.956", "8.956999999999999", "8.957999999999998", "8.959"], "p1_2_xs": ["8.9505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}803}{5{,}600}, \\dfrac{4{,}805}{5{,}600}, \\dfrac{4{,}814}{5{,}600}, \\dfrac{4{,}832}{5{,}600}, \\dfrac{4{,}844}{5{,}600}, \\dfrac{4{,}866}{5{,}600}, \\dfrac{4{,}870}{5{,}600}, \\dfrac{4{,}876}{5{,}600}, \\dfrac{4{,}877}{5{,}600}, \\dfrac{4{,}879}{5{,}600}, \\dfrac{4{,}882}{5{,}600}, \\text{ and } \\dfrac{4{,}890}{5{,}600}", "__seed__": "0499"}}, {"seed": 500, "data": {"p1_how_many": "13", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}138}{20{,}000}, \\dfrac{4{,}191}{20{,}000}, \\dfrac{4{,}289}{20{,}000}, \\dfrac{4{,}350}{20{,}000}, \\dfrac{4{,}418}{20{,}000}, \\dfrac{4{,}458}{20{,}000}, \\dfrac{4{,}559}{20{,}000}, \\dfrac{4{,}740}{20{,}000}, \\text{ and } \\dfrac{4{,}811}{20{,}000}", "__seed__": "0500"}}, {"seed": 501, "data": {"p1_how_many": "10", "p1_a": "9.83", "p1_b": "9.84", "p1_numbers": "9.8305, 9.831, 9.832, 9.833, 9.834, 9.835, 9.836, 9.837, 9.838, and 9.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.831", "9.832", "9.833", "9.834", "9.835", "9.836", "9.837", "9.838", "9.839"], "p1_2_xs": ["9.8305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{401}{2{,}000}, \\dfrac{405}{2{,}000}, \\dfrac{456}{2{,}000}, \\dfrac{466}{2{,}000}, \\dfrac{474}{2{,}000}, \\dfrac{477}{2{,}000}, \\dfrac{478}{2{,}000}, \\text{ and } \\dfrac{499}{2{,}000}", "__seed__": "0501"}}, {"seed": 502, "data": {"p1_how_many": "12", "p1_a": "9.85", "p1_b": "9.86", "p1_numbers": "9.8505, 9.851, 9.8515, 9.852, 9.8525, 9.853, 9.854, 9.855, 9.856, 9.857, 9.858, and 9.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.850999999999999", "9.852", "9.853", "9.854", "9.855", "9.856", "9.857", "9.857999999999999", "9.859"], "p1_2_xs": ["9.8505", "9.8515", "9.852500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}074}{20{,}000}, \\dfrac{5{,}192}{20{,}000}, \\dfrac{6{,}026}{20{,}000}, \\dfrac{6{,}069}{20{,}000}, \\dfrac{6{,}591}{20{,}000}, \\dfrac{6{,}860}{20{,}000}, \\dfrac{6{,}963}{20{,}000}, \\dfrac{7{,}217}{20{,}000}, \\text{ and } \\dfrac{7{,}804}{20{,}000}", "__seed__": "0502"}}, {"seed": 503, "data": {"p1_how_many": "13", "p1_a": "6.92", "p1_b": "6.93", "p1_numbers": "6.9205, 6.921, 6.9215, 6.922, 6.9225, 6.923, 6.9235, 6.924, 6.925, 6.926, 6.927, 6.928, and 6.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.921", "6.922", "6.923", "6.9239999999999995", "6.925", "6.926", "6.927", "6.928", "6.929"], "p1_2_xs": ["6.9205", "6.9215", "6.922499999999999", "6.9235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}358}{35{,}000}, \\dfrac{21{,}296}{35{,}000}, \\dfrac{23{,}012}{35{,}000}, \\dfrac{23{,}520}{35{,}000}, \\dfrac{24{,}047}{35{,}000}, \\dfrac{24{,}520}{35{,}000}, \\dfrac{24{,}751}{35{,}000}, \\dfrac{25{,}984}{35{,}000}, \\text{ and } \\dfrac{26{,}908}{35{,}000}", "__seed__": "0503"}}, {"seed": 504, "data": {"p1_how_many": "12", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}182}{20{,}000}, \\dfrac{4{,}268}{20{,}000}, \\dfrac{4{,}532}{20{,}000}, \\dfrac{4{,}802}{20{,}000}, \\dfrac{4{,}917}{20{,}000}, \\dfrac{4{,}920}{20{,}000}, \\dfrac{4{,}960}{20{,}000}, \\text{ and } \\dfrac{4{,}966}{20{,}000}", "__seed__": "0504"}}, {"seed": 505, "data": {"p1_how_many": "10", "p1_a": "3.26", "p1_b": "3.27", "p1_numbers": "3.2605, 3.261, 3.262, 3.263, 3.264, 3.265, 3.266, 3.267, 3.268, and 3.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.2609999999999997", "3.2619999999999996", "3.263", "3.264", "3.2649999999999997", "3.2659999999999996", "3.267", "3.268", "3.2689999999999997"], "p1_2_xs": ["3.2605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}216}{2{,}000}, \\dfrac{1{,}229}{2{,}000}, \\dfrac{1{,}323}{2{,}000}, \\dfrac{1{,}344}{2{,}000}, \\dfrac{1{,}362}{2{,}000}, \\dfrac{1{,}364}{2{,}000}, \\text{ and } \\dfrac{1{,}399}{2{,}000}", "__seed__": "0505"}}, {"seed": 506, "data": {"p1_how_many": "14", "p1_a": "9.9", "p1_b": "9.1", "p1_numbers": "9.9005, 9.901, 9.9015, 9.902, 9.9025, 9.903, 9.9035, 9.904, 9.9045, 9.905, 9.906, 9.907, 9.908, and 9.909", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.901", "9.902000000000001", "9.903", "9.904", "9.905000000000001", "9.906", "9.907", 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"6.470000000000001", "6.48", "6.49"], "p1_2_xs": ["6.405", "6.415", "6.425", "6.4350000000000005", "6.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}895}{56{,}000}, \\dfrac{35{,}908}{56{,}000}, \\dfrac{36{,}003}{56{,}000}, \\dfrac{37{,}767}{56{,}000}, \\dfrac{38{,}131}{56{,}000}, \\dfrac{38{,}258}{56{,}000}, \\dfrac{39{,}354}{56{,}000}, \\text{ and } \\dfrac{39{,}953}{56{,}000}", "__seed__": "0507"}}, {"seed": 508, "data": {"p1_how_many": "11", "p1_a": "9.83", "p1_b": "9.84", "p1_numbers": "9.8305, 9.831, 9.8315, 9.832, 9.833, 9.834, 9.835, 9.836, 9.837, 9.838, and 9.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.831", "9.832", "9.833", "9.834", "9.835", "9.836", "9.837", "9.838", "9.839"], "p1_2_xs": ["9.8305", "9.8315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}011}{56{,}000}, \\dfrac{48{,}031}{56{,}000}, \\dfrac{48{,}054}{56{,}000}, \\dfrac{48{,}131}{56{,}000}, \\dfrac{48{,}161}{56{,}000}, \\dfrac{48{,}303}{56{,}000}, \\dfrac{48{,}406}{56{,}000}, \\dfrac{48{,}628}{56{,}000}, \\dfrac{48{,}662}{56{,}000}, \\dfrac{48{,}699}{56{,}000}, \\dfrac{48{,}721}{56{,}000}, \\text{ and } \\dfrac{48{,}836}{56{,}000}", "__seed__": "0508"}}, {"seed": 509, "data": {"p1_how_many": "11", "p1_a": "5.82", "p1_b": "5.83", "p1_numbers": "5.8205, 5.821, 5.8215, 5.822, 5.823, 5.824, 5.825, 5.826, 5.827, 5.828, and 5.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.821000000000001", "5.822", "5.823", "5.824", "5.825", "5.8260000000000005", "5.827", "5.828", "5.829000000000001"], "p1_2_xs": ["5.8205", "5.8215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}154}{20{,}000}, \\dfrac{5{,}890}{20{,}000}, \\dfrac{6{,}020}{20{,}000}, \\dfrac{6{,}038}{20{,}000}, \\dfrac{6{,}560}{20{,}000}, \\dfrac{6{,}652}{20{,}000}, \\dfrac{7{,}122}{20{,}000}, \\dfrac{7{,}234}{20{,}000}, \\dfrac{7{,}275}{20{,}000}, \\dfrac{7{,}436}{20{,}000}, \\dfrac{7{,}682}{20{,}000}, \\text{ and } \\dfrac{7{,}915}{20{,}000}", "__seed__": "0509"}}, {"seed": 510, "data": {"p1_how_many": "11", "p1_a": "6.64", "p1_b": "6.65", "p1_numbers": "6.6405, 6.641, 6.6415, 6.642, 6.643, 6.644, 6.645, 6.646, 6.647, 6.648, and 6.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.641", "6.6419999999999995", "6.643", "6.643999999999999", "6.645", "6.646", "6.646999999999999", "6.648", "6.649"], "p1_2_xs": ["6.640499999999999", "6.6415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}495}{63{,}000}, \\dfrac{28{,}759}{63{,}000}, \\dfrac{29{,}127}{63{,}000}, \\dfrac{29{,}288}{63{,}000}, \\dfrac{30{,}829}{63{,}000}, \\dfrac{30{,}844}{63{,}000}, \\dfrac{31{,}710}{63{,}000}, \\dfrac{32{,}323}{63{,}000}, \\dfrac{32{,}370}{63{,}000}, \\text{ and } \\dfrac{35{,}606}{63{,}000}", "__seed__": "0510"}}, {"seed": 511, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}042}{15{,}000}, \\dfrac{5{,}056}{15{,}000}, \\dfrac{5{,}127}{15{,}000}, \\dfrac{5{,}190}{15{,}000}, \\dfrac{5{,}303}{15{,}000}, \\dfrac{5{,}375}{15{,}000}, \\dfrac{5{,}461}{15{,}000}, \\dfrac{5{,}692}{15{,}000}, \\dfrac{5{,}744}{15{,}000}, \\dfrac{5{,}938}{15{,}000}, \\text{ and } \\dfrac{5{,}972}{15{,}000}", "__seed__": "0511"}}, {"seed": 512, "data": {"p1_how_many": "10", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{702}{3{,}500}, \\dfrac{776}{3{,}500}, \\dfrac{825}{3{,}500}, \\dfrac{836}{3{,}500}, \\dfrac{844}{3{,}500}, \\dfrac{883}{3{,}500}, \\dfrac{888}{3{,}500}, \\dfrac{946}{3{,}500}, \\dfrac{959}{3{,}500}, \\dfrac{977}{3{,}500}, \\dfrac{994}{3{,}500}, \\text{ and } \\dfrac{995}{3{,}500}", "__seed__": "0512"}}, {"seed": 513, "data": {"p1_how_many": "12", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.015, 8.02, 8.025, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005", "8.015", "8.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}066}{63{,}000}, \\dfrac{9{,}714}{63{,}000}, \\dfrac{9{,}778}{63{,}000}, \\dfrac{10{,}756}{63{,}000}, \\dfrac{10{,}903}{63{,}000}, \\dfrac{11{,}302}{63{,}000}, \\dfrac{11{,}761}{63{,}000}, \\dfrac{11{,}789}{63{,}000}, \\dfrac{12{,}801}{63{,}000}, \\text{ and } \\dfrac{13{,}006}{63{,}000}", "__seed__": "0513"}}, {"seed": 514, "data": {"p1_how_many": "14", "p1_a": "5.05", "p1_b": "5.06", "p1_numbers": "5.0505, 5.051, 5.0515, 5.052, 5.0525, 5.053, 5.0535, 5.054, 5.0545, 5.055, 5.056, 5.057, 5.058, and 5.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.051", "5.052", "5.053", "5.053999999999999", "5.055", "5.056", "5.0569999999999995", "5.058", "5.059"], "p1_2_xs": ["5.0504999999999995", "5.0515", "5.052499999999999", "5.0535", "5.054499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}513}{35{,}000}, \\dfrac{11{,}498}{35{,}000}, \\dfrac{12{,}794}{35{,}000}, \\dfrac{12{,}948}{35{,}000}, \\dfrac{13{,}680}{35{,}000}, \\dfrac{13{,}868}{35{,}000}, \\dfrac{13{,}886}{35{,}000}, \\text{ and } \\dfrac{13{,}904}{35{,}000}", "__seed__": "0514"}}, {"seed": 515, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{714}{3{,}500}, \\dfrac{734}{3{,}500}, \\dfrac{868}{3{,}500}, \\dfrac{879}{3{,}500}, \\dfrac{902}{3{,}500}, \\dfrac{917}{3{,}500}, \\text{ and } \\dfrac{934}{3{,}500}", "__seed__": "0515"}}, {"seed": 516, "data": {"p1_how_many": "10", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.32, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0516"}}, {"seed": 517, "data": {"p1_how_many": "14", "p1_a": "4.36", "p1_b": "4.37", "p1_numbers": "4.3605, 4.361, 4.3615, 4.362, 4.3625, 4.363, 4.3635, 4.364, 4.3645, 4.365, 4.366, 4.367, 4.368, and 4.369", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.361000000000001", "4.362", "4.363", "4.364", "4.365", "4.3660000000000005", "4.367", "4.368", "4.369000000000001"], "p1_2_xs": ["4.3605", "4.3615", "4.3625", "4.3635", "4.3645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}073}{42{,}000}, \\dfrac{7{,}106}{42{,}000}, \\dfrac{7{,}314}{42{,}000}, \\dfrac{7{,}600}{42{,}000}, \\dfrac{8{,}041}{42{,}000}, \\dfrac{9{,}025}{42{,}000}, \\text{ and } \\dfrac{10{,}614}{42{,}000}", "__seed__": "0517"}}, {"seed": 518, "data": {"p1_how_many": "13", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}337}{77{,}000}, \\dfrac{42{,}634}{77{,}000}, \\dfrac{43{,}292}{77{,}000}, \\dfrac{45{,}663}{77{,}000}, \\dfrac{48{,}115}{77{,}000}, \\dfrac{49{,}453}{77{,}000}, \\dfrac{49{,}740}{77{,}000}, \\dfrac{50{,}224}{77{,}000}, \\text{ and } \\dfrac{51{,}358}{77{,}000}", "__seed__": "0518"}}, {"seed": 519, "data": {"p1_how_many": "11", "p1_a": "4.97", "p1_b": "4.98", "p1_numbers": "4.9705, 4.971, 4.9715, 4.972, 4.973, 4.974, 4.975, 4.976, 4.977, 4.978, and 4.979", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.971", "4.9719999999999995", "4.973", "4.973999999999999", "4.975", "4.976", "4.976999999999999", "4.978", "4.979"], "p1_2_xs": ["4.9704999999999995", "4.9715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\text{ and } \\dfrac{158}{200}", "__seed__": "0519"}}, {"seed": 520, "data": {"p1_how_many": "14", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.345, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335", "6.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{740}{3{,}500}, \\dfrac{755}{3{,}500}, \\dfrac{786}{3{,}500}, \\dfrac{830}{3{,}500}, \\dfrac{839}{3{,}500}, \\dfrac{861}{3{,}500}, \\dfrac{909}{3{,}500}, \\dfrac{938}{3{,}500}, \\dfrac{964}{3{,}500}, \\dfrac{976}{3{,}500}, \\dfrac{988}{3{,}500}, \\text{ and } \\dfrac{990}{3{,}500}", "__seed__": "0520"}}, {"seed": 521, "data": {"p1_how_many": "10", "p1_a": "1.77", "p1_b": "1.78", "p1_numbers": "1.7705, 1.771, 1.772, 1.773, 1.774, 1.775, 1.776, 1.777, 1.778, and 1.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.771", "1.772", "1.773", "1.774", "1.775", "1.776", "1.777", "1.778", "1.779"], "p1_2_xs": ["1.7705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}020}{20{,}000}, \\dfrac{4{,}099}{20{,}000}, \\dfrac{4{,}195}{20{,}000}, \\dfrac{4{,}200}{20{,}000}, \\dfrac{4{,}319}{20{,}000}, \\dfrac{4{,}430}{20{,}000}, \\dfrac{4{,}535}{20{,}000}, \\dfrac{4{,}673}{20{,}000}, \\dfrac{4{,}760}{20{,}000}, \\text{ and } \\dfrac{4{,}868}{20{,}000}", "__seed__": "0521"}}, {"seed": 522, "data": {"p1_how_many": "10", "p1_a": "9.33", 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"Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{622}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{670}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{674}{4{,}200}, \\text{ and } \\dfrac{688}{4{,}200}", "__seed__": "0526"}}, {"seed": 527, "data": {"p1_how_many": "11", "p1_a": "9.77", "p1_b": "9.78", "p1_numbers": "9.7705, 9.771, 9.7715, 9.772, 9.773, 9.774, 9.775, 9.776, 9.777, 9.778, and 9.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.770999999999999", "9.772", "9.773", "9.774", "9.775", "9.776", "9.777", "9.777999999999999", "9.779"], "p1_2_xs": ["9.7705", "9.7715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}917}{6{,}300}, 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\\dfrac{7{,}573}{15{,}000}, \\dfrac{8{,}206}{15{,}000}, \\dfrac{8{,}311}{15{,}000}, \\dfrac{8{,}508}{15{,}000}, \\dfrac{8{,}877}{15{,}000}, \\dfrac{9{,}115}{15{,}000}, \\text{ and } \\dfrac{9{,}194}{15{,}000}", "__seed__": "0528"}}, {"seed": 529, "data": {"p1_how_many": "12", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{67}{150}, \\dfrac{69}{150}, \\dfrac{72}{150}, \\dfrac{75}{150}, \\dfrac{76}{150}, \\dfrac{84}{150}, \\dfrac{89}{150}, \\dfrac{91}{150}, \\text{ and } \\dfrac{95}{150}", "__seed__": "0529"}}, {"seed": 530, "data": {"p1_how_many": "14", "p1_a": "9.5", "p1_b": "9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.545, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535", "9.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}582}{20{,}000}, \\dfrac{5{,}645}{20{,}000}, \\dfrac{5{,}680}{20{,}000}, \\dfrac{6{,}034}{20{,}000}, \\dfrac{6{,}074}{20{,}000}, \\dfrac{7{,}102}{20{,}000}, \\dfrac{7{,}334}{20{,}000}, \\text{ and } \\dfrac{7{,}458}{20{,}000}", "__seed__": "0530"}}, {"seed": 531, "data": {"p1_how_many": "12", "p1_a": "1.47", "p1_b": "1.48", "p1_numbers": "1.4705, 1.471, 1.4715, 1.472, 1.4725, 1.473, 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5.241, 5.242, 5.243, 5.244, 5.245, 5.246, 5.247, 5.248, and 5.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.2410000000000005", "5.242", "5.243", "5.244", "5.245", "5.246", "5.247", "5.248", "5.2490000000000006"], "p1_2_xs": ["5.2405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{102}{350}, \\dfrac{103}{350}, \\dfrac{104}{350}, \\dfrac{108}{350}, \\dfrac{113}{350}, \\dfrac{115}{350}, \\dfrac{137}{350}, \\text{ and } \\dfrac{138}{350}", "__seed__": "0532"}}, {"seed": 533, "data": {"p1_how_many": "11", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}296}{5{,}600}, \\dfrac{3{,}346}{5{,}600}, \\dfrac{3{,}363}{5{,}600}, \\dfrac{3{,}378}{5{,}600}, \\dfrac{3{,}383}{5{,}600}, \\dfrac{3{,}390}{5{,}600}, \\dfrac{3{,}391}{5{,}600}, \\dfrac{3{,}396}{5{,}600}, \\dfrac{3{,}435}{5{,}600}, \\dfrac{3{,}465}{5{,}600}, \\dfrac{3{,}476}{5{,}600}, \\text{ and } \\dfrac{3{,}480}{5{,}600}", "__seed__": "0533"}}, {"seed": 534, "data": {"p1_how_many": "14", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.325, 3.33, 3.335, 3.34, 3.345, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995", "3.3249999999999997", "3.3349999999999995", "3.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{705}{3{,}500}, \\dfrac{818}{3{,}500}, \\dfrac{833}{3{,}500}, \\dfrac{836}{3{,}500}, \\dfrac{853}{3{,}500}, \\dfrac{891}{3{,}500}, \\dfrac{907}{3{,}500}, \\text{ and } \\dfrac{934}{3{,}500}", "__seed__": "0534"}}, {"seed": 535, "data": {"p1_how_many": "11", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}003}{4{,}200}, \\dfrac{3{,}013}{4{,}200}, \\dfrac{3{,}028}{4{,}200}, \\dfrac{3{,}034}{4{,}200}, \\dfrac{3{,}047}{4{,}200}, \\dfrac{3{,}048}{4{,}200}, \\dfrac{3{,}158}{4{,}200}, \\dfrac{3{,}214}{4{,}200}, \\dfrac{3{,}257}{4{,}200}, \\dfrac{3{,}309}{4{,}200}, \\text{ and } \\dfrac{3{,}370}{4{,}200}", "__seed__": "0535"}}, {"seed": 536, "data": {"p1_how_many": "13", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315", "1.325", "1.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}694}{15{,}000}, \\dfrac{7{,}315}{15{,}000}, \\dfrac{7{,}583}{15{,}000}, \\dfrac{8{,}023}{15{,}000}, \\dfrac{8{,}113}{15{,}000}, \\dfrac{8{,}206}{15{,}000}, \\dfrac{9{,}405}{15{,}000}, \\dfrac{9{,}797}{15{,}000}, \\dfrac{9{,}849}{15{,}000}, \\text{ and } \\dfrac{9{,}956}{15{,}000}", "__seed__": "0536"}}, {"seed": 537, "data": {"p1_how_many": "14", "p1_a": "1.9", "p1_b": "1.1", "p1_numbers": "1.9005, 1.901, 1.9015, 1.902, 1.9025, 1.903, 1.9035, 1.904, 1.9045, 1.905, 1.906, 1.907, 1.908, and 1.909", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9009999999999998", "1.902", "1.9029999999999998", "1.904", "1.9049999999999998", "1.906", "1.9069999999999998", "1.908", "1.9089999999999998"], "p1_2_xs": ["1.9004999999999999", "1.9014999999999997", "1.9024999999999999", "1.9034999999999997", "1.9044999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}158}{56{,}000}, \\dfrac{36{,}370}{56{,}000}, \\dfrac{37{,}311}{56{,}000}, \\dfrac{37{,}692}{56{,}000}, \\dfrac{38{,}111}{56{,}000}, \\dfrac{38{,}316}{56{,}000}, \\text{ and } \\dfrac{39{,}223}{56{,}000}", "__seed__": "0537"}}, {"seed": 538, "data": {"p1_how_many": "10", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.6005, 4.601, 4.602, 4.603, 4.604, 4.605, 4.606, 4.607, 4.608, and 4.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.601", "4.601999999999999", "4.603", "4.603999999999999", "4.6049999999999995", "4.606", "4.606999999999999", "4.608", "4.609"], "p1_2_xs": ["4.600499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}021}{35{,}000}, \\dfrac{15{,}128}{35{,}000}, \\dfrac{16{,}261}{35{,}000}, \\dfrac{16{,}279}{35{,}000}, \\dfrac{18{,}272}{35{,}000}, \\dfrac{18{,}728}{35{,}000}, \\dfrac{19{,}044}{35{,}000}, \\dfrac{19{,}046}{35{,}000}, \\dfrac{20{,}188}{35{,}000}, \\dfrac{20{,}356}{35{,}000}, \\dfrac{20{,}660}{35{,}000}, \\text{ and } \\dfrac{20{,}796}{35{,}000}", "__seed__": "0538"}}, {"seed": 539, "data": {"p1_how_many": "13", "p1_a": "8.64", "p1_b": "8.65", "p1_numbers": "8.6405, 8.641, 8.6415, 8.642, 8.6425, 8.643, 8.6435, 8.644, 8.645, 8.646, 8.647, 8.648, and 8.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.641", "8.642000000000001", "8.643", "8.644", "8.645000000000001", "8.646", "8.647", "8.648", "8.649000000000001"], "p1_2_xs": ["8.640500000000001", "8.6415", "8.642500000000002", "8.643500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}218}{2{,}000}, \\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}251}{2{,}000}, \\dfrac{1{,}296}{2{,}000}, \\dfrac{1{,}352}{2{,}000}, \\dfrac{1{,}383}{2{,}000}, \\dfrac{1{,}387}{2{,}000}, \\dfrac{1{,}389}{2{,}000}, \\dfrac{1{,}396}{2{,}000}, \\dfrac{1{,}412}{2{,}000}, \\text{ and } \\dfrac{1{,}468}{2{,}000}", "__seed__": "0539"}}, {"seed": 540, "data": {"p1_how_many": "12", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0540"}}, {"seed": 541, "data": {"p1_how_many": "13", "p1_a": "7.75", "p1_b": "7.76", "p1_numbers": "7.7505, 7.751, 7.7515, 7.752, 7.7525, 7.753, 7.7535, 7.754, 7.755, 7.756, 7.757, 7.758, and 7.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.751", "7.752", "7.753", "7.754", "7.755", "7.756", "7.757", "7.758", "7.759"], "p1_2_xs": ["7.7505", "7.7515", "7.7524999999999995", "7.7535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}233}{2{,}000}, \\dfrac{1{,}237}{2{,}000}, \\dfrac{1{,}293}{2{,}000}, \\dfrac{1{,}296}{2{,}000}, \\dfrac{1{,}311}{2{,}000}, \\dfrac{1{,}379}{2{,}000}, \\dfrac{1{,}419}{2{,}000}, \\dfrac{1{,}437}{2{,}000}, \\dfrac{1{,}452}{2{,}000}, \\dfrac{1{,}462}{2{,}000}, \\dfrac{1{,}465}{2{,}000}, \\text{ and } \\dfrac{1{,}476}{2{,}000}", "__seed__": "0541"}}, {"seed": 542, "data": {"p1_how_many": "12", "p1_a": "1.44", "p1_b": "1.45", "p1_numbers": "1.4405, 1.441, 1.4415, 1.442, 1.4425, 1.443, 1.444, 1.445, 1.446, 1.447, 1.448, and 1.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4409999999999998", "1.442", "1.4429999999999998", "1.444", "1.4449999999999998", "1.446", "1.4469999999999998", "1.448", "1.4489999999999998"], "p1_2_xs": ["1.4405", "1.4414999999999998", "1.4425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{549}{2{,}000}, \\dfrac{563}{2{,}000}, \\dfrac{564}{2{,}000}, \\dfrac{634}{2{,}000}, \\dfrac{638}{2{,}000}, \\dfrac{653}{2{,}000}, \\dfrac{663}{2{,}000}, \\dfrac{674}{2{,}000}, \\dfrac{716}{2{,}000}, \\text{ and } \\dfrac{791}{2{,}000}", "__seed__": "0542"}}, {"seed": 543, "data": {"p1_how_many": "13", "p1_a": "9.51", "p1_b": "9.52", "p1_numbers": "9.5105, 9.511, 9.5115, 9.512, 9.5125, 9.513, 9.5135, 9.514, 9.515, 9.516, 9.517, 9.518, and 9.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.511", "9.512", "9.513", "9.514", "9.515", "9.516", "9.517", "9.517999999999999", "9.519"], "p1_2_xs": ["9.5105", "9.5115", "9.512500000000001", "9.5135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}112}{12{,}000}, \\dfrac{3{,}177}{12{,}000}, \\dfrac{3{,}256}{12{,}000}, \\dfrac{3{,}405}{12{,}000}, \\dfrac{3{,}484}{12{,}000}, \\dfrac{3{,}510}{12{,}000}, \\dfrac{3{,}613}{12{,}000}, \\dfrac{3{,}645}{12{,}000}, \\dfrac{3{,}932}{12{,}000}, \\dfrac{3{,}964}{12{,}000}, \\text{ and } \\dfrac{3{,}966}{12{,}000}", "__seed__": "0543"}}, {"seed": 544, "data": {"p1_how_many": "11", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.615, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995", "7.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\text{ and } \\dfrac{358}{420}", "__seed__": "0544"}}, {"seed": 545, "data": {"p1_how_many": "12", "p1_a": "2.35", "p1_b": "2.36", "p1_numbers": "2.3505, 2.351, 2.3515, 2.352, 2.3525, 2.353, 2.354, 2.355, 2.356, 2.357, 2.358, and 2.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.351", "2.352", "2.353", "2.354", "2.355", "2.356", "2.357", "2.358", "2.359"], "p1_2_xs": ["2.3505000000000003", "2.3515", "2.3525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{521}{3{,}000}, \\dfrac{525}{3{,}000}, \\dfrac{529}{3{,}000}, \\dfrac{551}{3{,}000}, \\dfrac{577}{3{,}000}, \\dfrac{583}{3{,}000}, \\dfrac{590}{3{,}000}, \\dfrac{591}{3{,}000}, \\text{ and } \\dfrac{593}{3{,}000}", "__seed__": "0545"}}, {"seed": 546, "data": {"p1_how_many": "14", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.525, 1.53, 1.535, 1.54, 1.545, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515", "1.525", "1.535", "1.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}250}{5{,}600}, \\dfrac{3{,}252}{5{,}600}, \\dfrac{3{,}308}{5{,}600}, \\dfrac{3{,}328}{5{,}600}, \\dfrac{3{,}361}{5{,}600}, \\dfrac{3{,}392}{5{,}600}, \\dfrac{3{,}456}{5{,}600}, \\dfrac{3{,}469}{5{,}600}, \\dfrac{3{,}471}{5{,}600}, \\dfrac{3{,}473}{5{,}600}, \\text{ and } \\dfrac{3{,}483}{5{,}600}", "__seed__": "0546"}}, {"seed": 547, "data": {"p1_how_many": "10", "p1_a": "4.95", "p1_b": "4.96", "p1_numbers": "4.9505, 4.951, 4.952, 4.953, 4.954, 4.955, 4.956, 4.957, 4.958, and 4.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.9510000000000005", "4.952", "4.953", "4.954", "4.955", "4.956", "4.957", "4.958", "4.9590000000000005"], "p1_2_xs": ["4.9505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}750}{20{,}000}, \\dfrac{5{,}835}{20{,}000}, \\dfrac{6{,}284}{20{,}000}, \\dfrac{6{,}469}{20{,}000}, \\dfrac{6{,}884}{20{,}000}, \\dfrac{7{,}438}{20{,}000}, \\text{ and } \\dfrac{7{,}631}{20{,}000}", "__seed__": "0547"}}, {"seed": 548, "data": {"p1_how_many": "13", "p1_a": "4.66", "p1_b": "4.67", "p1_numbers": "4.6605, 4.661, 4.6615, 4.662, 4.6625, 4.663, 4.6635, 4.664, 4.665, 4.666, 4.667, 4.668, and 4.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.6610000000000005", "4.662", "4.663", "4.664", "4.665", "4.666", "4.667", "4.668", "4.6690000000000005"], "p1_2_xs": ["4.6605", "4.6615", "4.6625", "4.6635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}111}{42{,}000}, \\dfrac{30{,}553}{42{,}000}, \\dfrac{31{,}272}{42{,}000}, \\dfrac{32{,}273}{42{,}000}, \\dfrac{32{,}735}{42{,}000}, \\dfrac{32{,}940}{42{,}000}, \\dfrac{32{,}994}{42{,}000}, \\dfrac{33{,}194}{42{,}000}, \\dfrac{33{,}506}{42{,}000}, \\dfrac{33{,}944}{42{,}000}, \\text{ and } \\dfrac{34{,}136}{42{,}000}", "__seed__": "0548"}}, {"seed": 549, "data": {"p1_how_many": "12", "p1_a": "2.87", "p1_b": "2.88", "p1_numbers": "2.8705, 2.871, 2.8715, 2.872, 2.8725, 2.873, 2.874, 2.875, 2.876, 2.877, 2.878, and 2.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.871", "2.872", "2.873", "2.874", "2.875", "2.876", "2.8770000000000002", "2.878", "2.879"], "p1_2_xs": ["2.8705000000000003", "2.8715", "2.8725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}131}{3{,}500}, \\dfrac{2{,}174}{3{,}500}, \\dfrac{2{,}203}{3{,}500}, \\dfrac{2{,}223}{3{,}500}, \\dfrac{2{,}325}{3{,}500}, \\dfrac{2{,}342}{3{,}500}, \\text{ and } \\dfrac{2{,}529}{3{,}500}", "__seed__": "0549"}}, {"seed": 550, "data": {"p1_how_many": "11", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.3005, 3.301, 3.3015, 3.302, 3.303, 3.304, 3.305, 3.306, 3.307, 3.308, and 3.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.3009999999999997", "3.3019999999999996", "3.303", "3.304", "3.3049999999999997", "3.3059999999999996", "3.307", "3.308", "3.3089999999999997"], "p1_2_xs": ["3.3005", "3.3015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{72}{420}, \\dfrac{84}{420}, \\dfrac{85}{420}, \\dfrac{88}{420}, \\dfrac{94}{420}, \\dfrac{105}{420}, \\dfrac{107}{420}, \\text{ and } \\dfrac{117}{420}", "__seed__": "0550"}}, {"seed": 551, "data": {"p1_how_many": "14", "p1_a": "7.01", "p1_b": "7.02", "p1_numbers": "7.0105, 7.011, 7.0115, 7.012, 7.0125, 7.013, 7.0135, 7.014, 7.0145, 7.015, 7.016, 7.017, 7.018, and 7.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.011", "7.012", "7.013", "7.013999999999999", "7.015", "7.016", "7.0169999999999995", "7.018", "7.019"], "p1_2_xs": ["7.0104999999999995", "7.0115", "7.012499999999999", "7.0135", "7.014499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}812}{15{,}000}, \\dfrac{6{,}975}{15{,}000}, \\dfrac{7{,}146}{15{,}000}, \\dfrac{7{,}922}{15{,}000}, \\dfrac{7{,}931}{15{,}000}, \\dfrac{8{,}248}{15{,}000}, \\dfrac{8{,}672}{15{,}000}, \\dfrac{8{,}725}{15{,}000}, \\dfrac{8{,}741}{15{,}000}, \\dfrac{9{,}355}{15{,}000}, \\dfrac{9{,}393}{15{,}000}, \\text{ and } \\dfrac{9{,}603}{15{,}000}", "__seed__": "0551"}}, {"seed": 552, "data": {"p1_how_many": "13", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.325, 8.33, 8.335, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001", "8.325000000000001", "8.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}406}{6{,}300}, \\dfrac{1{,}493}{6{,}300}, \\dfrac{1{,}616}{6{,}300}, \\dfrac{1{,}642}{6{,}300}, \\dfrac{1{,}655}{6{,}300}, \\dfrac{1{,}659}{6{,}300}, \\dfrac{1{,}737}{6{,}300}, \\text{ and } \\dfrac{1{,}751}{6{,}300}", "__seed__": "0552"}}, {"seed": 553, "data": {"p1_how_many": "11", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}236}{12{,}000}, \\dfrac{3{,}354}{12{,}000}, \\dfrac{3{,}366}{12{,}000}, \\dfrac{3{,}405}{12{,}000}, \\dfrac{3{,}502}{12{,}000}, \\dfrac{3{,}829}{12{,}000}, \\text{ and } \\dfrac{3{,}913}{12{,}000}", "__seed__": "0553"}}, {"seed": 554, "data": {"p1_how_many": "14", "p1_a": "7.03", "p1_b": "7.04", "p1_numbers": "7.0305, 7.031, 7.0315, 7.032, 7.0325, 7.033, 7.0335, 7.034, 7.0345, 7.035, 7.036, 7.037, 7.038, and 7.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.031000000000001", "7.032", "7.033", "7.034", "7.035", "7.0360000000000005", "7.037", "7.038", "7.039000000000001"], "p1_2_xs": ["7.0305", "7.0315", "7.0325", "7.0335", "7.0344999999999995"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{739}{4{,}200}, \\dfrac{815}{4{,}200}, \\dfrac{817}{4{,}200}, \\dfrac{819}{4{,}200}, \\dfrac{859}{4{,}200}, \\dfrac{967}{4{,}200}, \\dfrac{1{,}000}{4{,}200}, \\dfrac{1{,}011}{4{,}200}, \\dfrac{1{,}063}{4{,}200}, \\dfrac{1{,}069}{4{,}200}, \\dfrac{1{,}089}{4{,}200}, \\text{ and } \\dfrac{1{,}125}{4{,}200}", "__seed__": "0554"}}, {"seed": 555, "data": {"p1_how_many": "13", "p1_a": "4.15", "p1_b": "4.16", "p1_numbers": "4.1505, 4.151, 4.1515, 4.152, 4.1525, 4.153, 4.1535, 4.154, 4.155, 4.156, 4.157, 4.158, and 4.159", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.151000000000001", "4.152", "4.1530000000000005", "4.154", "4.155", "4.156000000000001", "4.157", "4.158", "4.159000000000001"], "p1_2_xs": ["4.1505", "4.1515", "4.1525", "4.1535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{618}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{648}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{676}{4{,}200}, \\dfrac{681}{4{,}200}, \\text{ and } \\dfrac{689}{4{,}200}", "__seed__": "0555"}}, {"seed": 556, "data": {"p1_how_many": "11", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}507}{5{,}600}, \\dfrac{3{,}525}{5{,}600}, \\dfrac{3{,}526}{5{,}600}, \\dfrac{3{,}606}{5{,}600}, \\dfrac{3{,}737}{5{,}600}, \\dfrac{3{,}847}{5{,}600}, \\dfrac{3{,}881}{5{,}600}, \\dfrac{3{,}912}{5{,}600}, \\dfrac{3{,}919}{5{,}600}, \\text{ and } \\dfrac{3{,}987}{5{,}600}", "__seed__": "0556"}}, {"seed": 557, "data": {"p1_how_many": "10", "p1_a": "5.83", "p1_b": "5.84", "p1_numbers": "5.8305, 5.831, 5.832, 5.833, 5.834, 5.835, 5.836, 5.837, 5.838, and 5.839", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.831", "5.832", "5.833", "5.834", "5.835", "5.836", "5.837", "5.838", "5.839"], "p1_2_xs": ["5.8305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}586}{56{,}000}, \\dfrac{21{,}991}{56{,}000}, \\dfrac{22{,}019}{56{,}000}, \\dfrac{22{,}051}{56{,}000}, \\dfrac{22{,}360}{56{,}000}, \\dfrac{22{,}368}{56{,}000}, \\dfrac{22{,}809}{56{,}000}, \\dfrac{23{,}138}{56{,}000}, \\dfrac{23{,}603}{56{,}000}, \\text{ and } \\dfrac{23{,}885}{56{,}000}", "__seed__": "0557"}}, {"seed": 558, "data": {"p1_how_many": "11", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}028}{20{,}000}, \\dfrac{12{,}490}{20{,}000}, \\dfrac{13{,}560}{20{,}000}, \\dfrac{13{,}868}{20{,}000}, \\dfrac{14{,}433}{20{,}000}, \\dfrac{14{,}436}{20{,}000}, \\dfrac{14{,}520}{20{,}000}, \\dfrac{14{,}660}{20{,}000}, \\dfrac{14{,}682}{20{,}000}, \\text{ and } \\dfrac{14{,}883}{20{,}000}", "__seed__": "0558"}}, {"seed": 559, "data": {"p1_how_many": "12", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}001}{20{,}000}, \\dfrac{5{,}026}{20{,}000}, \\dfrac{5{,}039}{20{,}000}, \\dfrac{5{,}754}{20{,}000}, \\dfrac{6{,}389}{20{,}000}, \\dfrac{6{,}817}{20{,}000}, \\dfrac{6{,}829}{20{,}000}, \\dfrac{6{,}970}{20{,}000}, \\dfrac{7{,}231}{20{,}000}, \\dfrac{7{,}826}{20{,}000}, \\dfrac{7{,}848}{20{,}000}, \\text{ and } \\dfrac{7{,}954}{20{,}000}", "__seed__": "0559"}}, {"seed": 560, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}029}{35{,}000}, \\dfrac{14{,}073}{35{,}000}, \\dfrac{14{,}123}{35{,}000}, \\dfrac{14{,}151}{35{,}000}, \\dfrac{14{,}504}{35{,}000}, \\dfrac{14{,}542}{35{,}000}, \\dfrac{14{,}583}{35{,}000}, \\dfrac{14{,}726}{35{,}000}, \\dfrac{14{,}730}{35{,}000}, \\dfrac{14{,}788}{35{,}000}, \\dfrac{14{,}954}{35{,}000}, \\text{ and } \\dfrac{14{,}973}{35{,}000}", "__seed__": "0560"}}, {"seed": 561, "data": {"p1_how_many": "12", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}478}{42{,}000}, \\dfrac{7{,}504}{42{,}000}, \\dfrac{7{,}616}{42{,}000}, \\dfrac{7{,}837}{42{,}000}, \\dfrac{8{,}780}{42{,}000}, \\dfrac{10{,}378}{42{,}000}, \\dfrac{10{,}388}{42{,}000}, \\dfrac{11{,}038}{42{,}000}, \\dfrac{11{,}515}{42{,}000}, \\dfrac{11{,}549}{42{,}000}, \\text{ and } \\dfrac{11{,}756}{42{,}000}", "__seed__": "0561"}}, {"seed": 562, "data": {"p1_how_many": "12", "p1_a": "6.4", "p1_b": "6.5", "p1_numbers": "6.405, 6.41, 6.415, 6.42, 6.425, 6.43, 6.44, 6.45, 6.46, 6.47, 6.48, and 6.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.41", "6.42", "6.430000000000001", "6.44", "6.45", "6.46", "6.470000000000001", "6.48", "6.49"], "p1_2_xs": ["6.405", "6.415", "6.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, \\dfrac{243}{300}, \\dfrac{244}{300}, \\dfrac{245}{300}, \\dfrac{246}{300}, \\dfrac{247}{300}, \\dfrac{248}{300}, \\text{ and } \\dfrac{249}{300}", "__seed__": "0562"}}, {"seed": 563, "data": {"p1_how_many": "12", "p1_a": "8.14", "p1_b": "8.15", "p1_numbers": "8.1405, 8.141, 8.1415, 8.142, 8.1425, 8.143, 8.144, 8.145, 8.146, 8.147, 8.148, and 8.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.141", "8.142000000000001", "8.143", "8.144", "8.145000000000001", "8.146", "8.147", "8.148", "8.149000000000001"], "p1_2_xs": ["8.140500000000001", "8.1415", "8.142500000000002"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}426}{6{,}300}, \\dfrac{1{,}466}{6{,}300}, \\dfrac{1{,}499}{6{,}300}, \\dfrac{1{,}557}{6{,}300}, \\dfrac{1{,}563}{6{,}300}, \\dfrac{1{,}628}{6{,}300}, \\dfrac{1{,}644}{6{,}300}, \\dfrac{1{,}646}{6{,}300}, \\dfrac{1{,}793}{6{,}300}, \\text{ and } \\dfrac{1{,}798}{6{,}300}", "__seed__": "0563"}}, {"seed": 564, "data": {"p1_how_many": "13", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{612}{4{,}200}, \\dfrac{616}{4{,}200}, \\dfrac{620}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{629}{4{,}200}, \\dfrac{635}{4{,}200}, \\dfrac{644}{4{,}200}, \\dfrac{647}{4{,}200}, \\dfrac{653}{4{,}200}, \\text{ and } \\dfrac{680}{4{,}200}", "__seed__": "0564"}}, {"seed": 565, "data": {"p1_how_many": "12", "p1_a": "6.12", "p1_b": "6.13", "p1_numbers": "6.1205, 6.121, 6.1215, 6.122, 6.1225, 6.123, 6.124, 6.125, 6.126, 6.127, 6.128, and 6.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.121", "6.122", "6.123", "6.124", "6.125", "6.126", "6.127", "6.128", "6.1290000000000004"], "p1_2_xs": ["6.1205", "6.1215", "6.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{719}{4{,}200}, \\dfrac{893}{4{,}200}, \\dfrac{913}{4{,}200}, \\dfrac{939}{4{,}200}, \\dfrac{964}{4{,}200}, \\dfrac{1{,}000}{4{,}200}, \\dfrac{1{,}056}{4{,}200}, \\dfrac{1{,}097}{4{,}200}, \\dfrac{1{,}106}{4{,}200}, \\dfrac{1{,}115}{4{,}200}, \\text{ and } \\dfrac{1{,}189}{4{,}200}", "__seed__": "0565"}}, {"seed": 566, "data": {"p1_how_many": "10", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.52, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{795}{3{,}500}, \\dfrac{810}{3{,}500}, \\dfrac{822}{3{,}500}, \\dfrac{853}{3{,}500}, \\dfrac{854}{3{,}500}, \\dfrac{966}{3{,}500}, \\text{ and } \\dfrac{991}{3{,}500}", "__seed__": "0566"}}, {"seed": 567, "data": {"p1_how_many": "13", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.325, 8.33, 8.335, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001", "8.325000000000001", "8.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{500}{770}, \\dfrac{505}{770}, \\dfrac{518}{770}, \\dfrac{550}{770}, \\dfrac{557}{770}, \\dfrac{579}{770}, \\dfrac{599}{770}, \\text{ and } \\dfrac{600}{770}", "__seed__": "0567"}}, {"seed": 568, "data": {"p1_how_many": "13", "p1_a": "4.71", "p1_b": "4.72", "p1_numbers": "4.7105, 4.711, 4.7115, 4.712, 4.7125, 4.713, 4.7135, 4.714, 4.715, 4.716, 4.717, 4.718, and 4.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.711", "4.712", "4.713", "4.7139999999999995", "4.715", "4.716", "4.717", "4.718", "4.719"], "p1_2_xs": ["4.7105", "4.7115", "4.7124999999999995", "4.7135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{307}{1{,}200}, \\dfrac{309}{1{,}200}, \\dfrac{314}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{362}{1{,}200}, \\dfrac{368}{1{,}200}, \\dfrac{370}{1{,}200}, \\dfrac{374}{1{,}200}, \\dfrac{375}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0568"}}, {"seed": 569, "data": {"p1_how_many": "13", "p1_a": "3.12", "p1_b": "3.13", "p1_numbers": "3.1205, 3.121, 3.1215, 3.122, 3.1225, 3.123, 3.1235, 3.124, 3.125, 3.126, 3.127, 3.128, and 3.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.121", "3.122", "3.123", "3.124", "3.125", "3.126", "3.1270000000000002", "3.128", "3.129"], "p1_2_xs": ["3.1205000000000003", "3.1215", "3.1225", "3.1235000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{803}{1{,}200}, \\dfrac{828}{1{,}200}, \\dfrac{842}{1{,}200}, \\dfrac{844}{1{,}200}, \\dfrac{847}{1{,}200}, \\dfrac{849}{1{,}200}, \\dfrac{863}{1{,}200}, \\dfrac{875}{1{,}200}, \\dfrac{877}{1{,}200}, \\dfrac{882}{1{,}200}, \\text{ and } \\dfrac{889}{1{,}200}", "__seed__": "0569"}}, {"seed": 570, "data": {"p1_how_many": "14", "p1_a": "7.04", "p1_b": "7.05", "p1_numbers": "7.0405, 7.041, 7.0415, 7.042, 7.0425, 7.043, 7.0435, 7.044, 7.0445, 7.045, 7.046, 7.047, 7.048, and 7.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.041", "7.042", "7.043", "7.044", "7.045", "7.046", "7.047", "7.048", "7.049"], "p1_2_xs": ["7.0405", "7.0415", "7.0424999999999995", "7.0435", "7.044499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}052}{77{,}000}, \\dfrac{42{,}479}{77{,}000}, \\dfrac{42{,}694}{77{,}000}, \\dfrac{43{,}171}{77{,}000}, \\dfrac{44{,}397}{77{,}000}, \\dfrac{44{,}912}{77{,}000}, \\dfrac{48{,}293}{77{,}000}, \\dfrac{48{,}617}{77{,}000}, \\dfrac{49{,}973}{77{,}000}, \\dfrac{51{,}378}{77{,}000}, \\text{ and } \\dfrac{54{,}596}{77{,}000}", "__seed__": "0570"}}, {"seed": 571, "data": {"p1_how_many": "11", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{525}{2{,}000}, \\dfrac{568}{2{,}000}, \\dfrac{598}{2{,}000}, \\dfrac{617}{2{,}000}, \\dfrac{669}{2{,}000}, \\dfrac{745}{2{,}000}, \\text{ and } \\dfrac{792}{2{,}000}", "__seed__": "0571"}}, {"seed": 572, "data": {"p1_how_many": "12", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{74}{150}, \\dfrac{75}{150}, \\dfrac{87}{150}, \\dfrac{88}{150}, \\dfrac{89}{150}, \\dfrac{91}{150}, \\dfrac{92}{150}, \\text{ and } \\dfrac{97}{150}", "__seed__": "0572"}}, {"seed": 573, "data": {"p1_how_many": "10", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}505}{4{,}200}, \\dfrac{3{,}514}{4{,}200}, \\dfrac{3{,}518}{4{,}200}, \\dfrac{3{,}524}{4{,}200}, \\dfrac{3{,}527}{4{,}200}, \\dfrac{3{,}536}{4{,}200}, \\dfrac{3{,}542}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}567}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\dfrac{3{,}596}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0573"}}, {"seed": 574, "data": {"p1_how_many": "10", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}061}{20{,}000}, \\dfrac{12{,}266}{20{,}000}, \\dfrac{12{,}334}{20{,}000}, \\dfrac{12{,}693}{20{,}000}, \\dfrac{13{,}094}{20{,}000}, \\dfrac{13{,}140}{20{,}000}, \\dfrac{13{,}572}{20{,}000}, \\dfrac{14{,}423}{20{,}000}, \\dfrac{14{,}434}{20{,}000}, \\text{ and } \\dfrac{14{,}836}{20{,}000}", "__seed__": "0574"}}, {"seed": 575, "data": {"p1_how_many": "11", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}024}{42{,}000}, \\dfrac{35{,}050}{42{,}000}, \\dfrac{35{,}362}{42{,}000}, \\dfrac{35{,}545}{42{,}000}, \\dfrac{35{,}640}{42{,}000}, \\dfrac{35{,}682}{42{,}000}, \\dfrac{35{,}842}{42{,}000}, \\text{ and } \\dfrac{35{,}984}{42{,}000}", "__seed__": "0575"}}, {"seed": 576, "data": {"p1_how_many": "13", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{76}{420}, \\dfrac{77}{420}, \\dfrac{85}{420}, \\dfrac{93}{420}, \\dfrac{98}{420}, \\dfrac{99}{420}, \\dfrac{112}{420}, \\dfrac{115}{420}, \\text{ and } \\dfrac{119}{420}", "__seed__": "0576"}}, {"seed": 577, "data": {"p1_how_many": "12", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}257}{2{,}000}, \\dfrac{1{,}299}{2{,}000}, \\dfrac{1{,}301}{2{,}000}, \\dfrac{1{,}355}{2{,}000}, \\dfrac{1{,}367}{2{,}000}, \\dfrac{1{,}373}{2{,}000}, \\dfrac{1{,}449}{2{,}000}, \\text{ and } \\dfrac{1{,}464}{2{,}000}", "__seed__": "0577"}}, {"seed": 578, "data": {"p1_how_many": "13", "p1_a": "7.64", "p1_b": "7.65", "p1_numbers": "7.6405, 7.641, 7.6415, 7.642, 7.6425, 7.643, 7.6435, 7.644, 7.645, 7.646, 7.647, 7.648, and 7.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.641", "7.6419999999999995", "7.643", "7.643999999999999", "7.645", "7.646", "7.646999999999999", "7.648", "7.649"], "p1_2_xs": ["7.640499999999999", "7.6415", "7.642499999999999", "7.6434999999999995"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}202}{2{,}000}, \\dfrac{1{,}213}{2{,}000}, \\dfrac{1{,}336}{2{,}000}, \\dfrac{1{,}395}{2{,}000}, \\dfrac{1{,}404}{2{,}000}, \\dfrac{1{,}424}{2{,}000}, \\dfrac{1{,}462}{2{,}000}, \\text{ and } \\dfrac{1{,}485}{2{,}000}", "__seed__": "0578"}}, {"seed": 579, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{51}{300}, \\dfrac{52}{300}, \\dfrac{53}{300}, \\dfrac{54}{300}, \\dfrac{55}{300}, \\dfrac{56}{300}, \\dfrac{57}{300}, \\dfrac{58}{300}, \\text{ and } \\dfrac{59}{300}", "__seed__": "0579"}}, {"seed": 580, "data": {"p1_how_many": "14", "p1_a": "4.32", "p1_b": "4.33", "p1_numbers": "4.3205, 4.321, 4.3215, 4.322, 4.3225, 4.323, 4.3235, 4.324, 4.3245, 4.325, 4.326, 4.327, 4.328, and 4.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.321000000000001", "4.322", "4.323", "4.324", "4.325", "4.3260000000000005", "4.327", "4.328", "4.329000000000001"], "p1_2_xs": ["4.3205", "4.3215", "4.3225", "4.3235", "4.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{52}{200}, \\dfrac{57}{200}, \\dfrac{58}{200}, \\dfrac{72}{200}, \\dfrac{74}{200}, \\dfrac{75}{200}, \\dfrac{77}{200}, \\text{ and } \\dfrac{78}{200}", "__seed__": "0580"}}, {"seed": 581, "data": {"p1_how_many": "12", "p1_a": "9.12", "p1_b": "9.13", "p1_numbers": "9.1205, 9.121, 9.1215, 9.122, 9.1225, 9.123, 9.124, 9.125, 9.126, 9.127, 9.128, and 9.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.120999999999999", "9.122", "9.123", "9.123999999999999", "9.125", "9.126", "9.126999999999999", "9.127999999999998", "9.129"], "p1_2_xs": ["9.1205", "9.1215", "9.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{504}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{512}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{536}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{547}{1{,}500}, \\dfrac{548}{1{,}500}, \\dfrac{591}{1{,}500}, \\text{ and } \\dfrac{595}{1{,}500}", "__seed__": "0581"}}, {"seed": 582, "data": {"p1_how_many": "10", "p1_a": "4.02", "p1_b": "4.03", "p1_numbers": "4.0205, 4.021, 4.022, 4.023, 4.024, 4.025, 4.026, 4.027, 4.028, and 4.029", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.021", "4.021999999999999", "4.023", "4.023999999999999", "4.0249999999999995", "4.026", "4.026999999999999", "4.028", "4.029"], "p1_2_xs": ["4.020499999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{45{,}174}{77{,}000}, \\dfrac{46{,}256}{77{,}000}, \\dfrac{46{,}808}{77{,}000}, \\dfrac{47{,}751}{77{,}000}, \\dfrac{47{,}963}{77{,}000}, \\dfrac{48{,}391}{77{,}000}, \\dfrac{49{,}502}{77{,}000}, \\dfrac{50{,}683}{77{,}000}, \\dfrac{51{,}258}{77{,}000}, \\dfrac{53{,}747}{77{,}000}, \\text{ and } \\dfrac{54{,}216}{77{,}000}", "__seed__": "0582"}}, {"seed": 583, "data": {"p1_how_many": "13", "p1_a": "4.95", "p1_b": "4.96", "p1_numbers": "4.9505, 4.951, 4.9515, 4.952, 4.9525, 4.953, 4.9535, 4.954, 4.955, 4.956, 4.957, 4.958, and 4.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.9510000000000005", "4.952", "4.953", "4.954", "4.955", "4.956", "4.957", "4.958", "4.9590000000000005"], "p1_2_xs": ["4.9505", "4.9515", "4.9525", "4.9535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}491}{12{,}000}, \\dfrac{3{,}500}{12{,}000}, \\dfrac{3{,}511}{12{,}000}, \\dfrac{3{,}522}{12{,}000}, \\dfrac{3{,}531}{12{,}000}, \\dfrac{3{,}647}{12{,}000}, \\dfrac{3{,}665}{12{,}000}, \\dfrac{3{,}673}{12{,}000}, \\dfrac{3{,}789}{12{,}000}, \\dfrac{3{,}858}{12{,}000}, \\dfrac{3{,}928}{12{,}000}, \\text{ and } \\dfrac{3{,}935}{12{,}000}", "__seed__": "0583"}}, {"seed": 584, "data": {"p1_how_many": "11", "p1_a": "7.67", "p1_b": "7.68", "p1_numbers": "7.6705, 7.671, 7.6715, 7.672, 7.673, 7.674, 7.675, 7.676, 7.677, 7.678, and 7.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.671", "7.672", "7.673", "7.6739999999999995", "7.675", "7.676", "7.677", "7.678", "7.679"], "p1_2_xs": ["7.6705", "7.6715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}069}{42{,}000}, \\dfrac{6{,}116}{42{,}000}, \\dfrac{6{,}231}{42{,}000}, \\dfrac{6{,}311}{42{,}000}, \\dfrac{6{,}585}{42{,}000}, \\dfrac{6{,}593}{42{,}000}, \\dfrac{6{,}655}{42{,}000}, \\dfrac{6{,}708}{42{,}000}, \\dfrac{6{,}782}{42{,}000}, \\text{ and } \\dfrac{6{,}903}{42{,}000}", "__seed__": "0584"}}, {"seed": 585, "data": {"p1_how_many": "11", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}003}{42{,}000}, \\dfrac{6{,}091}{42{,}000}, \\dfrac{6{,}191}{42{,}000}, \\dfrac{6{,}232}{42{,}000}, \\dfrac{6{,}489}{42{,}000}, \\dfrac{6{,}592}{42{,}000}, \\dfrac{6{,}697}{42{,}000}, \\dfrac{6{,}787}{42{,}000}, \\dfrac{6{,}874}{42{,}000}, \\dfrac{6{,}884}{42{,}000}, \\dfrac{6{,}934}{42{,}000}, \\text{ and } \\dfrac{6{,}960}{42{,}000}", "__seed__": "0585"}}, {"seed": 586, "data": {"p1_how_many": "13", "p1_a": "4.6", "p1_b": "4.7", "p1_numbers": "4.605, 4.61, 4.615, 4.62, 4.625, 4.63, 4.635, 4.64, 4.65, 4.66, 4.67, 4.68, and 4.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.609999999999999", "4.619999999999999", "4.63", "4.64", "4.6499999999999995", "4.659999999999999", "4.67", "4.68", "4.6899999999999995"], "p1_2_xs": ["4.6049999999999995", "4.614999999999999", "4.624999999999999", "4.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}035}{30{,}000}, \\dfrac{24{,}067}{30{,}000}, \\dfrac{24{,}125}{30{,}000}, \\dfrac{24{,}138}{30{,}000}, \\dfrac{24{,}182}{30{,}000}, \\dfrac{24{,}394}{30{,}000}, \\dfrac{24{,}536}{30{,}000}, \\dfrac{24{,}551}{30{,}000}, \\dfrac{24{,}613}{30{,}000}, \\dfrac{24{,}664}{30{,}000}, \\dfrac{24{,}786}{30{,}000}, \\text{ and } \\dfrac{24{,}830}{30{,}000}", "__seed__": "0586"}}, {"seed": 587, "data": {"p1_how_many": "14", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.545, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997", "3.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{606}{4{,}200}, \\dfrac{614}{4{,}200}, \\dfrac{629}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{651}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{672}{4{,}200}, \\dfrac{686}{4{,}200}, \\dfrac{690}{4{,}200}, 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"__seed__": "0588"}}, {"seed": 589, "data": {"p1_how_many": "12", "p1_a": "3.87", "p1_b": "3.88", "p1_numbers": "3.8705, 3.871, 3.8715, 3.872, 3.8725, 3.873, 3.874, 3.875, 3.876, 3.877, 3.878, and 3.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.871", "3.872", "3.873", "3.874", "3.875", "3.876", "3.8770000000000002", "3.878", "3.879"], "p1_2_xs": ["3.8705000000000003", "3.8715", "3.8725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}100}{56{,}000}, \\dfrac{35{,}269}{56{,}000}, \\dfrac{35{,}369}{56{,}000}, \\dfrac{35{,}975}{56{,}000}, \\dfrac{37{,}847}{56{,}000}, \\dfrac{38{,}101}{56{,}000}, \\dfrac{38{,}256}{56{,}000}, \\dfrac{39{,}015}{56{,}000}, \\dfrac{39{,}466}{56{,}000}, \\text{ and } \\dfrac{39{,}815}{56{,}000}", "__seed__": "0589"}}, {"seed": 590, "data": {"p1_how_many": "11", "p1_a": 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the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}557}{35{,}000}, \\dfrac{15{,}621}{35{,}000}, \\dfrac{17{,}112}{35{,}000}, \\dfrac{18{,}570}{35{,}000}, \\dfrac{18{,}571}{35{,}000}, \\dfrac{18{,}624}{35{,}000}, \\dfrac{18{,}712}{35{,}000}, \\text{ and } \\dfrac{20{,}771}{35{,}000}", "__seed__": "0592"}}, {"seed": 593, "data": {"p1_how_many": "10", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.72, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}519}{4{,}200}, 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"num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{51}{300}, \\dfrac{53}{300}, \\dfrac{54}{300}, \\dfrac{55}{300}, \\dfrac{56}{300}, \\dfrac{57}{300}, \\dfrac{58}{300}, \\text{ and } \\dfrac{59}{300}", "__seed__": "0598"}}, {"seed": 599, "data": {"p1_how_many": "11", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.73, 4.74, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{762}{4{,}200}, \\dfrac{776}{4{,}200}, \\dfrac{787}{4{,}200}, 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\\dfrac{35{,}640}{42{,}000}, \\dfrac{35{,}656}{42{,}000}, \\dfrac{35{,}927}{42{,}000}, \\dfrac{35{,}936}{42{,}000}, \\dfrac{35{,}976}{42{,}000}, \\text{ and } \\dfrac{35{,}984}{42{,}000}", "__seed__": "0601"}}, {"seed": 602, "data": {"p1_how_many": "12", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{127}{200}, \\dfrac{131}{200}, \\dfrac{132}{200}, \\dfrac{133}{200}, \\dfrac{138}{200}, \\dfrac{139}{200}, \\text{ and } 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"10", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0604"}}, {"seed": 605, "data": {"p1_how_many": "10", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.42, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", 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"10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}051}{20{,}000}, \\dfrac{12{,}342}{20{,}000}, \\dfrac{12{,}358}{20{,}000}, \\dfrac{12{,}805}{20{,}000}, \\dfrac{12{,}860}{20{,}000}, \\dfrac{13{,}031}{20{,}000}, \\dfrac{13{,}253}{20{,}000}, \\dfrac{13{,}472}{20{,}000}, \\dfrac{14{,}526}{20{,}000}, \\text{ and } \\dfrac{14{,}551}{20{,}000}", "__seed__": "0608"}}, {"seed": 609, "data": {"p1_how_many": "12", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.415, 3.42, 3.425, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996", "3.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}175}{15{,}000}, \\dfrac{5{,}228}{15{,}000}, \\dfrac{5{,}267}{15{,}000}, \\dfrac{5{,}348}{15{,}000}, \\dfrac{5{,}416}{15{,}000}, \\dfrac{5{,}476}{15{,}000}, \\dfrac{5{,}601}{15{,}000}, \\dfrac{5{,}705}{15{,}000}, \\dfrac{5{,}758}{15{,}000}, \\dfrac{5{,}793}{15{,}000}, \\dfrac{5{,}942}{15{,}000}, \\text{ and } \\dfrac{5{,}982}{15{,}000}", "__seed__": "0609"}}, {"seed": 610, "data": {"p1_how_many": "14", "p1_a": "9.92", "p1_b": "9.93", "p1_numbers": "9.9205, 9.921, 9.9215, 9.922, 9.9225, 9.923, 9.9235, 9.924, 9.9245, 9.925, 9.926, 9.927, 9.928, and 9.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.921", "9.922", "9.923", "9.924", "9.925", "9.926", "9.927", "9.927999999999999", "9.929"], "p1_2_xs": ["9.9205", "9.9215", "9.922500000000001", "9.9235", "9.9245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}041}{42{,}000}, \\dfrac{6{,}103}{42{,}000}, \\dfrac{6{,}121}{42{,}000}, \\dfrac{6{,}134}{42{,}000}, \\dfrac{6{,}249}{42{,}000}, \\dfrac{6{,}618}{42{,}000}, \\dfrac{6{,}648}{42{,}000}, \\dfrac{6{,}851}{42{,}000}, \\dfrac{6{,}862}{42{,}000}, \\dfrac{6{,}891}{42{,}000}, \\text{ and } \\dfrac{6{,}987}{42{,}000}", "__seed__": "0610"}}, {"seed": 611, "data": {"p1_how_many": "10", "p1_a": "2.16", "p1_b": "2.17", "p1_numbers": "2.1605, 2.161, 2.162, 2.163, 2.164, 2.165, 2.166, 2.167, 2.168, and 2.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.161", "2.162", "2.1630000000000003", "2.164", "2.165", "2.166", "2.1670000000000003", "2.168", "2.169"], "p1_2_xs": ["2.1605000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}403}{3{,}500}, \\dfrac{1{,}411}{3{,}500}, \\dfrac{1{,}416}{3{,}500}, \\dfrac{1{,}417}{3{,}500}, \\dfrac{1{,}420}{3{,}500}, \\dfrac{1{,}429}{3{,}500}, \\dfrac{1{,}457}{3{,}500}, \\dfrac{1{,}458}{3{,}500}, \\dfrac{1{,}464}{3{,}500}, \\dfrac{1{,}466}{3{,}500}, \\dfrac{1{,}471}{3{,}500}, \\text{ and } \\dfrac{1{,}475}{3{,}500}", "__seed__": "0611"}}, {"seed": 612, "data": {"p1_how_many": "10", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}061}{3{,}500}, \\dfrac{1{,}063}{3{,}500}, \\dfrac{1{,}070}{3{,}500}, \\dfrac{1{,}106}{3{,}500}, \\dfrac{1{,}111}{3{,}500}, \\dfrac{1{,}120}{3{,}500}, \\dfrac{1{,}169}{3{,}500}, \\dfrac{1{,}230}{3{,}500}, \\dfrac{1{,}236}{3{,}500}, \\dfrac{1{,}270}{3{,}500}, \\text{ and } \\dfrac{1{,}368}{3{,}500}", "__seed__": "0612"}}, {"seed": 613, "data": {"p1_how_many": "14", "p1_a": "8.75", "p1_b": "8.76", "p1_numbers": "8.7505, 8.751, 8.7515, 8.752, 8.7525, 8.753, 8.7535, 8.754, 8.7545, 8.755, 8.756, 8.757, 8.758, and 8.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.751", "8.752", "8.753", "8.754", "8.755", "8.756", "8.757", "8.758", "8.759"], "p1_2_xs": ["8.7505", "8.7515", "8.752500000000001", "8.7535", "8.7545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{141}{350}, \\dfrac{143}{350}, \\dfrac{144}{350}, \\dfrac{145}{350}, \\dfrac{146}{350}, \\dfrac{147}{350}, \\text{ and } \\dfrac{148}{350}", "__seed__": "0613"}}, {"seed": 614, "data": {"p1_how_many": "13", "p1_a": "3.07", "p1_b": "3.08", "p1_numbers": "3.0705, 3.071, 3.0715, 3.072, 3.0725, 3.073, 3.0735, 3.074, 3.075, 3.076, 3.077, 3.078, and 3.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.0709999999999997", "3.0719999999999996", "3.073", "3.074", "3.0749999999999997", "3.0759999999999996", "3.077", "3.078", "3.0789999999999997"], "p1_2_xs": ["3.0705", "3.0715", "3.0725", "3.0735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}828}{5{,}600}, \\dfrac{4{,}833}{5{,}600}, \\dfrac{4{,}844}{5{,}600}, \\dfrac{4{,}845}{5{,}600}, \\dfrac{4{,}849}{5{,}600}, \\dfrac{4{,}850}{5{,}600}, \\dfrac{4{,}867}{5{,}600}, \\dfrac{4{,}868}{5{,}600}, \\dfrac{4{,}880}{5{,}600}, \\dfrac{4{,}881}{5{,}600}, \\text{ and } \\dfrac{4{,}892}{5{,}600}", "__seed__": "0614"}}, {"seed": 615, "data": {"p1_how_many": "11", "p1_a": "8.67", "p1_b": "8.68", "p1_numbers": "8.6705, 8.671, 8.6715, 8.672, 8.673, 8.674, 8.675, 8.676, 8.677, 8.678, and 8.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.671", "8.672", "8.673", "8.674", "8.675", "8.676", "8.677", "8.677999999999999", "8.679"], "p1_2_xs": ["8.6705", "8.6715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}056}{56{,}000}, \\dfrac{48{,}089}{56{,}000}, \\dfrac{48{,}148}{56{,}000}, \\dfrac{48{,}173}{56{,}000}, \\dfrac{48{,}194}{56{,}000}, \\dfrac{48{,}283}{56{,}000}, \\dfrac{48{,}308}{56{,}000}, \\dfrac{48{,}395}{56{,}000}, \\dfrac{48{,}517}{56{,}000}, \\dfrac{48{,}784}{56{,}000}, \\text{ and } \\dfrac{48{,}828}{56{,}000}", "__seed__": "0615"}}, {"seed": 616, "data": {"p1_how_many": "14", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.4005, 5.401, 5.4015, 5.402, 5.4025, 5.403, 5.4035, 5.404, 5.4045, 5.405, 5.406, 5.407, 5.408, and 5.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.401000000000001", "5.402", "5.4030000000000005", "5.404", "5.405", "5.406000000000001", "5.407", "5.408", "5.409000000000001"], "p1_2_xs": ["5.4005", "5.4015", "5.4025", "5.4035", "5.4045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}046}{35{,}000}, \\dfrac{20{,}136}{35{,}000}, \\dfrac{20{,}302}{35{,}000}, \\dfrac{20{,}312}{35{,}000}, \\dfrac{20{,}319}{35{,}000}, \\dfrac{20{,}324}{35{,}000}, \\dfrac{20{,}502}{35{,}000}, \\dfrac{20{,}724}{35{,}000}, \\dfrac{20{,}824}{35{,}000}, \\text{ and } \\dfrac{20{,}916}{35{,}000}", "__seed__": 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"\\frac{1}{100}", "p1_1_xs": ["9.11", "9.12", "9.129999999999999", "9.139999999999999", "9.15", "9.16", "9.17", "9.18", "9.19"], "p1_2_xs": ["9.105", "9.115", "9.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}338}{20{,}000}, \\dfrac{15{,}379}{20{,}000}, \\dfrac{15{,}403}{20{,}000}, \\dfrac{15{,}643}{20{,}000}, \\dfrac{15{,}689}{20{,}000}, \\dfrac{15{,}780}{20{,}000}, \\text{ and } \\dfrac{15{,}885}{20{,}000}", "__seed__": "0618"}}, {"seed": 619, "data": {"p1_how_many": "13", "p1_a": "8.54", "p1_b": "8.55", "p1_numbers": "8.5405, 8.541, 8.5415, 8.542, 8.5425, 8.543, 8.5435, 8.544, 8.545, 8.546, 8.547, 8.548, and 8.549", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.540999999999999", "8.542", "8.543", "8.543999999999999", "8.545", "8.546", "8.546999999999999", "8.547999999999998", "8.549"], "p1_2_xs": ["8.5405", "8.5415", "8.5425", "8.5435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{614}{4{,}200}, \\dfrac{620}{4{,}200}, \\dfrac{634}{4{,}200}, \\dfrac{640}{4{,}200}, \\dfrac{645}{4{,}200}, \\dfrac{652}{4{,}200}, \\dfrac{653}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{687}{4{,}200}, \\dfrac{690}{4{,}200}, \\dfrac{695}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0619"}}, {"seed": 620, "data": {"p1_how_many": "11", "p1_a": "8.41", "p1_b": "8.42", "p1_numbers": "8.4105, 8.411, 8.4115, 8.412, 8.413, 8.414, 8.415, 8.416, 8.417, 8.418, and 8.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.411", "8.412", "8.413", "8.414", "8.415000000000001", "8.416", "8.417", "8.418", "8.419"], "p1_2_xs": ["8.4105", "8.4115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{610}{1{,}500}, \\dfrac{618}{1{,}500}, \\dfrac{627}{1{,}500}, \\dfrac{695}{1{,}500}, \\dfrac{716}{1{,}500}, \\dfrac{745}{1{,}500}, \\dfrac{754}{1{,}500}, \\dfrac{761}{1{,}500}, \\dfrac{787}{1{,}500}, \\dfrac{828}{1{,}500}, \\dfrac{991}{1{,}500}, \\text{ and } \\dfrac{994}{1{,}500}", "__seed__": "0620"}}, {"seed": 621, "data": {"p1_how_many": "13", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{710}{4{,}200}, \\dfrac{719}{4{,}200}, \\dfrac{720}{4{,}200}, \\dfrac{777}{4{,}200}, \\dfrac{836}{4{,}200}, \\dfrac{916}{4{,}200}, \\dfrac{929}{4{,}200}, \\dfrac{982}{4{,}200}, \\dfrac{1{,}134}{4{,}200}, \\text{ and } \\dfrac{1{,}168}{4{,}200}", "__seed__": "0621"}}, {"seed": 622, "data": {"p1_how_many": "14", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.535, 4.54, 4.545, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995", "4.535", "4.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}771}{42{,}000}, \\dfrac{31{,}263}{42{,}000}, \\dfrac{31{,}665}{42{,}000}, \\dfrac{31{,}742}{42{,}000}, \\dfrac{33{,}233}{42{,}000}, \\dfrac{33{,}348}{42{,}000}, \\dfrac{34{,}046}{42{,}000}, \\dfrac{34{,}105}{42{,}000}, \\dfrac{34{,}455}{42{,}000}, \\dfrac{34{,}456}{42{,}000}, \\dfrac{34{,}481}{42{,}000}, \\text{ and } \\dfrac{34{,}799}{42{,}000}", "__seed__": "0622"}}, {"seed": 623, "data": {"p1_how_many": "14", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.645, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635", "1.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{512}{3{,}000}, \\dfrac{518}{3{,}000}, \\dfrac{523}{3{,}000}, \\dfrac{524}{3{,}000}, \\dfrac{533}{3{,}000}, \\dfrac{545}{3{,}000}, \\dfrac{564}{3{,}000}, \\dfrac{566}{3{,}000}, \\text{ and } \\dfrac{578}{3{,}000}", "__seed__": "0623"}}, {"seed": 624, "data": {"p1_how_many": "14", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.445, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435", "9.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}087}{20{,}000}, \\dfrac{4{,}188}{20{,}000}, \\dfrac{4{,}223}{20{,}000}, \\dfrac{4{,}338}{20{,}000}, \\dfrac{4{,}459}{20{,}000}, \\dfrac{4{,}487}{20{,}000}, \\dfrac{4{,}528}{20{,}000}, \\dfrac{4{,}631}{20{,}000}, \\dfrac{4{,}850}{20{,}000}, \\text{ and } \\dfrac{4{,}956}{20{,}000}", "__seed__": "0624"}}, {"seed": 625, "data": {"p1_how_many": "12", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}151}{5{,}600}, \\dfrac{2{,}174}{5{,}600}, \\dfrac{2{,}196}{5{,}600}, \\dfrac{2{,}210}{5{,}600}, \\dfrac{2{,}229}{5{,}600}, \\dfrac{2{,}231}{5{,}600}, \\dfrac{2{,}232}{5{,}600}, \\dfrac{2{,}310}{5{,}600}, \\dfrac{2{,}346}{5{,}600}, \\dfrac{2{,}358}{5{,}600}, \\text{ and } \\dfrac{2{,}370}{5{,}600}", "__seed__": "0625"}}, {"seed": 626, "data": {"p1_how_many": "10", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{73}{150}, \\dfrac{74}{150}, \\dfrac{77}{150}, \\dfrac{81}{150}, \\dfrac{85}{150}, \\dfrac{87}{150}, \\dfrac{96}{150}, \\text{ and } \\dfrac{98}{150}", "__seed__": "0626"}}, {"seed": 627, "data": {"p1_how_many": "14", "p1_a": "4.81", "p1_b": "4.82", "p1_numbers": "4.8105, 4.811, 4.8115, 4.812, 4.8125, 4.813, 4.8135, 4.814, 4.8145, 4.815, 4.816, 4.817, 4.818, and 4.819", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.811", "4.811999999999999", "4.813", "4.813999999999999", "4.8149999999999995", "4.816", "4.816999999999999", "4.818", "4.819"], "p1_2_xs": ["4.810499999999999", "4.8115", "4.812499999999999", "4.8134999999999994", "4.814499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}291}{7{,}700}, \\dfrac{4{,}304}{7{,}700}, \\dfrac{4{,}589}{7{,}700}, \\dfrac{4{,}811}{7{,}700}, \\dfrac{4{,}833}{7{,}700}, \\dfrac{5{,}007}{7{,}700}, \\text{ and } \\dfrac{5{,}723}{7{,}700}", "__seed__": "0627"}}, {"seed": 628, "data": {"p1_how_many": "11", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{409}{2{,}000}, \\dfrac{410}{2{,}000}, \\dfrac{413}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{427}{2{,}000}, \\dfrac{429}{2{,}000}, \\dfrac{455}{2{,}000}, \\dfrac{459}{2{,}000}, \\dfrac{477}{2{,}000}, \\dfrac{486}{2{,}000}, \\dfrac{497}{2{,}000}, \\text{ and } \\dfrac{499}{2{,}000}", "__seed__": "0628"}}, {"seed": 629, "data": {"p1_how_many": "10", "p1_a": "1.53", "p1_b": "1.54", "p1_numbers": "1.5305, 1.531, 1.532, 1.533, 1.534, 1.535, 1.536, 1.537, 1.538, and 1.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.531", "1.532", "1.533", "1.534", "1.535", "1.536", "1.537", "1.538", "1.539"], "p1_2_xs": ["1.5305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{720}{5{,}600}, \\dfrac{723}{5{,}600}, \\dfrac{734}{5{,}600}, \\dfrac{748}{5{,}600}, \\dfrac{757}{5{,}600}, \\dfrac{764}{5{,}600}, \\dfrac{786}{5{,}600}, \\text{ and } \\dfrac{793}{5{,}600}", "__seed__": "0629"}}, {"seed": 630, "data": {"p1_how_many": "13", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.735, 3.74, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725", "3.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}047}{20{,}000}, \\dfrac{15{,}154}{20{,}000}, \\dfrac{15{,}251}{20{,}000}, \\dfrac{15{,}259}{20{,}000}, \\dfrac{15{,}338}{20{,}000}, \\dfrac{15{,}428}{20{,}000}, \\dfrac{15{,}609}{20{,}000}, \\dfrac{15{,}737}{20{,}000}, \\text{ and } \\dfrac{15{,}830}{20{,}000}", "__seed__": "0630"}}, {"seed": 631, "data": {"p1_how_many": "10", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}504}{4{,}200}, \\dfrac{3{,}520}{4{,}200}, \\dfrac{3{,}525}{4{,}200}, \\dfrac{3{,}534}{4{,}200}, \\dfrac{3{,}537}{4{,}200}, \\dfrac{3{,}540}{4{,}200}, \\dfrac{3{,}552}{4{,}200}, \\dfrac{3{,}565}{4{,}200}, \\dfrac{3{,}567}{4{,}200}, \\dfrac{3{,}584}{4{,}200}, \\text{ and } \\dfrac{3{,}588}{4{,}200}", "__seed__": "0631"}}, {"seed": 632, "data": {"p1_how_many": "14", "p1_a": "2.57", "p1_b": "2.58", "p1_numbers": "2.5705, 2.571, 2.5715, 2.572, 2.5725, 2.573, 2.5735, 2.574, 2.5745, 2.575, 2.576, 2.577, 2.578, and 2.579", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5709999999999997", "2.5719999999999996", "2.573", "2.574", "2.5749999999999997", "2.5759999999999996", "2.577", "2.578", "2.5789999999999997"], "p1_2_xs": ["2.5705", "2.5715", "2.5725", "2.5735", "2.5745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}528}{2{,}000}, \\dfrac{1{,}533}{2{,}000}, \\dfrac{1{,}541}{2{,}000}, \\dfrac{1{,}544}{2{,}000}, \\dfrac{1{,}546}{2{,}000}, \\dfrac{1{,}552}{2{,}000}, \\dfrac{1{,}576}{2{,}000}, \\text{ and } \\dfrac{1{,}592}{2{,}000}", "__seed__": "0632"}}, {"seed": 633, "data": {"p1_how_many": "14", "p1_a": "6.91", "p1_b": "6.92", "p1_numbers": "6.9105, 6.911, 6.9115, 6.912, 6.9125, 6.913, 6.9135, 6.914, 6.9145, 6.915, 6.916, 6.917, 6.918, and 6.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.9110000000000005", "6.912", "6.913", "6.914", "6.915", "6.916", "6.917", "6.918", "6.9190000000000005"], "p1_2_xs": ["6.9105", "6.9115", "6.9125", "6.9135", "6.914499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{42{,}317}{77{,}000}, \\dfrac{44{,}171}{77{,}000}, \\dfrac{48{,}524}{77{,}000}, \\dfrac{49{,}685}{77{,}000}, \\dfrac{52{,}123}{77{,}000}, \\dfrac{54{,}135}{77{,}000}, \\dfrac{55{,}484}{77{,}000}, \\dfrac{59{,}204}{77{,}000}, \\dfrac{60{,}823}{77{,}000}, \\text{ and } \\dfrac{64{,}306}{77{,}000}", "__seed__": "0633"}}, {"seed": 634, "data": {"p1_how_many": "12", "p1_a": "1.31", "p1_b": "1.32", "p1_numbers": "1.3105, 1.311, 1.3115, 1.312, 1.3125, 1.313, 1.314, 1.315, 1.316, 1.317, 1.318, and 1.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.311", "1.312", "1.313", "1.314", "1.315", "1.316", "1.317", "1.318", "1.319"], "p1_2_xs": ["1.3105", "1.3114999999999999", "1.3125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0634"}}, {"seed": 635, "data": {"p1_how_many": "12", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}449}{6{,}300}, \\dfrac{1{,}471}{6{,}300}, \\dfrac{1{,}574}{6{,}300}, \\dfrac{1{,}583}{6{,}300}, \\dfrac{1{,}605}{6{,}300}, \\dfrac{1{,}688}{6{,}300}, \\dfrac{1{,}693}{6{,}300}, \\text{ and } \\dfrac{1{,}773}{6{,}300}", "__seed__": "0635"}}, {"seed": 636, "data": {"p1_how_many": "14", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.1005, 5.101, 5.1015, 5.102, 5.1025, 5.103, 5.1035, 5.104, 5.1045, 5.105, 5.106, 5.107, 5.108, and 5.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.101", "5.101999999999999", "5.103", "5.103999999999999", "5.1049999999999995", "5.106", "5.106999999999999", "5.108", "5.109"], "p1_2_xs": ["5.100499999999999", "5.1015", "5.102499999999999", "5.1034999999999995", "5.104499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{606}{4{,}200}, \\dfrac{623}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{657}{4{,}200}, \\dfrac{664}{4{,}200}, \\dfrac{673}{4{,}200}, \\dfrac{676}{4{,}200}, \\dfrac{687}{4{,}200}, \\text{ and } \\dfrac{695}{4{,}200}", "__seed__": "0636"}}, {"seed": 637, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{307}{1{,}200}, \\dfrac{308}{1{,}200}, \\dfrac{310}{1{,}200}, \\dfrac{332}{1{,}200}, \\dfrac{337}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{354}{1{,}200}, \\dfrac{355}{1{,}200}, \\dfrac{365}{1{,}200}, \\dfrac{377}{1{,}200}, \\dfrac{396}{1{,}200}, \\text{ and } \\dfrac{399}{1{,}200}", "__seed__": "0637"}}, {"seed": 638, "data": {"p1_how_many": "12", "p1_a": "1.72", "p1_b": "1.73", "p1_numbers": "1.7205, 1.721, 1.7215, 1.722, 1.7225, 1.723, 1.724, 1.725, 1.726, 1.727, 1.728, and 1.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.7209999999999999", "1.722", "1.7229999999999999", "1.724", "1.7249999999999999", "1.726", "1.7269999999999999", "1.728", "1.7289999999999999"], "p1_2_xs": ["1.7205", "1.7214999999999998", "1.7225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{217}{560}, \\dfrac{218}{560}, \\dfrac{221}{560}, \\dfrac{223}{560}, \\dfrac{227}{560}, \\dfrac{231}{560}, \\dfrac{232}{560}, \\text{ and } \\dfrac{233}{560}", "__seed__": "0638"}}, {"seed": 639, "data": {"p1_how_many": "11", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.215, 6.22, 6.23, 6.24, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205", "6.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}439}{42{,}000}, \\dfrac{30{,}807}{42{,}000}, \\dfrac{30{,}869}{42{,}000}, \\dfrac{30{,}965}{42{,}000}, \\dfrac{31{,}725}{42{,}000}, \\dfrac{31{,}815}{42{,}000}, \\dfrac{32{,}123}{42{,}000}, \\dfrac{32{,}185}{42{,}000}, \\dfrac{32{,}671}{42{,}000}, \\dfrac{32{,}737}{42{,}000}, \\text{ and } \\dfrac{34{,}340}{42{,}000}", "__seed__": "0639"}}, {"seed": 640, "data": {"p1_how_many": "14", "p1_a": "7.16", "p1_b": "7.17", "p1_numbers": "7.1605, 7.161, 7.1615, 7.162, 7.1625, 7.163, 7.1635, 7.164, 7.1645, 7.165, 7.166, 7.167, 7.168, and 7.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.1610000000000005", "7.162", "7.163", "7.164", "7.165", "7.166", "7.167", "7.168", "7.1690000000000005"], "p1_2_xs": ["7.1605", "7.1615", "7.1625", "7.1635", "7.164499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}075}{20{,}000}, \\dfrac{4{,}149}{20{,}000}, \\dfrac{4{,}269}{20{,}000}, \\dfrac{4{,}352}{20{,}000}, \\dfrac{4{,}399}{20{,}000}, \\dfrac{4{,}631}{20{,}000}, \\dfrac{4{,}794}{20{,}000}, \\dfrac{4{,}886}{20{,}000}, \\text{ and } \\dfrac{4{,}970}{20{,}000}", "__seed__": "0640"}}, {"seed": 641, "data": {"p1_how_many": "13", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.535, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995", "6.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{123}{200}, \\dfrac{130}{200}, \\dfrac{133}{200}, \\dfrac{135}{200}, \\dfrac{136}{200}, \\dfrac{143}{200}, \\dfrac{146}{200}, \\text{ and } \\dfrac{147}{200}", "__seed__": "0641"}}, {"seed": 642, "data": {"p1_how_many": "13", "p1_a": "5.8", "p1_b": "5.9", "p1_numbers": "5.8005, 5.801, 5.8015, 5.802, 5.8025, 5.803, 5.8035, 5.804, 5.805, 5.806, 5.807, 5.808, and 5.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.801", "5.802", "5.803", "5.803999999999999", "5.805", "5.806", "5.8069999999999995", "5.808", "5.809"], "p1_2_xs": ["5.8004999999999995", "5.8015", "5.802499999999999", "5.8035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}405}{3{,}000}, \\dfrac{2{,}444}{3{,}000}, \\dfrac{2{,}460}{3{,}000}, \\dfrac{2{,}466}{3{,}000}, \\dfrac{2{,}471}{3{,}000}, \\dfrac{2{,}479}{3{,}000}, \\dfrac{2{,}484}{3{,}000}, \\dfrac{2{,}491}{3{,}000}, \\text{ and } \\dfrac{2{,}498}{3{,}000}", "__seed__": "0642"}}, {"seed": 643, "data": {"p1_how_many": "13", "p1_a": "4.25", "p1_b": "4.26", "p1_numbers": "4.2505, 4.251, 4.2515, 4.252, 4.2525, 4.253, 4.2535, 4.254, 4.255, 4.256, 4.257, 4.258, and 4.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.251", "4.252", "4.253", "4.254", "4.255", "4.256", "4.257", "4.258", "4.259"], "p1_2_xs": ["4.2505", "4.2515", "4.2524999999999995", "4.2535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}213}{12{,}000}, \\dfrac{3{,}440}{12{,}000}, \\dfrac{3{,}448}{12{,}000}, \\dfrac{3{,}455}{12{,}000}, \\dfrac{3{,}656}{12{,}000}, \\dfrac{3{,}865}{12{,}000}, \\dfrac{3{,}899}{12{,}000}, \\text{ and } \\dfrac{3{,}974}{12{,}000}", "__seed__": "0643"}}, {"seed": 644, "data": {"p1_how_many": "11", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.205, 6.21, 6.215, 6.22, 6.23, 6.24, 6.25, 6.26, 6.27, 6.28, and 6.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.21", "6.22", "6.23", "6.24", "6.25", "6.26", "6.2700000000000005", "6.28", "6.29"], "p1_2_xs": ["6.205", "6.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}219}{2{,}000}, \\dfrac{1{,}275}{2{,}000}, \\dfrac{1{,}279}{2{,}000}, \\dfrac{1{,}340}{2{,}000}, \\dfrac{1{,}341}{2{,}000}, \\dfrac{1{,}353}{2{,}000}, \\dfrac{1{,}411}{2{,}000}, \\dfrac{1{,}448}{2{,}000}, \\dfrac{1{,}454}{2{,}000}, \\text{ and } \\dfrac{1{,}497}{2{,}000}", "__seed__": "0644"}}, {"seed": 645, "data": {"p1_how_many": "10", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.02, 9.03, 9.04, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{28{,}434}{63{,}000}, \\dfrac{29{,}295}{63{,}000}, \\dfrac{31{,}429}{63{,}000}, \\dfrac{31{,}455}{63{,}000}, \\dfrac{32{,}604}{63{,}000}, \\dfrac{32{,}777}{63{,}000}, \\dfrac{33{,}316}{63{,}000}, \\dfrac{33{,}761}{63{,}000}, \\dfrac{34{,}296}{63{,}000}, \\dfrac{34{,}313}{63{,}000}, \\dfrac{34{,}567}{63{,}000}, \\text{ and } \\dfrac{35{,}141}{63{,}000}", "__seed__": "0645"}}, {"seed": 646, "data": {"p1_how_many": "13", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.335, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999", "7.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}299}{42{,}000}, \\dfrac{35{,}331}{42{,}000}, \\dfrac{35{,}372}{42{,}000}, \\dfrac{35{,}448}{42{,}000}, \\dfrac{35{,}638}{42{,}000}, \\dfrac{35{,}672}{42{,}000}, \\text{ and } \\dfrac{35{,}858}{42{,}000}", "__seed__": "0646"}}, {"seed": 647, "data": {"p1_how_many": "12", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.705, 5.71, 5.715, 5.72, 5.725, 5.73, 5.74, 5.75, 5.76, 5.77, 5.78, and 5.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.71", "5.72", "5.73", "5.74", "5.75", "5.76", "5.7700000000000005", "5.78", "5.79"], "p1_2_xs": ["5.705", "5.715", "5.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}102}{30{,}000}, \\dfrac{24{,}114}{30{,}000}, \\dfrac{24{,}148}{30{,}000}, \\dfrac{24{,}343}{30{,}000}, \\dfrac{24{,}434}{30{,}000}, \\dfrac{24{,}480}{30{,}000}, \\dfrac{24{,}517}{30{,}000}, \\dfrac{24{,}604}{30{,}000}, \\text{ and } \\dfrac{24{,}626}{30{,}000}", "__seed__": "0647"}}, {"seed": 648, "data": {"p1_how_many": "11", "p1_a": "8.03", "p1_b": "8.04", "p1_numbers": "8.0305, 8.031, 8.0315, 8.032, 8.033, 8.034, 8.035, 8.036, 8.037, 8.038, and 8.039", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.030999999999999", "8.032", "8.033", "8.033999999999999", "8.035", "8.036", "8.036999999999999", "8.037999999999998", "8.039"], "p1_2_xs": ["8.0305", "8.0315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}238}{56{,}000}, \\dfrac{16{,}807}{56{,}000}, \\dfrac{16{,}946}{56{,}000}, \\dfrac{16{,}979}{56{,}000}, \\dfrac{17{,}095}{56{,}000}, \\dfrac{18{,}208}{56{,}000}, \\dfrac{19{,}237}{56{,}000}, \\dfrac{20{,}063}{56{,}000}, \\text{ and } \\dfrac{20{,}426}{56{,}000}", "__seed__": "0648"}}, {"seed": 649, "data": {"p1_how_many": "14", "p1_a": "6.34", "p1_b": "6.35", "p1_numbers": "6.3405, 6.341, 6.3415, 6.342, 6.3425, 6.343, 6.3435, 6.344, 6.3445, 6.345, 6.346, 6.347, 6.348, and 6.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.341", "6.342", "6.343", "6.343999999999999", "6.345", "6.346", "6.3469999999999995", "6.348", "6.349"], "p1_2_xs": ["6.3405", "6.3415", "6.342499999999999", "6.3435", "6.344499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}021}{12{,}000}, \\dfrac{8{,}197}{12{,}000}, \\dfrac{8{,}358}{12{,}000}, \\dfrac{8{,}400}{12{,}000}, \\dfrac{8{,}520}{12{,}000}, \\dfrac{8{,}626}{12{,}000}, \\dfrac{8{,}743}{12{,}000}, \\dfrac{8{,}764}{12{,}000}, \\dfrac{8{,}895}{12{,}000}, \\dfrac{8{,}910}{12{,}000}, \\text{ and } \\dfrac{8{,}976}{12{,}000}", "__seed__": "0649"}}, {"seed": 650, "data": {"p1_how_many": "14", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.135, 8.14, 8.145, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125", "8.135", "8.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{97}{630}, \\dfrac{104}{630}, \\dfrac{106}{630}, \\dfrac{110}{630}, \\dfrac{111}{630}, \\dfrac{117}{630}, \\dfrac{126}{630}, \\dfrac{129}{630}, \\text{ and } \\dfrac{136}{630}", "__seed__": "0650"}}, {"seed": 651, "data": {"p1_how_many": "10", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.705, 5.71, 5.72, 5.73, 5.74, 5.75, 5.76, 5.77, 5.78, and 5.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.71", "5.72", "5.73", "5.74", "5.75", "5.76", "5.7700000000000005", "5.78", "5.79"], "p1_2_xs": ["5.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}706}{6{,}300}, \\dfrac{2{,}712}{6{,}300}, \\dfrac{2{,}720}{6{,}300}, \\dfrac{2{,}736}{6{,}300}, \\dfrac{2{,}755}{6{,}300}, \\dfrac{2{,}767}{6{,}300}, \\text{ and } \\dfrac{2{,}781}{6{,}300}", "__seed__": "0651"}}, {"seed": 652, "data": {"p1_how_many": "11", "p1_a": "1.5", "p1_b": "1.6", "p1_numbers": "1.505, 1.51, 1.515, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, and 1.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.51", "1.52", "1.53", "1.54", "1.55", "1.56", "1.57", "1.58", "1.59"], "p1_2_xs": ["1.505", "1.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}005}{42{,}000}, \\dfrac{6{,}062}{42{,}000}, \\dfrac{6{,}169}{42{,}000}, \\dfrac{6{,}283}{42{,}000}, \\dfrac{6{,}328}{42{,}000}, \\dfrac{6{,}382}{42{,}000}, \\dfrac{6{,}520}{42{,}000}, \\dfrac{6{,}809}{42{,}000}, \\text{ and } \\dfrac{6{,}920}{42{,}000}", "__seed__": "0652"}}, {"seed": 653, "data": {"p1_how_many": "10", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}536}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}560}{4{,}200}, \\dfrac{3{,}575}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0653"}}, {"seed": 654, "data": {"p1_how_many": "13", "p1_a": "9.32", "p1_b": "9.33", "p1_numbers": "9.3205, 9.321, 9.3215, 9.322, 9.3225, 9.323, 9.3235, 9.324, 9.325, 9.326, 9.327, 9.328, and 9.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.321", "9.322000000000001", "9.323", "9.324", "9.325000000000001", "9.326", "9.327", "9.328", "9.329"], "p1_2_xs": ["9.320500000000001", "9.3215", "9.322500000000002", "9.323500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}725}{56{,}000}, \\dfrac{17{,}107}{56{,}000}, \\dfrac{17{,}338}{56{,}000}, \\dfrac{17{,}394}{56{,}000}, \\dfrac{17{,}401}{56{,}000}, \\dfrac{18{,}134}{56{,}000}, \\dfrac{18{,}299}{56{,}000}, \\dfrac{18{,}739}{56{,}000}, \\dfrac{19{,}246}{56{,}000}, \\dfrac{19{,}292}{56{,}000}, \\text{ and } \\dfrac{20{,}151}{56{,}000}", "__seed__": "0654"}}, {"seed": 655, "data": {"p1_how_many": "10", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.72, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{78}{420}, \\dfrac{83}{420}, \\dfrac{87}{420}, \\dfrac{106}{420}, \\dfrac{110}{420}, \\dfrac{111}{420}, \\text{ and } \\dfrac{115}{420}", "__seed__": "0655"}}, {"seed": 656, "data": {"p1_how_many": "12", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}134}{35{,}000}, \\dfrac{14{,}197}{35{,}000}, \\dfrac{14{,}615}{35{,}000}, \\dfrac{14{,}679}{35{,}000}, \\dfrac{14{,}709}{35{,}000}, \\dfrac{14{,}788}{35{,}000}, \\text{ and } \\dfrac{14{,}937}{35{,}000}", "__seed__": "0656"}}, {"seed": 657, "data": {"p1_how_many": "14", "p1_a": "4.67", "p1_b": "4.68", "p1_numbers": "4.6705, 4.671, 4.6715, 4.672, 4.6725, 4.673, 4.6735, 4.674, 4.6745, 4.675, 4.676, 4.677, 4.678, and 4.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.671", "4.672", "4.673", "4.6739999999999995", "4.675", "4.676", "4.677", "4.678", "4.679"], "p1_2_xs": ["4.6705", "4.6715", "4.672499999999999", "4.6735", "4.674499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}804}{6{,}300}, \\dfrac{2{,}810}{6{,}300}, \\dfrac{2{,}872}{6{,}300}, \\dfrac{2{,}945}{6{,}300}, \\dfrac{3{,}119}{6{,}300}, \\dfrac{3{,}151}{6{,}300}, \\dfrac{3{,}278}{6{,}300}, \\dfrac{3{,}352}{6{,}300}, \\dfrac{3{,}371}{6{,}300}, \\dfrac{3{,}403}{6{,}300}, \\dfrac{3{,}458}{6{,}300}, \\text{ and } \\dfrac{3{,}524}{6{,}300}", "__seed__": "0657"}}, {"seed": 658, "data": {"p1_how_many": "12", "p1_a": "7.06", "p1_b": "7.07", "p1_numbers": "7.0605, 7.061, 7.0615, 7.062, 7.0625, 7.063, 7.064, 7.065, 7.066, 7.067, 7.068, and 7.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.061", "7.061999999999999", "7.063", "7.063999999999999", "7.0649999999999995", "7.066", "7.066999999999999", "7.068", "7.069"], "p1_2_xs": ["7.060499999999999", "7.0615", "7.062499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{150}, \\dfrac{52}{150}, \\dfrac{53}{150}, \\dfrac{54}{150}, \\dfrac{55}{150}, \\dfrac{57}{150}, \\dfrac{58}{150}, \\text{ and } \\dfrac{59}{150}", "__seed__": "0658"}}, {"seed": 659, "data": {"p1_how_many": "11", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.615, 6.62, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995", "6.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}031}{3{,}500}, \\dfrac{2{,}060}{3{,}500}, \\dfrac{2{,}107}{3{,}500}, \\dfrac{2{,}163}{3{,}500}, \\dfrac{2{,}166}{3{,}500}, \\dfrac{2{,}169}{3{,}500}, \\dfrac{2{,}316}{3{,}500}, \\dfrac{2{,}503}{3{,}500}, \\dfrac{2{,}660}{3{,}500}, \\dfrac{2{,}685}{3{,}500}, \\text{ and } \\dfrac{2{,}730}{3{,}500}", "__seed__": "0659"}}, {"seed": 660, "data": {"p1_how_many": "13", "p1_a": "8.67", "p1_b": "8.68", "p1_numbers": "8.6705, 8.671, 8.6715, 8.672, 8.6725, 8.673, 8.6735, 8.674, 8.675, 8.676, 8.677, 8.678, and 8.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.671", "8.672", "8.673", "8.674", "8.675", "8.676", "8.677", "8.677999999999999", "8.679"], "p1_2_xs": ["8.6705", "8.6715", "8.672500000000001", "8.6735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}863}{6{,}300}, \\dfrac{2{,}946}{6{,}300}, \\dfrac{2{,}961}{6{,}300}, \\dfrac{2{,}991}{6{,}300}, \\dfrac{3{,}038}{6{,}300}, \\dfrac{3{,}137}{6{,}300}, \\dfrac{3{,}194}{6{,}300}, \\dfrac{3{,}336}{6{,}300}, \\dfrac{3{,}350}{6{,}300}, \\dfrac{3{,}354}{6{,}300}, \\dfrac{3{,}387}{6{,}300}, \\text{ and } \\dfrac{3{,}499}{6{,}300}", "__seed__": "0660"}}, {"seed": 661, "data": {"p1_how_many": "11", "p1_a": "2.3", 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"p1_a": "8.91", "p1_b": "8.92", "p1_numbers": "8.9105, 8.911, 8.9115, 8.912, 8.913, 8.914, 8.915, 8.916, 8.917, 8.918, and 8.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.911", "8.912", "8.913", "8.914", "8.915000000000001", "8.916", "8.917", "8.918", "8.919"], "p1_2_xs": ["8.9105", "8.9115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}498}{6{,}300}, \\dfrac{1{,}599}{6{,}300}, \\dfrac{1{,}607}{6{,}300}, \\dfrac{1{,}619}{6{,}300}, \\dfrac{1{,}640}{6{,}300}, \\dfrac{1{,}690}{6{,}300}, \\dfrac{1{,}731}{6{,}300}, \\text{ and } \\dfrac{1{,}732}{6{,}300}", "__seed__": "0662"}}, {"seed": 663, "data": {"p1_how_many": "14", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.345, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315", "1.325", "1.335", "1.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{502}{3{,}000}, \\dfrac{515}{3{,}000}, \\dfrac{534}{3{,}000}, \\dfrac{536}{3{,}000}, \\dfrac{539}{3{,}000}, \\dfrac{546}{3{,}000}, \\dfrac{559}{3{,}000}, \\dfrac{567}{3{,}000}, \\text{ and } \\dfrac{590}{3{,}000}", "__seed__": "0663"}}, {"seed": 664, "data": {"p1_how_many": "10", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{162}{560}, \\dfrac{174}{560}, \\dfrac{179}{560}, \\dfrac{205}{560}, \\dfrac{206}{560}, \\dfrac{207}{560}, \\text{ and } \\dfrac{209}{560}", "__seed__": "0664"}}, {"seed": 665, "data": {"p1_how_many": "13", "p1_a": "4.71", "p1_b": "4.72", "p1_numbers": "4.7105, 4.711, 4.7115, 4.712, 4.7125, 4.713, 4.7135, 4.714, 4.715, 4.716, 4.717, 4.718, and 4.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.711", "4.712", "4.713", "4.7139999999999995", "4.715", "4.716", "4.717", "4.718", "4.719"], "p1_2_xs": ["4.7105", "4.7115", "4.7124999999999995", "4.7135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}033}{56{,}000}, \\dfrac{16{,}087}{56{,}000}, \\dfrac{17{,}070}{56{,}000}, \\dfrac{17{,}333}{56{,}000}, \\dfrac{17{,}661}{56{,}000}, \\dfrac{18{,}633}{56{,}000}, \\dfrac{19{,}058}{56{,}000}, \\dfrac{19{,}225}{56{,}000}, \\dfrac{19{,}675}{56{,}000}, \\dfrac{20{,}017}{56{,}000}, \\dfrac{20{,}247}{56{,}000}, \\text{ and } \\dfrac{20{,}359}{56{,}000}", "__seed__": "0665"}}, {"seed": 666, "data": {"p1_how_many": "11", "p1_a": "4.0", "p1_b": "4.1", "p1_numbers": "4.005, 4.01, 4.015, 4.02, 4.03, 4.04, 4.05, 4.06, 4.07, 4.08, and 4.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.01", "4.02", "4.03", "4.04", "4.05", "4.06", "4.07", "4.08", "4.09"], "p1_2_xs": ["4.005", "4.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{31}{120}, \\dfrac{32}{120}, \\dfrac{33}{120}, \\dfrac{35}{120}, \\dfrac{36}{120}, \\dfrac{37}{120}, \\dfrac{38}{120}, \\text{ and } \\dfrac{39}{120}", "__seed__": "0666"}}, {"seed": 667, "data": {"p1_how_many": "12", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}091}{35{,}000}, \\dfrac{7{,}196}{35{,}000}, \\dfrac{7{,}211}{35{,}000}, \\dfrac{7{,}429}{35{,}000}, \\dfrac{7{,}552}{35{,}000}, \\dfrac{7{,}769}{35{,}000}, \\dfrac{8{,}357}{35{,}000}, \\dfrac{8{,}786}{35{,}000}, \\dfrac{9{,}102}{35{,}000}, \\text{ and } \\dfrac{9{,}160}{35{,}000}", "__seed__": "0667"}}, {"seed": 668, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{21{,}002}{35{,}000}, \\dfrac{21{,}273}{35{,}000}, \\dfrac{21{,}347}{35{,}000}, \\dfrac{21{,}617}{35{,}000}, \\dfrac{21{,}925}{35{,}000}, \\dfrac{22{,}181}{35{,}000}, \\dfrac{22{,}844}{35{,}000}, \\dfrac{23{,}106}{35{,}000}, \\dfrac{25{,}376}{35{,}000}, \\dfrac{26{,}323}{35{,}000}, \\dfrac{26{,}336}{35{,}000}, \\text{ and } \\dfrac{27{,}480}{35{,}000}", "__seed__": "0668"}}, {"seed": 669, "data": {"p1_how_many": "14", "p1_a": "8.8", "p1_b": "8.9", "p1_numbers": "8.8005, 8.801, 8.8015, 8.802, 8.8025, 8.803, 8.8035, 8.804, 8.8045, 8.805, 8.806, 8.807, 8.808, and 8.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.801", "8.802000000000001", "8.803", "8.804", "8.805000000000001", "8.806000000000001", "8.807", "8.808", "8.809000000000001"], "p1_2_xs": ["8.800500000000001", "8.8015", "8.802500000000002", "8.803500000000001", "8.8045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}015}{4{,}200}, \\dfrac{3{,}193}{4{,}200}, \\dfrac{3{,}230}{4{,}200}, \\dfrac{3{,}276}{4{,}200}, \\dfrac{3{,}324}{4{,}200}, \\dfrac{3{,}341}{4{,}200}, \\dfrac{3{,}368}{4{,}200}, \\dfrac{3{,}374}{4{,}200}, \\dfrac{3{,}403}{4{,}200}, \\dfrac{3{,}419}{4{,}200}, \\dfrac{3{,}490}{4{,}200}, \\text{ and } 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"data": {"p1_how_many": "11", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.015, 3.02, 3.03, 3.04, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005", "3.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{502}{1{,}500}, \\dfrac{508}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{547}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{565}{1{,}500}, \\dfrac{585}{1{,}500}, \\text{ and } \\dfrac{591}{1{,}500}", "__seed__": "0671"}}, {"seed": 672, "data": {"p1_how_many": "14", "p1_a": "5.55", "p1_b": "5.56", "p1_numbers": "5.5505, 5.551, 5.5515, 5.552, 5.5525, 5.553, 5.5535, 5.554, 5.5545, 5.555, 5.556, 5.557, 5.558, and 5.559", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.551", "5.552", "5.553", "5.553999999999999", "5.555", "5.556", "5.5569999999999995", "5.558", "5.559"], "p1_2_xs": ["5.5504999999999995", "5.5515", "5.552499999999999", "5.5535", "5.554499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}119}{20{,}000}, \\dfrac{15{,}335}{20{,}000}, \\dfrac{15{,}466}{20{,}000}, \\dfrac{15{,}470}{20{,}000}, \\dfrac{15{,}492}{20{,}000}, \\dfrac{15{,}581}{20{,}000}, \\dfrac{15{,}649}{20{,}000}, \\dfrac{15{,}796}{20{,}000}, \\dfrac{15{,}983}{20{,}000}, \\text{ and } \\dfrac{15{,}985}{20{,}000}", "__seed__": "0672"}}, {"seed": 673, "data": {"p1_how_many": "12", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}015}{3{,}500}, \\dfrac{1{,}049}{3{,}500}, \\dfrac{1{,}055}{3{,}500}, \\dfrac{1{,}072}{3{,}500}, \\dfrac{1{,}090}{3{,}500}, \\dfrac{1{,}148}{3{,}500}, \\dfrac{1{,}154}{3{,}500}, \\dfrac{1{,}219}{3{,}500}, \\dfrac{1{,}262}{3{,}500}, \\dfrac{1{,}351}{3{,}500}, \\text{ and } \\dfrac{1{,}368}{3{,}500}", "__seed__": "0673"}}, {"seed": 674, "data": {"p1_how_many": "12", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.625, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998", "2.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{620}{4{,}200}, \\dfrac{622}{4{,}200}, \\dfrac{627}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{643}{4{,}200}, \\dfrac{661}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{680}{4{,}200}, \\text{ and } \\dfrac{682}{4{,}200}", "__seed__": "0674"}}, {"seed": 675, "data": {"p1_how_many": "12", "p1_a": "2.2", "p1_b": "2.3", "p1_numbers": "2.205, 2.21, 2.215, 2.22, 2.225, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, and 2.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.21", "2.22", "2.23", "2.24", "2.25", "2.2600000000000002", "2.27", "2.2800000000000002", "2.29"], "p1_2_xs": ["2.205", "2.215", "2.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{31{,}308}{42{,}000}, \\dfrac{31{,}375}{42{,}000}, \\dfrac{32{,}177}{42{,}000}, \\dfrac{32{,}219}{42{,}000}, \\dfrac{32{,}262}{42{,}000}, \\dfrac{32{,}690}{42{,}000}, \\dfrac{33{,}164}{42{,}000}, \\dfrac{33{,}562}{42{,}000}, \\dfrac{33{,}825}{42{,}000}, \\text{ and } \\dfrac{34{,}307}{42{,}000}", "__seed__": "0675"}}, {"seed": 676, "data": {"p1_how_many": "12", "p1_a": "3.01", "p1_b": "3.02", "p1_numbers": "3.0105, 3.011, 3.0115, 3.012, 3.0125, 3.013, 3.014, 3.015, 3.016, 3.017, 3.018, and 3.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.0109999999999997", "3.0119999999999996", "3.013", "3.014", "3.0149999999999997", "3.0159999999999996", "3.017", "3.018", "3.0189999999999997"], "p1_2_xs": ["3.0105", "3.0115", "3.0124999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}149}{15{,}000}, \\dfrac{5{,}233}{15{,}000}, \\dfrac{5{,}264}{15{,}000}, \\dfrac{5{,}323}{15{,}000}, \\dfrac{5{,}342}{15{,}000}, \\dfrac{5{,}595}{15{,}000}, \\dfrac{5{,}630}{15{,}000}, \\dfrac{5{,}706}{15{,}000}, \\dfrac{5{,}784}{15{,}000}, \\dfrac{5{,}805}{15{,}000}, \\text{ and } \\dfrac{5{,}816}{15{,}000}", "__seed__": "0676"}}, {"seed": 677, "data": {"p1_how_many": "13", "p1_a": "9.94", "p1_b": "9.95", "p1_numbers": "9.9405, 9.941, 9.9415, 9.942, 9.9425, 9.943, 9.9435, 9.944, 9.945, 9.946, 9.947, 9.948, and 9.949", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.940999999999999", "9.942", "9.943", "9.943999999999999", "9.945", "9.946", "9.947", "9.947999999999999", "9.949"], "p1_2_xs": ["9.9405", "9.9415", "9.9425", "9.9435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{285}{630}, \\dfrac{299}{630}, \\dfrac{304}{630}, \\dfrac{314}{630}, \\dfrac{330}{630}, \\dfrac{337}{630}, \\dfrac{341}{630}, \\dfrac{344}{630}, \\text{ and } \\dfrac{351}{630}", "__seed__": "0677"}}, {"seed": 678, "data": {"p1_how_many": "13", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.735, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725", "8.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{403}{2{,}000}, \\dfrac{417}{2{,}000}, \\dfrac{422}{2{,}000}, \\dfrac{430}{2{,}000}, \\dfrac{447}{2{,}000}, \\dfrac{448}{2{,}000}, \\dfrac{450}{2{,}000}, \\dfrac{470}{2{,}000}, \\dfrac{484}{2{,}000}, \\dfrac{490}{2{,}000}, \\dfrac{493}{2{,}000}, \\text{ and } \\dfrac{495}{2{,}000}", "__seed__": "0678"}}, {"seed": 679, "data": {"p1_how_many": "14", "p1_a": "3.56", "p1_b": "3.57", "p1_numbers": "3.5605, 3.561, 3.5615, 3.562, 3.5625, 3.563, 3.5635, 3.564, 3.5645, 3.565, 3.566, 3.567, 3.568, and 3.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.561", "3.562", "3.563", "3.564", "3.565", "3.566", "3.567", "3.568", "3.569"], "p1_2_xs": ["3.5605", "3.5615", "3.5625", "3.5635000000000003", "3.5645000000000002"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}246}{2{,}000}, \\dfrac{1{,}257}{2{,}000}, \\dfrac{1{,}268}{2{,}000}, \\dfrac{1{,}270}{2{,}000}, \\dfrac{1{,}317}{2{,}000}, \\dfrac{1{,}318}{2{,}000}, \\dfrac{1{,}340}{2{,}000}, \\dfrac{1{,}384}{2{,}000}, \\dfrac{1{,}453}{2{,}000}, \\text{ and } \\dfrac{1{,}463}{2{,}000}", "__seed__": "0679"}}, {"seed": 680, "data": {"p1_how_many": "11", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}413}{7{,}700}, \\dfrac{4{,}590}{7{,}700}, \\dfrac{4{,}848}{7{,}700}, \\dfrac{4{,}854}{7{,}700}, \\dfrac{5{,}318}{7{,}700}, \\dfrac{5{,}488}{7{,}700}, \\dfrac{5{,}502}{7{,}700}, \\dfrac{5{,}866}{7{,}700}, \\dfrac{6{,}210}{7{,}700}, \\dfrac{6{,}388}{7{,}700}, \\dfrac{6{,}397}{7{,}700}, \\text{ and } \\dfrac{6{,}515}{7{,}700}", "__seed__": "0680"}}, {"seed": 681, "data": {"p1_how_many": "10", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.22, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}117}{15{,}000}, \\dfrac{6{,}766}{15{,}000}, \\dfrac{7{,}594}{15{,}000}, \\dfrac{7{,}653}{15{,}000}, \\dfrac{7{,}866}{15{,}000}, \\dfrac{8{,}233}{15{,}000}, \\dfrac{8{,}305}{15{,}000}, \\dfrac{8{,}435}{15{,}000}, \\dfrac{8{,}733}{15{,}000}, \\text{ and } \\dfrac{9{,}320}{15{,}000}", "__seed__": "0681"}}, {"seed": 682, "data": {"p1_how_many": "10", "p1_a": "3.0", "p1_b": "3.1", "p1_numbers": "3.005, 3.01, 3.02, 3.03, 3.04, 3.05, 3.06, 3.07, 3.08, and 3.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.01", "3.02", "3.03", "3.04", "3.05", "3.06", "3.07", "3.08", "3.09"], "p1_2_xs": ["3.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{308}{420}, \\dfrac{313}{420}, \\dfrac{323}{420}, \\dfrac{324}{420}, \\dfrac{329}{420}, \\dfrac{335}{420}, \\dfrac{341}{420}, \\text{ and } \\dfrac{345}{420}", "__seed__": "0682"}}, {"seed": 683, "data": {"p1_how_many": "11", "p1_a": "6.65", "p1_b": "6.66", "p1_numbers": "6.6505, 6.651, 6.6515, 6.652, 6.653, 6.654, 6.655, 6.656, 6.657, 6.658, and 6.659", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.651000000000001", "6.652", "6.6530000000000005", "6.654", "6.655", "6.656000000000001", "6.657", "6.658", "6.659000000000001"], "p1_2_xs": ["6.6505", "6.6515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{2{,}001}{3{,}500}, \\dfrac{2{,}011}{3{,}500}, \\dfrac{2{,}014}{3{,}500}, \\dfrac{2{,}015}{3{,}500}, \\dfrac{2{,}017}{3{,}500}, \\dfrac{2{,}032}{3{,}500}, \\dfrac{2{,}033}{3{,}500}, \\dfrac{2{,}057}{3{,}500}, \\dfrac{2{,}080}{3{,}500}, \\text{ and } \\dfrac{2{,}093}{3{,}500}", "__seed__": "0683"}}, {"seed": 684, "data": {"p1_how_many": "11", "p1_a": "5.07", "p1_b": "5.08", "p1_numbers": "5.0705, 5.071, 5.0715, 5.072, 5.073, 5.074, 5.075, 5.076, 5.077, 5.078, and 5.079", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.071000000000001", "5.072", "5.073", "5.074", "5.075", "5.0760000000000005", "5.077", "5.078", "5.079000000000001"], "p1_2_xs": ["5.0705", "5.0715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}025}{20{,}000}, \\dfrac{4{,}041}{20{,}000}, \\dfrac{4{,}063}{20{,}000}, \\dfrac{4{,}064}{20{,}000}, \\dfrac{4{,}313}{20{,}000}, \\dfrac{4{,}693}{20{,}000}, \\dfrac{4{,}821}{20{,}000}, \\dfrac{4{,}857}{20{,}000}, \\dfrac{4{,}951}{20{,}000}, \\text{ and } \\dfrac{4{,}963}{20{,}000}", "__seed__": "0684"}}, {"seed": 685, "data": {"p1_how_many": "13", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}332}{20{,}000}, \\dfrac{12{,}782}{20{,}000}, \\dfrac{12{,}908}{20{,}000}, \\dfrac{13{,}254}{20{,}000}, \\dfrac{14{,}137}{20{,}000}, \\dfrac{14{,}169}{20{,}000}, \\dfrac{14{,}233}{20{,}000}, \\dfrac{14{,}305}{20{,}000}, \\dfrac{14{,}306}{20{,}000}, \\text{ and } \\dfrac{14{,}515}{20{,}000}", "__seed__": "0685"}}, {"seed": 686, "data": {"p1_how_many": "14", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.125, 1.13, 1.135, 1.14, 1.145, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115", "1.125", "1.135", "1.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{45{,}417}{77{,}000}, \\dfrac{45{,}788}{77{,}000}, \\dfrac{46{,}924}{77{,}000}, \\dfrac{50{,}961}{77{,}000}, \\dfrac{54{,}205}{77{,}000}, \\dfrac{55{,}249}{77{,}000}, \\dfrac{58{,}328}{77{,}000}, \\dfrac{58{,}876}{77{,}000}, \\dfrac{60{,}520}{77{,}000}, \\dfrac{62{,}609}{77{,}000}, \\text{ and } \\dfrac{64{,}320}{77{,}000}", "__seed__": "0686"}}, {"seed": 687, "data": {"p1_how_many": "10", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.42, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}196}{20{,}000}, \\dfrac{5{,}304}{20{,}000}, \\dfrac{5{,}332}{20{,}000}, \\dfrac{5{,}378}{20{,}000}, \\dfrac{6{,}108}{20{,}000}, \\dfrac{6{,}190}{20{,}000}, \\dfrac{6{,}397}{20{,}000}, \\dfrac{6{,}411}{20{,}000}, \\dfrac{6{,}647}{20{,}000}, \\text{ and } \\dfrac{7{,}509}{20{,}000}", "__seed__": "0687"}}, {"seed": 688, "data": {"p1_how_many": "11", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.2005, 5.201, 5.2015, 5.202, 5.203, 5.204, 5.205, 5.206, 5.207, 5.208, and 5.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.2010000000000005", "5.202", "5.203", "5.204", "5.205", "5.206", "5.207", "5.208", "5.2090000000000005"], "p1_2_xs": ["5.2005", "5.2015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}077}{12{,}000}, \\dfrac{8{,}090}{12{,}000}, \\dfrac{8{,}249}{12{,}000}, \\dfrac{8{,}321}{12{,}000}, \\dfrac{8{,}369}{12{,}000}, \\dfrac{8{,}379}{12{,}000}, \\dfrac{8{,}587}{12{,}000}, \\dfrac{8{,}596}{12{,}000}, \\dfrac{8{,}620}{12{,}000}, \\dfrac{8{,}637}{12{,}000}, \\dfrac{8{,}654}{12{,}000}, \\text{ and } \\dfrac{8{,}852}{12{,}000}", "__seed__": "0688"}}, {"seed": 689, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.4005, 1.401, 1.402, 1.403, 1.404, 1.405, 1.406, 1.407, 1.408, and 1.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4009999999999998", "1.402", "1.4029999999999998", "1.404", "1.4049999999999998", "1.406", "1.4069999999999998", "1.408", "1.4089999999999998"], "p1_2_xs": ["1.4004999999999999"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}050}{56{,}000}, \\dfrac{48{,}068}{56{,}000}, \\dfrac{48{,}177}{56{,}000}, \\dfrac{48{,}365}{56{,}000}, \\dfrac{48{,}509}{56{,}000}, \\dfrac{48{,}608}{56{,}000}, \\dfrac{48{,}701}{56{,}000}, \\dfrac{48{,}714}{56{,}000}, \\dfrac{48{,}729}{56{,}000}, \\dfrac{48{,}754}{56{,}000}, \\text{ and } \\dfrac{48{,}811}{56{,}000}", "__seed__": "0689"}}, {"seed": 690, "data": {"p1_how_many": "14", "p1_a": "6.56", "p1_b": "6.57", "p1_numbers": "6.5605, 6.561, 6.5615, 6.562, 6.5625, 6.563, 6.5635, 6.564, 6.5645, 6.565, 6.566, 6.567, 6.568, and 6.569", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.561", "6.561999999999999", "6.563", "6.563999999999999", "6.5649999999999995", "6.566", "6.566999999999999", "6.568", "6.569"], "p1_2_xs": ["6.560499999999999", "6.5615", "6.562499999999999", "6.5634999999999994", "6.564499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0690"}}, {"seed": 691, "data": {"p1_how_many": "10", "p1_a": "4.37", "p1_b": "4.38", "p1_numbers": "4.3705, 4.371, 4.372, 4.373, 4.374, 4.375, 4.376, 4.377, 4.378, and 4.379", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.371", "4.372", "4.373", "4.374", "4.375", "4.376", "4.377", "4.378", "4.3790000000000004"], "p1_2_xs": ["4.3705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{616}{1{,}500}, \\dfrac{632}{1{,}500}, \\dfrac{679}{1{,}500}, \\dfrac{704}{1{,}500}, \\dfrac{784}{1{,}500}, \\dfrac{786}{1{,}500}, \\dfrac{874}{1{,}500}, \\dfrac{879}{1{,}500}, \\dfrac{903}{1{,}500}, \\dfrac{910}{1{,}500}, \\text{ and } \\dfrac{978}{1{,}500}", "__seed__": "0691"}}, {"seed": 692, "data": {"p1_how_many": "10", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.72, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}063}{56{,}000}, \\dfrac{17{,}061}{56{,}000}, \\dfrac{17{,}374}{56{,}000}, \\dfrac{18{,}068}{56{,}000}, \\dfrac{18{,}802}{56{,}000}, \\dfrac{19{,}176}{56{,}000}, \\dfrac{19{,}320}{56{,}000}, \\text{ and } \\dfrac{20{,}591}{56{,}000}", "__seed__": "0692"}}, {"seed": 693, "data": {"p1_how_many": "12", "p1_a": "3.26", "p1_b": "3.27", "p1_numbers": 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{"seed": 695, "data": {"p1_how_many": "14", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.015, 6.02, 6.025, 6.03, 6.035, 6.04, 6.045, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005", "6.015", "6.0249999999999995", "6.035", "6.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}250}{5{,}600}, \\dfrac{3{,}315}{5{,}600}, \\dfrac{3{,}317}{5{,}600}, \\dfrac{3{,}344}{5{,}600}, \\dfrac{3{,}433}{5{,}600}, \\dfrac{3{,}452}{5{,}600}, \\dfrac{3{,}473}{5{,}600}, \\text{ and } \\dfrac{3{,}481}{5{,}600}", "__seed__": "0695"}}, {"seed": 696, "data": {"p1_how_many": "12", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.74, 3.75, 3.76, 3.77, 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"p1_1_xs": ["4.051", "4.052", "4.053", "4.053999999999999", "4.055", "4.056", "4.0569999999999995", "4.058", "4.059"], "p1_2_xs": ["4.0504999999999995", "4.0515", "4.052499999999999", "4.0535", "4.054499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}821}{5{,}600}, \\dfrac{4{,}829}{5{,}600}, \\dfrac{4{,}845}{5{,}600}, \\dfrac{4{,}847}{5{,}600}, \\dfrac{4{,}863}{5{,}600}, \\dfrac{4{,}867}{5{,}600}, \\dfrac{4{,}875}{5{,}600}, \\dfrac{4{,}886}{5{,}600}, \\dfrac{4{,}893}{5{,}600}, \\dfrac{4{,}894}{5{,}600}, \\text{ and } \\dfrac{4{,}896}{5{,}600}", "__seed__": "0697"}}, {"seed": 698, "data": {"p1_how_many": "14", "p1_a": "9.24", "p1_b": "9.25", "p1_numbers": "9.2405, 9.241, 9.2415, 9.242, 9.2425, 9.243, 9.2435, 9.244, 9.2445, 9.245, 9.246, 9.247, 9.248, and 9.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.241", "9.242", "9.243", "9.244", "9.245000000000001", "9.246", "9.247", "9.248", "9.249"], "p1_2_xs": ["9.2405", "9.2415", "9.242500000000001", "9.243500000000001", "9.2445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{324}{1{,}200}, \\dfrac{334}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{371}{1{,}200}, \\dfrac{387}{1{,}200}, \\dfrac{390}{1{,}200}, \\text{ and } \\dfrac{397}{1{,}200}", "__seed__": "0698"}}, {"seed": 699, "data": {"p1_how_many": "12", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.725, 4.73, 4.74, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715", "4.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}256}{3{,}500}, \\dfrac{2{,}272}{3{,}500}, \\dfrac{2{,}302}{3{,}500}, \\dfrac{2{,}383}{3{,}500}, \\dfrac{2{,}469}{3{,}500}, \\dfrac{2{,}584}{3{,}500}, \\dfrac{2{,}655}{3{,}500}, \\text{ and } \\dfrac{2{,}725}{3{,}500}", "__seed__": "0699"}}, {"seed": 700, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}067}{42{,}000}, \\dfrac{35{,}071}{42{,}000}, \\dfrac{35{,}166}{42{,}000}, \\dfrac{35{,}169}{42{,}000}, \\dfrac{35{,}265}{42{,}000}, \\dfrac{35{,}270}{42{,}000}, \\dfrac{35{,}423}{42{,}000}, \\dfrac{35{,}501}{42{,}000}, \\dfrac{35{,}587}{42{,}000}, \\dfrac{35{,}706}{42{,}000}, \\dfrac{35{,}936}{42{,}000}, \\text{ and } \\dfrac{35{,}957}{42{,}000}", "__seed__": "0700"}}, {"seed": 701, "data": {"p1_how_many": "11", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.43, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{24{,}038}{30{,}000}, \\dfrac{24{,}076}{30{,}000}, \\dfrac{24{,}304}{30{,}000}, \\dfrac{24{,}330}{30{,}000}, \\dfrac{24{,}595}{30{,}000}, \\dfrac{24{,}632}{30{,}000}, \\dfrac{24{,}719}{30{,}000}, \\dfrac{24{,}720}{30{,}000}, \\dfrac{24{,}842}{30{,}000}, \\dfrac{24{,}863}{30{,}000}, \\text{ and } \\dfrac{24{,}987}{30{,}000}", "__seed__": "0701"}}, {"seed": 702, "data": {"p1_how_many": "10", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.52, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{312}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{353}{1{,}200}, \\dfrac{358}{1{,}200}, 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\\dfrac{35{,}988}{42{,}000}", "__seed__": "0703"}}, {"seed": 704, "data": {"p1_how_many": "14", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.625, 5.63, 5.635, 5.64, 5.645, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999", "5.635", "5.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{87}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0704"}}, {"seed": 705, "data": {"p1_how_many": "12", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.2005, 8.201, 8.2015, 8.202, 8.2025, 8.203, 8.204, 8.205, 8.206, 8.207, 8.208, and 8.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.200999999999999", "8.202", "8.203", "8.203999999999999", "8.205", "8.206", "8.206999999999999", "8.207999999999998", "8.209"], "p1_2_xs": ["8.2005", "8.2015", "8.2025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{762}{3{,}500}, \\dfrac{828}{3{,}500}, \\dfrac{831}{3{,}500}, \\dfrac{876}{3{,}500}, \\dfrac{882}{3{,}500}, \\dfrac{904}{3{,}500}, \\dfrac{937}{3{,}500}, \\dfrac{972}{3{,}500}, \\text{ and } \\dfrac{994}{3{,}500}", "__seed__": "0705"}}, {"seed": 706, "data": {"p1_how_many": "12", "p1_a": "7.71", "p1_b": "7.72", "p1_numbers": "7.7105, 7.711, 7.7115, 7.712, 7.7125, 7.713, 7.714, 7.715, 7.716, 7.717, 7.718, and 7.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.711", "7.712", "7.713", "7.7139999999999995", "7.715", "7.716", "7.717", "7.718", "7.719"], "p1_2_xs": ["7.7105", "7.7115", "7.7124999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}052}{20{,}000}, \\dfrac{15{,}261}{20{,}000}, \\dfrac{15{,}452}{20{,}000}, \\dfrac{15{,}549}{20{,}000}, \\dfrac{15{,}650}{20{,}000}, \\dfrac{15{,}675}{20{,}000}, \\dfrac{15{,}706}{20{,}000}, \\dfrac{15{,}804}{20{,}000}, \\dfrac{15{,}840}{20{,}000}, \\text{ and } \\dfrac{15{,}850}{20{,}000}", "__seed__": "0706"}}, {"seed": 707, "data": {"p1_how_many": "14", "p1_a": "9.7", "p1_b": "9.8", "p1_numbers": "9.705, 9.71, 9.715, 9.72, 9.725, 9.73, 9.735, 9.74, 9.745, 9.75, 9.76, 9.77, 9.78, and 9.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.709999999999999", "9.719999999999999", "9.729999999999999", "9.739999999999998", "9.75", "9.76", "9.77", "9.78", "9.79"], "p1_2_xs": ["9.705", "9.715", "9.725", "9.735", "9.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{143}{630}, \\dfrac{145}{630}, \\dfrac{146}{630}, \\dfrac{147}{630}, \\dfrac{152}{630}, \\dfrac{153}{630}, \\dfrac{155}{630}, \\dfrac{170}{630}, \\text{ and } \\dfrac{178}{630}", "__seed__": "0707"}}, {"seed": 708, "data": {"p1_how_many": "14", "p1_a": "3.51", "p1_b": "3.52", "p1_numbers": "3.5105, 3.511, 3.5115, 3.512, 3.5125, 3.513, 3.5135, 3.514, 3.5145, 3.515, 3.516, 3.517, 3.518, and 3.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.5109999999999997", "3.5119999999999996", "3.513", "3.514", "3.5149999999999997", "3.5159999999999996", "3.517", "3.518", "3.5189999999999997"], "p1_2_xs": ["3.5105", "3.5115", "3.5124999999999997", "3.5135", "3.5145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}530}{56{,}000}, \\dfrac{16{,}580}{56{,}000}, \\dfrac{16{,}654}{56{,}000}, \\dfrac{16{,}923}{56{,}000}, \\dfrac{16{,}950}{56{,}000}, \\dfrac{17{,}361}{56{,}000}, \\dfrac{18{,}505}{56{,}000}, \\dfrac{19{,}744}{56{,}000}, \\dfrac{19{,}965}{56{,}000}, \\dfrac{20{,}451}{56{,}000}, \\text{ and } \\dfrac{20{,}560}{56{,}000}", "__seed__": "0708"}}, {"seed": 709, "data": {"p1_how_many": "14", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.335, 2.34, 2.345, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997", "2.3349999999999995", "2.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}526}{20{,}000}, \\dfrac{12{,}641}{20{,}000}, \\dfrac{13{,}230}{20{,}000}, \\dfrac{13{,}296}{20{,}000}, \\dfrac{13{,}500}{20{,}000}, \\dfrac{13{,}652}{20{,}000}, \\dfrac{13{,}695}{20{,}000}, \\dfrac{13{,}943}{20{,}000}, \\dfrac{14{,}341}{20{,}000}, \\text{ and } \\dfrac{14{,}671}{20{,}000}", "__seed__": "0709"}}, {"seed": 710, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}414}{3{,}000}, \\dfrac{2{,}415}{3{,}000}, \\dfrac{2{,}442}{3{,}000}, \\dfrac{2{,}445}{3{,}000}, \\dfrac{2{,}446}{3{,}000}, \\dfrac{2{,}454}{3{,}000}, \\dfrac{2{,}457}{3{,}000}, \\dfrac{2{,}475}{3{,}000}, \\dfrac{2{,}479}{3{,}000}, \\dfrac{2{,}482}{3{,}000}, \\text{ and } \\dfrac{2{,}483}{3{,}000}", "__seed__": "0710"}}, {"seed": 711, "data": {"p1_how_many": "11", "p1_a": "6.1", "p1_b": "6.2", "p1_numbers": "6.105, 6.11, 6.115, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17, 6.18, and 6.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.109999999999999", "6.119999999999999", "6.13", "6.14", "6.1499999999999995", "6.159999999999999", "6.17", "6.18", "6.1899999999999995"], "p1_2_xs": ["6.1049999999999995", "6.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{103}{350}, \\dfrac{104}{350}, \\dfrac{105}{350}, \\dfrac{113}{350}, \\dfrac{123}{350}, \\dfrac{135}{350}, \\dfrac{136}{350}, \\text{ and } \\dfrac{138}{350}", "__seed__": "0711"}}, {"seed": 712, "data": {"p1_how_many": "14", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.125, 4.13, 4.135, 4.14, 4.145, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999", "4.124999999999999", "4.135", "4.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}007}{3{,}500}, \\dfrac{1{,}033}{3{,}500}, \\dfrac{1{,}038}{3{,}500}, \\dfrac{1{,}044}{3{,}500}, \\dfrac{1{,}071}{3{,}500}, \\dfrac{1{,}160}{3{,}500}, \\text{ and } \\dfrac{1{,}209}{3{,}500}", "__seed__": "0712"}}, {"seed": 713, "data": {"p1_how_many": "14", "p1_a": "8.93", "p1_b": "8.94", "p1_numbers": "8.9305, 8.931, 8.9315, 8.932, 8.9325, 8.933, 8.9335, 8.934, 8.9345, 8.935, 8.936, 8.937, 8.938, and 8.939", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.931", "8.932", "8.933", "8.934", "8.935", "8.936", "8.937", "8.937999999999999", "8.939"], "p1_2_xs": ["8.9305", "8.9315", "8.932500000000001", "8.9335", "8.9345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{424}{2{,}000}, \\dfrac{426}{2{,}000}, \\dfrac{432}{2{,}000}, \\dfrac{433}{2{,}000}, \\dfrac{437}{2{,}000}, \\dfrac{460}{2{,}000}, \\dfrac{468}{2{,}000}, \\dfrac{482}{2{,}000}, \\dfrac{493}{2{,}000}, \\text{ and } \\dfrac{495}{2{,}000}", "__seed__": "0713"}}, {"seed": 714, "data": {"p1_how_many": "10", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{157}{630}, \\dfrac{161}{630}, \\dfrac{164}{630}, \\dfrac{166}{630}, \\dfrac{167}{630}, \\dfrac{170}{630}, \\text{ and } \\dfrac{174}{630}", "__seed__": "0714"}}, {"seed": 715, "data": {"p1_how_many": "11", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.73, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{16{,}152}{35{,}000}, \\dfrac{16{,}197}{35{,}000}, \\dfrac{16{,}302}{35{,}000}, \\dfrac{16{,}870}{35{,}000}, \\dfrac{16{,}972}{35{,}000}, \\dfrac{17{,}156}{35{,}000}, \\dfrac{17{,}474}{35{,}000}, \\dfrac{17{,}592}{35{,}000}, \\text{ and } \\dfrac{20{,}575}{35{,}000}", "__seed__": "0715"}}, {"seed": 716, "data": {"p1_how_many": "11", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}182}{35{,}000}, \\dfrac{7{,}352}{35{,}000}, \\dfrac{7{,}728}{35{,}000}, \\dfrac{7{,}768}{35{,}000}, \\dfrac{7{,}864}{35{,}000}, \\dfrac{8{,}466}{35{,}000}, \\dfrac{8{,}494}{35{,}000}, \\dfrac{8{,}836}{35{,}000}, \\dfrac{8{,}873}{35{,}000}, \\text{ and } \\dfrac{9{,}522}{35{,}000}", "__seed__": "0716"}}, {"seed": 717, "data": {"p1_how_many": "12", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{305}{1{,}200}, \\dfrac{327}{1{,}200}, \\dfrac{329}{1{,}200}, \\dfrac{346}{1{,}200}, \\dfrac{350}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{369}{1{,}200}, \\text{ and } \\dfrac{374}{1{,}200}", "__seed__": "0717"}}, {"seed": 718, "data": {"p1_how_many": "11", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}544}{5{,}600}, \\dfrac{3{,}595}{5{,}600}, \\dfrac{3{,}609}{5{,}600}, \\dfrac{3{,}666}{5{,}600}, \\dfrac{3{,}713}{5{,}600}, \\dfrac{3{,}739}{5{,}600}, \\dfrac{3{,}839}{5{,}600}, \\dfrac{3{,}879}{5{,}600}, \\dfrac{3{,}907}{5{,}600}, \\dfrac{3{,}917}{5{,}600}, \\dfrac{3{,}931}{5{,}600}, \\text{ and } \\dfrac{3{,}933}{5{,}600}", "__seed__": "0718"}}, {"seed": 719, "data": {"p1_how_many": "13", "p1_a": "7.86", "p1_b": "7.87", "p1_numbers": "7.8605, 7.861, 7.8615, 7.862, 7.8625, 7.863, 7.8635, 7.864, 7.865, 7.866, 7.867, 7.868, and 7.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.861000000000001", "7.862", "7.863", "7.864", "7.865", "7.8660000000000005", "7.867", "7.868", "7.869000000000001"], "p1_2_xs": ["7.8605", "7.8615", "7.8625", "7.8635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}918}{20{,}000}, \\dfrac{6{,}064}{20{,}000}, \\dfrac{6{,}287}{20{,}000}, \\dfrac{6{,}751}{20{,}000}, \\dfrac{6{,}965}{20{,}000}, \\dfrac{7{,}396}{20{,}000}, \\dfrac{7{,}496}{20{,}000}, \\dfrac{7{,}735}{20{,}000}, \\dfrac{7{,}867}{20{,}000}, \\text{ and } \\dfrac{7{,}883}{20{,}000}", "__seed__": "0719"}}, {"seed": 720, "data": {"p1_how_many": "13", "p1_a": "2.96", "p1_b": "2.97", "p1_numbers": "2.9605, 2.961, 2.9615, 2.962, 2.9625, 2.963, 2.9635, 2.964, 2.965, 2.966, 2.967, 2.968, and 2.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.961", "2.9619999999999997", "2.963", "2.964", "2.965", "2.9659999999999997", "2.967", "2.968", "2.969"], "p1_2_xs": ["2.9605", "2.9615", "2.9625", "2.9635000000000002"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}117}{20{,}000}, \\dfrac{4{,}183}{20{,}000}, \\dfrac{4{,}368}{20{,}000}, \\dfrac{4{,}614}{20{,}000}, \\dfrac{4{,}674}{20{,}000}, \\dfrac{4{,}712}{20{,}000}, \\dfrac{4{,}831}{20{,}000}, \\text{ and } \\dfrac{4{,}837}{20{,}000}", "__seed__": "0720"}}, {"seed": 721, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{73}{420}, \\dfrac{80}{420}, \\dfrac{81}{420}, \\dfrac{86}{420}, \\dfrac{93}{420}, \\dfrac{97}{420}, \\text{ and } \\dfrac{105}{420}", "__seed__": "0721"}}, {"seed": 722, "data": {"p1_how_many": "10", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.42, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{618}{4{,}200}, \\dfrac{623}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{644}{4{,}200}, \\dfrac{646}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{666}{4{,}200}, \\dfrac{681}{4{,}200}, \\dfrac{696}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0722"}}, {"seed": 723, "data": {"p1_how_many": "14", "p1_a": "9.32", "p1_b": "9.33", "p1_numbers": "9.3205, 9.321, 9.3215, 9.322, 9.3225, 9.323, 9.3235, 9.324, 9.3245, 9.325, 9.326, 9.327, 9.328, and 9.329", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.321", "9.322000000000001", "9.323", "9.324", "9.325000000000001", "9.326", "9.327", "9.328", "9.329"], "p1_2_xs": ["9.320500000000001", "9.3215", "9.322500000000002", "9.323500000000001", "9.3245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{7{,}132}{56{,}000}, \\dfrac{7{,}311}{56{,}000}, \\dfrac{7{,}334}{56{,}000}, \\dfrac{7{,}596}{56{,}000}, \\dfrac{7{,}643}{56{,}000}, \\dfrac{7{,}660}{56{,}000}, \\dfrac{7{,}696}{56{,}000}, \\dfrac{7{,}816}{56{,}000}, \\dfrac{7{,}861}{56{,}000}, \\text{ and } \\dfrac{7{,}882}{56{,}000}", "__seed__": "0723"}}, {"seed": 724, "data": {"p1_how_many": "12", "p1_a": "5.01", "p1_b": "5.02", "p1_numbers": "5.0105, 5.011, 5.0115, 5.012, 5.0125, 5.013, 5.014, 5.015, 5.016, 5.017, 5.018, and 5.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.011", "5.012", "5.013", "5.013999999999999", "5.015", "5.016", "5.0169999999999995", "5.018", "5.019"], "p1_2_xs": ["5.0104999999999995", "5.0115", "5.012499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}120}{12{,}000}, \\dfrac{8{,}146}{12{,}000}, \\dfrac{8{,}516}{12{,}000}, \\dfrac{8{,}588}{12{,}000}, \\dfrac{8{,}831}{12{,}000}, \\dfrac{8{,}940}{12{,}000}, \\text{ and } \\dfrac{8{,}973}{12{,}000}", "__seed__": "0724"}}, {"seed": 725, "data": {"p1_how_many": "12", "p1_a": "3.51", "p1_b": "3.52", "p1_numbers": "3.5105, 3.511, 3.5115, 3.512, 3.5125, 3.513, 3.514, 3.515, 3.516, 3.517, 3.518, and 3.519", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.5109999999999997", "3.5119999999999996", "3.513", "3.514", "3.5149999999999997", "3.5159999999999996", "3.517", "3.518", "3.5189999999999997"], "p1_2_xs": ["3.5105", "3.5115", "3.5124999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0725"}}, {"seed": 726, "data": {"p1_how_many": "13", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": "1.305, 1.31, 1.315, 1.32, 1.325, 1.33, 1.335, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.31", "1.32", "1.33", "1.34", "1.35", "1.36", "1.37", "1.3800000000000001", "1.3900000000000001"], "p1_2_xs": ["1.305", "1.315", "1.325", "1.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}335}{42{,}000}, \\dfrac{7{,}874}{42{,}000}, \\dfrac{7{,}923}{42{,}000}, \\dfrac{9{,}014}{42{,}000}, \\dfrac{9{,}311}{42{,}000}, \\dfrac{9{,}785}{42{,}000}, \\dfrac{10{,}109}{42{,}000}, \\dfrac{10{,}809}{42{,}000}, \\dfrac{11{,}152}{42{,}000}, \\dfrac{11{,}531}{42{,}000}, \\dfrac{11{,}550}{42{,}000}, \\text{ and } \\dfrac{11{,}602}{42{,}000}", "__seed__": "0726"}}, {"seed": 727, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{604}{4{,}200}, \\dfrac{605}{4{,}200}, \\dfrac{620}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{641}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{664}{4{,}200}, \\dfrac{666}{4{,}200}, \\dfrac{668}{4{,}200}, \\text{ and } \\dfrac{676}{4{,}200}", "__seed__": "0727"}}, {"seed": 728, "data": {"p1_how_many": "12", "p1_a": "7.57", "p1_b": "7.58", "p1_numbers": "7.5705, 7.571, 7.5715, 7.572, 7.5725, 7.573, 7.574, 7.575, 7.576, 7.577, 7.578, and 7.579", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.571000000000001", "7.572", "7.573", "7.574", "7.575", "7.5760000000000005", "7.577", "7.578", "7.579000000000001"], "p1_2_xs": ["7.5705", "7.5715", "7.5725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0728"}}, {"seed": 729, "data": {"p1_how_many": "13", "p1_a": "6.74", "p1_b": "6.75", "p1_numbers": "6.7405, 6.741, 6.7415, 6.742, 6.7425, 6.743, 6.7435, 6.744, 6.745, 6.746, 6.747, 6.748, and 6.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.7410000000000005", "6.742", "6.743", "6.744", "6.745", "6.746", "6.747", "6.748", "6.7490000000000006"], "p1_2_xs": ["6.7405", "6.7415", "6.7425", "6.7435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{751}{4{,}200}, \\dfrac{788}{4{,}200}, \\dfrac{807}{4{,}200}, \\dfrac{893}{4{,}200}, \\dfrac{926}{4{,}200}, \\dfrac{951}{4{,}200}, \\dfrac{963}{4{,}200}, \\dfrac{999}{4{,}200}, \\dfrac{1{,}103}{4{,}200}, \\text{ and } \\dfrac{1{,}145}{4{,}200}", "__seed__": "0729"}}, {"seed": 730, "data": {"p1_how_many": "11", "p1_a": "9.13", "p1_b": "9.14", "p1_numbers": "9.1305, 9.131, 9.1315, 9.132, 9.133, 9.134, 9.135, 9.136, 9.137, 9.138, and 9.139", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.131", "9.132000000000001", "9.133000000000001", "9.134", "9.135000000000002", "9.136000000000001", "9.137", "9.138", "9.139000000000001"], "p1_2_xs": ["9.130500000000001", "9.1315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{733}{4{,}200}, \\dfrac{769}{4{,}200}, \\dfrac{775}{4{,}200}, \\dfrac{841}{4{,}200}, \\dfrac{847}{4{,}200}, \\dfrac{855}{4{,}200}, \\dfrac{912}{4{,}200}, \\dfrac{1{,}004}{4{,}200}, \\dfrac{1{,}018}{4{,}200}, \\dfrac{1{,}019}{4{,}200}, \\text{ and } \\dfrac{1{,}171}{4{,}200}", "__seed__": "0730"}}, {"seed": 731, "data": {"p1_how_many": "10", "p1_a": "6.22", "p1_b": "6.23", "p1_numbers": "6.2205, 6.221, 6.222, 6.223, 6.224, 6.225, 6.226, 6.227, 6.228, and 6.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.221", "6.2219999999999995", "6.223", "6.223999999999999", "6.225", "6.226", "6.226999999999999", "6.228", "6.229"], "p1_2_xs": ["6.2204999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}175}{42{,}000}, \\dfrac{35{,}229}{42{,}000}, \\dfrac{35{,}343}{42{,}000}, \\dfrac{35{,}391}{42{,}000}, \\dfrac{35{,}512}{42{,}000}, \\dfrac{35{,}870}{42{,}000}, \\text{ and } \\dfrac{35{,}882}{42{,}000}", "__seed__": "0731"}}, {"seed": 732, "data": {"p1_how_many": "10", "p1_a": "6.0", "p1_b": "6.1", "p1_numbers": "6.005, 6.01, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, and 6.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.01", "6.02", "6.03", "6.04", "6.05", "6.06", "6.07", "6.08", "6.09"], "p1_2_xs": ["6.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{10{,}232}{35{,}000}, \\dfrac{10{,}332}{35{,}000}, \\dfrac{10{,}580}{35{,}000}, \\dfrac{10{,}797}{35{,}000}, \\dfrac{11{,}008}{35{,}000}, \\dfrac{11{,}561}{35{,}000}, \\dfrac{11{,}631}{35{,}000}, \\dfrac{11{,}664}{35{,}000}, \\dfrac{11{,}823}{35{,}000}, \\dfrac{11{,}958}{35{,}000}, \\text{ and } \\dfrac{13{,}455}{35{,}000}", "__seed__": "0732"}}, {"seed": 733, "data": {"p1_how_many": "13", "p1_a": "9.06", "p1_b": "9.07", "p1_numbers": "9.0605, 9.061, 9.0615, 9.062, 9.0625, 9.063, 9.0635, 9.064, 9.065, 9.066, 9.067, 9.068, and 9.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.061", "9.062000000000001", "9.063", "9.064", "9.065000000000001", "9.066", "9.067", "9.068", "9.069"], "p1_2_xs": ["9.060500000000001", "9.0615", "9.062500000000002", "9.063500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}830}{6{,}300}, \\dfrac{2{,}912}{6{,}300}, \\dfrac{2{,}930}{6{,}300}, \\dfrac{3{,}224}{6{,}300}, \\dfrac{3{,}279}{6{,}300}, \\dfrac{3{,}330}{6{,}300}, \\dfrac{3{,}356}{6{,}300}, \\dfrac{3{,}402}{6{,}300}, \\dfrac{3{,}477}{6{,}300}, \\dfrac{3{,}530}{6{,}300}, \\text{ and } \\dfrac{3{,}596}{6{,}300}", "__seed__": "0733"}}, {"seed": 734, "data": {"p1_how_many": "13", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.035, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995", "7.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{71}{350}, \\dfrac{75}{350}, \\dfrac{76}{350}, \\dfrac{86}{350}, \\dfrac{88}{350}, \\dfrac{89}{350}, \\dfrac{95}{350}, \\text{ and } \\dfrac{97}{350}", "__seed__": "0734"}}, {"seed": 735, "data": {"p1_how_many": "10", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{502}{1{,}500}, \\dfrac{510}{1{,}500}, \\dfrac{522}{1{,}500}, \\dfrac{523}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{568}{1{,}500}, \\text{ and } \\dfrac{594}{1{,}500}", "__seed__": "0735"}}, {"seed": 736, "data": {"p1_how_many": "14", "p1_a": "3.96", "p1_b": "3.97", "p1_numbers": "3.9605, 3.961, 3.9615, 3.962, 3.9625, 3.963, 3.9635, 3.964, 3.9645, 3.965, 3.966, 3.967, 3.968, and 3.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.961", "3.9619999999999997", "3.963", "3.964", "3.965", "3.9659999999999997", "3.967", "3.968", "3.969"], "p1_2_xs": ["3.9605", "3.9615", "3.9625", "3.9635000000000002", "3.9645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}047}{4{,}200}, \\dfrac{3{,}074}{4{,}200}, \\dfrac{3{,}120}{4{,}200}, \\dfrac{3{,}122}{4{,}200}, \\dfrac{3{,}149}{4{,}200}, \\dfrac{3{,}227}{4{,}200}, \\dfrac{3{,}234}{4{,}200}, \\dfrac{3{,}290}{4{,}200}, \\dfrac{3{,}353}{4{,}200}, \\dfrac{3{,}416}{4{,}200}, \\text{ and } \\dfrac{3{,}496}{4{,}200}", "__seed__": "0736"}}, {"seed": 737, "data": {"p1_how_many": "13", "p1_a": "2.34", "p1_b": "2.35", "p1_numbers": "2.3405, 2.341, 2.3415, 2.342, 2.3425, 2.343, 2.3435, 2.344, 2.345, 2.346, 2.347, 2.348, and 2.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3409999999999997", "2.3419999999999996", "2.343", "2.344", "2.3449999999999998", "2.3459999999999996", "2.347", "2.348", "2.3489999999999998"], "p1_2_xs": ["2.3405", "2.3415", "2.3425", "2.3435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{511}{2{,}000}, \\dfrac{542}{2{,}000}, \\dfrac{555}{2{,}000}, \\dfrac{601}{2{,}000}, \\dfrac{632}{2{,}000}, \\dfrac{640}{2{,}000}, \\dfrac{657}{2{,}000}, \\dfrac{724}{2{,}000}, \\dfrac{746}{2{,}000}, \\text{ and } \\dfrac{749}{2{,}000}", "__seed__": "0737"}}, {"seed": 738, "data": {"p1_how_many": "14", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.3005, 6.301, 6.3015, 6.302, 6.3025, 6.303, 6.3035, 6.304, 6.3045, 6.305, 6.306, 6.307, 6.308, and 6.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.301", "6.302", "6.303", "6.303999999999999", "6.305", "6.306", "6.3069999999999995", "6.308", "6.309"], "p1_2_xs": ["6.3004999999999995", "6.3015", "6.302499999999999", "6.3035", "6.304499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{508}{3{,}000}, \\dfrac{532}{3{,}000}, \\dfrac{538}{3{,}000}, \\dfrac{542}{3{,}000}, \\dfrac{550}{3{,}000}, \\dfrac{556}{3{,}000}, \\dfrac{558}{3{,}000}, \\dfrac{561}{3{,}000}, \\dfrac{568}{3{,}000}, \\dfrac{579}{3{,}000}, \\text{ and } \\dfrac{581}{3{,}000}", "__seed__": "0738"}}, {"seed": 739, "data": {"p1_how_many": "14", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.545, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997", "3.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}510}{6{,}300}, \\dfrac{1{,}540}{6{,}300}, \\dfrac{1{,}581}{6{,}300}, \\dfrac{1{,}685}{6{,}300}, \\dfrac{1{,}708}{6{,}300}, \\dfrac{1{,}748}{6{,}300}, \\text{ and } \\dfrac{1{,}770}{6{,}300}", "__seed__": "0739"}}, {"seed": 740, "data": {"p1_how_many": "11", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{35{,}068}{42{,}000}, \\dfrac{35{,}263}{42{,}000}, \\dfrac{35{,}385}{42{,}000}, \\dfrac{35{,}398}{42{,}000}, \\dfrac{35{,}443}{42{,}000}, \\dfrac{35{,}458}{42{,}000}, \\text{ and } \\dfrac{35{,}703}{42{,}000}", "__seed__": "0740"}}, {"seed": 741, "data": {"p1_how_many": "14", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135", "2.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0741"}}, {"seed": 742, "data": {"p1_how_many": "14", "p1_a": "1.65", "p1_b": "1.66", "p1_numbers": "1.6505, 1.651, 1.6515, 1.652, 1.6525, 1.653, 1.6535, 1.654, 1.6545, 1.655, 1.656, 1.657, 1.658, and 1.659", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.6509999999999998", "1.652", "1.6529999999999998", "1.654", "1.6549999999999998", "1.656", "1.6569999999999998", "1.658", "1.6589999999999998"], "p1_2_xs": ["1.6504999999999999", "1.6514999999999997", "1.6524999999999999", "1.6534999999999997", "1.6544999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}419}{3{,}000}, \\dfrac{2{,}432}{3{,}000}, \\dfrac{2{,}446}{3{,}000}, \\dfrac{2{,}447}{3{,}000}, \\dfrac{2{,}450}{3{,}000}, \\dfrac{2{,}457}{3{,}000}, \\dfrac{2{,}464}{3{,}000}, \\dfrac{2{,}475}{3{,}000}, \\dfrac{2{,}476}{3{,}000}, \\dfrac{2{,}486}{3{,}000}, \\dfrac{2{,}493}{3{,}000}, \\text{ and } \\dfrac{2{,}494}{3{,}000}", "__seed__": "0742"}}, {"seed": 743, "data": {"p1_how_many": "10", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}160}{35{,}000}, \\dfrac{20{,}306}{35{,}000}, \\dfrac{20{,}472}{35{,}000}, \\dfrac{20{,}560}{35{,}000}, \\dfrac{20{,}573}{35{,}000}, \\dfrac{20{,}746}{35{,}000}, \\dfrac{20{,}813}{35{,}000}, \\dfrac{20{,}879}{35{,}000}, \\dfrac{20{,}923}{35{,}000}, \\dfrac{20{,}925}{35{,}000}, \\text{ and } \\dfrac{20{,}995}{35{,}000}", "__seed__": "0743"}}, {"seed": 744, "data": {"p1_how_many": "12", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.7005, 5.701, 5.7015, 5.702, 5.7025, 5.703, 5.704, 5.705, 5.706, 5.707, 5.708, and 5.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7010000000000005", "5.702", "5.703", "5.704", "5.705", "5.706", "5.707", "5.708", "5.7090000000000005"], "p1_2_xs": ["5.7005", "5.7015", "5.7025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}113}{56{,}000}, \\dfrac{33{,}446}{56{,}000}, \\dfrac{33{,}553}{56{,}000}, \\dfrac{33{,}844}{56{,}000}, \\dfrac{34{,}004}{56{,}000}, \\dfrac{34{,}098}{56{,}000}, \\dfrac{34{,}573}{56{,}000}, \\text{ and } \\dfrac{34{,}771}{56{,}000}", "__seed__": "0744"}}, {"seed": 745, "data": {"p1_how_many": "12", "p1_a": "9.53", "p1_b": "9.54", "p1_numbers": "9.5305, 9.531, 9.5315, 9.532, 9.5325, 9.533, 9.534, 9.535, 9.536, 9.537, 9.538, and 9.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.530999999999999", "9.532", "9.533", "9.533999999999999", "9.535", "9.536", "9.536999999999999", "9.537999999999998", "9.539"], "p1_2_xs": ["9.5305", "9.5315", "9.5325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}002}{20{,}000}, \\dfrac{15{,}014}{20{,}000}, \\dfrac{15{,}055}{20{,}000}, \\dfrac{15{,}092}{20{,}000}, \\dfrac{15{,}103}{20{,}000}, \\dfrac{15{,}126}{20{,}000}, \\dfrac{15{,}143}{20{,}000}, \\dfrac{15{,}248}{20{,}000}, \\dfrac{15{,}363}{20{,}000}, \\dfrac{15{,}385}{20{,}000}, \\text{ and } \\dfrac{15{,}964}{20{,}000}", "__seed__": "0745"}}, {"seed": 746, "data": {"p1_how_many": "13", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.425, 5.43, 5.435, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415", "5.425", "5.4350000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{635}{1{,}500}, \\dfrac{659}{1{,}500}, \\dfrac{677}{1{,}500}, \\dfrac{709}{1{,}500}, \\dfrac{757}{1{,}500}, \\dfrac{844}{1{,}500}, \\dfrac{859}{1{,}500}, \\dfrac{923}{1{,}500}, \\text{ and } \\dfrac{930}{1{,}500}", "__seed__": "0746"}}, {"seed": 747, "data": {"p1_how_many": "11", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.73, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{15{,}392}{35{,}000}, \\dfrac{15{,}416}{35{,}000}, \\dfrac{15{,}587}{35{,}000}, \\dfrac{15{,}620}{35{,}000}, \\dfrac{15{,}829}{35{,}000}, \\dfrac{16{,}149}{35{,}000}, \\dfrac{16{,}900}{35{,}000}, \\dfrac{17{,}302}{35{,}000}, \\dfrac{19{,}210}{35{,}000}, \\text{ and } \\dfrac{19{,}620}{35{,}000}", "__seed__": "0747"}}, {"seed": 748, "data": {"p1_how_many": "11", "p1_a": "9.62", "p1_b": "9.63", "p1_numbers": "9.6205, 9.621, 9.6215, 9.622, 9.623, 9.624, 9.625, 9.626, 9.627, 9.628, and 9.629", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.620999999999999", "9.622", "9.623", "9.623999999999999", "9.625", "9.626", "9.626999999999999", "9.627999999999998", "9.629"], "p1_2_xs": ["9.6205", "9.6215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{8}", "p2_b": "\\dfrac{1}{7}", "p2_numbers": "\\dfrac{710}{5{,}600}, \\dfrac{713}{5{,}600}, \\dfrac{724}{5{,}600}, \\dfrac{730}{5{,}600}, \\dfrac{740}{5{,}600}, \\dfrac{755}{5{,}600}, \\dfrac{757}{5{,}600}, \\dfrac{759}{5{,}600}, \\dfrac{785}{5{,}600}, \\dfrac{788}{5{,}600}, \\text{ and } \\dfrac{798}{5{,}600}", "__seed__": "0748"}}, {"seed": 749, "data": {"p1_how_many": "13", "p1_a": "4.43", "p1_b": "4.44", "p1_numbers": "4.4305, 4.431, 4.4315, 4.432, 4.4325, 4.433, 4.4335, 4.434, 4.435, 4.436, 4.437, 4.438, and 4.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.431", "4.4319999999999995", "4.433", "4.433999999999999", "4.435", "4.436", "4.436999999999999", "4.438", "4.439"], "p1_2_xs": ["4.430499999999999", "4.4315", "4.432499999999999", "4.4334999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}507}{4{,}200}, \\dfrac{3{,}513}{4{,}200}, \\dfrac{3{,}531}{4{,}200}, \\dfrac{3{,}534}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}536}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}554}{4{,}200}, \\dfrac{3{,}568}{4{,}200}, \\dfrac{3{,}582}{4{,}200}, \\text{ and } \\dfrac{3{,}594}{4{,}200}", "__seed__": "0749"}}, {"seed": 750, "data": {"p1_how_many": "13", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.535, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995", "7.535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}211}{2{,}000}, \\dfrac{1{,}246}{2{,}000}, \\dfrac{1{,}414}{2{,}000}, \\dfrac{1{,}417}{2{,}000}, \\dfrac{1{,}424}{2{,}000}, \\dfrac{1{,}429}{2{,}000}, \\dfrac{1{,}459}{2{,}000}, \\text{ and } \\dfrac{1{,}460}{2{,}000}", "__seed__": "0750"}}, {"seed": 751, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}130}{15{,}000}, \\dfrac{5{,}211}{15{,}000}, \\dfrac{5{,}264}{15{,}000}, \\dfrac{5{,}287}{15{,}000}, \\dfrac{5{,}348}{15{,}000}, \\dfrac{5{,}370}{15{,}000}, \\dfrac{5{,}388}{15{,}000}, \\dfrac{5{,}543}{15{,}000}, \\dfrac{5{,}738}{15{,}000}, \\dfrac{5{,}825}{15{,}000}, \\dfrac{5{,}937}{15{,}000}, \\text{ and } \\dfrac{5{,}996}{15{,}000}", "__seed__": "0751"}}, {"seed": 752, "data": {"p1_how_many": "11", "p1_a": "8.06", "p1_b": "8.07", "p1_numbers": "8.0605, 8.061, 8.0615, 8.062, 8.063, 8.064, 8.065, 8.066, 8.067, 8.068, and 8.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.061", "8.062000000000001", "8.063", "8.064", "8.065000000000001", "8.066", "8.067", "8.068", "8.069"], "p1_2_xs": ["8.060500000000001", "8.0615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{934}{6{,}300}, \\dfrac{1{,}045}{6{,}300}, \\dfrac{1{,}076}{6{,}300}, \\dfrac{1{,}089}{6{,}300}, \\dfrac{1{,}202}{6{,}300}, \\dfrac{1{,}244}{6{,}300}, \\dfrac{1{,}254}{6{,}300}, \\dfrac{1{,}257}{6{,}300}, \\dfrac{1{,}313}{6{,}300}, \\dfrac{1{,}319}{6{,}300}, \\dfrac{1{,}346}{6{,}300}, \\text{ and } \\dfrac{1{,}398}{6{,}300}", "__seed__": "0752"}}, {"seed": 753, "data": {"p1_how_many": "13", "p1_a": "2.45", "p1_b": "2.46", "p1_numbers": "2.4505, 2.451, 2.4515, 2.452, 2.4525, 2.453, 2.4535, 2.454, 2.455, 2.456, 2.457, 2.458, and 2.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.451", "2.452", "2.4530000000000003", "2.454", "2.455", "2.456", "2.4570000000000003", "2.458", "2.459"], "p1_2_xs": ["2.4505000000000003", "2.4515000000000002", "2.4525", "2.4535000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0753"}}, {"seed": 754, "data": {"p1_how_many": "13", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}305}{12{,}000}, \\dfrac{3{,}516}{12{,}000}, \\dfrac{3{,}634}{12{,}000}, \\dfrac{3{,}738}{12{,}000}, \\dfrac{3{,}775}{12{,}000}, \\dfrac{3{,}865}{12{,}000}, \\text{ and } \\dfrac{3{,}888}{12{,}000}", "__seed__": "0754"}}, {"seed": 755, "data": {"p1_how_many": "11", "p1_a": "2.21", "p1_b": "2.22", "p1_numbers": "2.2105, 2.211, 2.2115, 2.212, 2.213, 2.214, 2.215, 2.216, 2.217, 2.218, and 2.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.211", "2.2119999999999997", "2.213", "2.214", "2.215", "2.2159999999999997", "2.217", "2.218", "2.219"], "p1_2_xs": ["2.2105", "2.2115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{608}{1{,}500}, \\dfrac{664}{1{,}500}, \\dfrac{761}{1{,}500}, \\dfrac{865}{1{,}500}, \\dfrac{916}{1{,}500}, \\dfrac{973}{1{,}500}, \\text{ and } \\dfrac{977}{1{,}500}", "__seed__": "0755"}}, {"seed": 756, "data": {"p1_how_many": "13", "p1_a": "7.7", "p1_b": "7.8", "p1_numbers": "7.705, 7.71, 7.715, 7.72, 7.725, 7.73, 7.735, 7.74, 7.75, 7.76, 7.77, 7.78, and 7.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.71", "7.72", "7.73", "7.74", "7.75", "7.76", "7.7700000000000005", "7.78", "7.79"], "p1_2_xs": ["7.705", "7.715", "7.725", "7.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}071}{63{,}000}, \\dfrac{27{,}198}{63{,}000}, \\dfrac{27{,}302}{63{,}000}, \\dfrac{27{,}335}{63{,}000}, \\dfrac{27{,}351}{63{,}000}, \\dfrac{27{,}398}{63{,}000}, \\dfrac{27{,}447}{63{,}000}, \\text{ and } \\dfrac{27{,}506}{63{,}000}", "__seed__": "0756"}}, {"seed": 757, "data": {"p1_how_many": "13", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}507}{5{,}600}, \\dfrac{3{,}675}{5{,}600}, \\dfrac{3{,}751}{5{,}600}, \\dfrac{3{,}787}{5{,}600}, \\dfrac{3{,}800}{5{,}600}, \\dfrac{3{,}805}{5{,}600}, \\dfrac{3{,}825}{5{,}600}, \\dfrac{3{,}831}{5{,}600}, \\dfrac{3{,}870}{5{,}600}, \\text{ and } \\dfrac{3{,}958}{5{,}600}", "__seed__": "0757"}}, {"seed": 758, "data": {"p1_how_many": "13", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.125, 1.13, 1.135, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115", "1.125", "1.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{295}{630}, \\dfrac{307}{630}, \\dfrac{309}{630}, \\dfrac{310}{630}, \\dfrac{337}{630}, \\dfrac{346}{630}, \\dfrac{353}{630}, \\text{ and } \\dfrac{359}{630}", "__seed__": "0758"}}, {"seed": 759, "data": {"p1_how_many": "12", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.025, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015", "1.025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}406}{3{,}500}, \\dfrac{1{,}412}{3{,}500}, \\dfrac{1{,}427}{3{,}500}, \\dfrac{1{,}436}{3{,}500}, \\dfrac{1{,}440}{3{,}500}, \\dfrac{1{,}442}{3{,}500}, \\dfrac{1{,}446}{3{,}500}, \\dfrac{1{,}450}{3{,}500}, \\dfrac{1{,}461}{3{,}500}, \\dfrac{1{,}465}{3{,}500}, \\dfrac{1{,}493}{3{,}500}, \\text{ and } \\dfrac{1{,}497}{3{,}500}", "__seed__": "0759"}}, {"seed": 760, "data": {"p1_how_many": "13", "p1_a": "3.64", "p1_b": "3.65", "p1_numbers": 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4.715, 4.72, 4.73, 4.74, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{517}{2{,}000}, \\dfrac{557}{2{,}000}, \\dfrac{594}{2{,}000}, \\dfrac{612}{2{,}000}, \\dfrac{632}{2{,}000}, \\dfrac{661}{2{,}000}, \\dfrac{678}{2{,}000}, \\dfrac{687}{2{,}000}, \\dfrac{694}{2{,}000}, \\text{ and } \\dfrac{772}{2{,}000}", "__seed__": "0762"}}, {"seed": 763, "data": {"p1_how_many": "13", "p1_a": "2.76", "p1_b": "2.77", "p1_numbers": "2.7605, 2.761, 2.7615, 2.762, 2.7625, 2.763, 2.7635, 2.764, 2.765, 2.766, 2.767, 2.768, and 2.769", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.7609999999999997", "2.7619999999999996", "2.763", "2.764", "2.7649999999999997", "2.7659999999999996", "2.767", "2.768", "2.7689999999999997"], "p1_2_xs": ["2.7605", "2.7615", "2.7624999999999997", "2.7635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{304}{1{,}200}, \\dfrac{327}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{337}{1{,}200}, \\dfrac{346}{1{,}200}, \\dfrac{348}{1{,}200}, \\dfrac{355}{1{,}200}, \\dfrac{365}{1{,}200}, \\dfrac{366}{1{,}200}, \\dfrac{373}{1{,}200}, \\dfrac{393}{1{,}200}, \\text{ and } \\dfrac{398}{1{,}200}", "__seed__": "0763"}}, {"seed": 764, "data": {"p1_how_many": "10", "p1_a": "8.43", "p1_b": "8.44", "p1_numbers": "8.4305, 8.431, 8.432, 8.433, 8.434, 8.435, 8.436, 8.437, 8.438, and 8.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.431", "8.432", "8.433", "8.434", "8.435", "8.436", "8.437", "8.437999999999999", "8.439"], "p1_2_xs": ["8.4305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}025}{12{,}000}, \\dfrac{3{,}107}{12{,}000}, \\dfrac{3{,}121}{12{,}000}, \\dfrac{3{,}252}{12{,}000}, \\dfrac{3{,}411}{12{,}000}, \\dfrac{3{,}428}{12{,}000}, \\dfrac{3{,}527}{12{,}000}, \\dfrac{3{,}584}{12{,}000}, \\text{ and } \\dfrac{3{,}725}{12{,}000}", "__seed__": "0764"}}, {"seed": 765, "data": {"p1_how_many": "11", "p1_a": "1.87", "p1_b": "1.88", "p1_numbers": "1.8705, 1.871, 1.8715, 1.872, 1.873, 1.874, 1.875, 1.876, 1.877, 1.878, and 1.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.871", "1.872", "1.873", "1.874", "1.875", "1.8760000000000001", "1.877", "1.8780000000000001", "1.879"], "p1_2_xs": ["1.8705", "1.8715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}403}{3{,}500}, \\dfrac{1{,}406}{3{,}500}, \\dfrac{1{,}407}{3{,}500}, \\dfrac{1{,}421}{3{,}500}, \\dfrac{1{,}424}{3{,}500}, \\dfrac{1{,}425}{3{,}500}, \\dfrac{1{,}445}{3{,}500}, \\dfrac{1{,}458}{3{,}500}, \\dfrac{1{,}461}{3{,}500}, \\dfrac{1{,}465}{3{,}500}, \\dfrac{1{,}477}{3{,}500}, \\text{ and } \\dfrac{1{,}498}{3{,}500}", "__seed__": "0765"}}, {"seed": 766, "data": {"p1_how_many": "11", "p1_a": "5.86", "p1_b": "5.87", "p1_numbers": "5.8605, 5.861, 5.8615, 5.862, 5.863, 5.864, 5.865, 5.866, 5.867, 5.868, and 5.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.861000000000001", "5.862", "5.863", "5.864", "5.865", "5.8660000000000005", "5.867", "5.868", "5.869000000000001"], "p1_2_xs": ["5.8605", "5.8615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}009}{3{,}500}, \\dfrac{2{,}090}{3{,}500}, \\dfrac{2{,}190}{3{,}500}, \\dfrac{2{,}301}{3{,}500}, \\dfrac{2{,}315}{3{,}500}, \\dfrac{2{,}399}{3{,}500}, \\dfrac{2{,}673}{3{,}500}, \\dfrac{2{,}713}{3{,}500}, \\text{ and } \\dfrac{2{,}777}{3{,}500}", "__seed__": "0766"}}, {"seed": 767, "data": {"p1_how_many": "10", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}146}{20{,}000}, \\dfrac{5{,}510}{20{,}000}, \\dfrac{5{,}870}{20{,}000}, \\dfrac{5{,}903}{20{,}000}, \\dfrac{6{,}013}{20{,}000}, \\dfrac{6{,}118}{20{,}000}, \\dfrac{6{,}737}{20{,}000}, \\dfrac{7{,}157}{20{,}000}, \\dfrac{7{,}525}{20{,}000}, \\dfrac{7{,}562}{20{,}000}, \\text{ and } \\dfrac{7{,}962}{20{,}000}", "__seed__": "0767"}}, {"seed": 768, "data": {"p1_how_many": "13", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.135, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125", "3.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}026}{42{,}000}, \\dfrac{6{,}057}{42{,}000}, \\dfrac{6{,}309}{42{,}000}, \\dfrac{6{,}396}{42{,}000}, \\dfrac{6{,}582}{42{,}000}, \\dfrac{6{,}674}{42{,}000}, \\dfrac{6{,}762}{42{,}000}, \\dfrac{6{,}778}{42{,}000}, \\dfrac{6{,}810}{42{,}000}, \\dfrac{6{,}857}{42{,}000}, \\text{ and } \\dfrac{6{,}935}{42{,}000}", "__seed__": "0768"}}, {"seed": 769, "data": {"p1_how_many": "12", "p1_a": "8.26", "p1_b": "8.27", "p1_numbers": "8.2605, 8.261, 8.2615, 8.262, 8.2625, 8.263, 8.264, 8.265, 8.266, 8.267, 8.268, and 8.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.261", "8.262", "8.263", "8.264", "8.265", "8.266", "8.267", "8.267999999999999", "8.269"], "p1_2_xs": ["8.2605", "8.2615", "8.262500000000001"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{81}{120}, \\dfrac{82}{120}, \\dfrac{83}{120}, \\dfrac{84}{120}, \\dfrac{85}{120}, \\dfrac{86}{120}, \\dfrac{88}{120}, \\text{ and } \\dfrac{89}{120}", "__seed__": "0769"}}, {"seed": 770, "data": {"p1_how_many": "11", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.105, 5.11, 5.115, 5.12, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, and 5.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.109999999999999", "5.119999999999999", "5.13", "5.14", "5.1499999999999995", "5.159999999999999", "5.17", "5.18", "5.1899999999999995"], "p1_2_xs": ["5.1049999999999995", "5.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{516}{2{,}000}, \\dfrac{593}{2{,}000}, \\dfrac{637}{2{,}000}, \\dfrac{643}{2{,}000}, \\dfrac{669}{2{,}000}, \\dfrac{699}{2{,}000}, \\dfrac{701}{2{,}000}, \\dfrac{714}{2{,}000}, \\dfrac{754}{2{,}000}, \\dfrac{755}{2{,}000}, \\text{ and } \\dfrac{784}{2{,}000}", "__seed__": "0770"}}, {"seed": 771, "data": {"p1_how_many": "13", "p1_a": "3.44", "p1_b": "3.45", "p1_numbers": "3.4405, 3.441, 3.4415, 3.442, 3.4425, 3.443, 3.4435, 3.444, 3.445, 3.446, 3.447, 3.448, and 3.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.441", "3.4419999999999997", "3.443", "3.444", "3.445", "3.4459999999999997", "3.447", "3.448", "3.449"], "p1_2_xs": ["3.4405", "3.4415", "3.4425", "3.4435000000000002"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{22{,}431}{35{,}000}, \\dfrac{22{,}906}{35{,}000}, \\dfrac{23{,}468}{35{,}000}, \\dfrac{23{,}765}{35{,}000}, \\dfrac{25{,}507}{35{,}000}, \\dfrac{26{,}118}{35{,}000}, \\dfrac{26{,}325}{35{,}000}, \\dfrac{27{,}208}{35{,}000}, \\text{ and } \\dfrac{27{,}430}{35{,}000}", "__seed__": "0771"}}, {"seed": 772, "data": {"p1_how_many": "13", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.735, 3.74, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725", "3.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}430}{6{,}300}, \\dfrac{1{,}441}{6{,}300}, \\dfrac{1{,}507}{6{,}300}, \\dfrac{1{,}523}{6{,}300}, \\dfrac{1{,}636}{6{,}300}, \\dfrac{1{,}702}{6{,}300}, \\dfrac{1{,}720}{6{,}300}, \\dfrac{1{,}758}{6{,}300}, \\dfrac{1{,}778}{6{,}300}, \\text{ and } \\dfrac{1{,}781}{6{,}300}", "__seed__": "0772"}}, {"seed": 773, "data": {"p1_how_many": "10", "p1_a": "5.87", "p1_b": "5.88", "p1_numbers": "5.8705, 5.871, 5.872, 5.873, 5.874, 5.875, 5.876, 5.877, 5.878, and 5.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.871", "5.872", "5.873", "5.874", "5.875", "5.876", "5.877", "5.878", "5.8790000000000004"], "p1_2_xs": ["5.8705"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{809}{1{,}200}, \\dfrac{818}{1{,}200}, \\dfrac{822}{1{,}200}, \\dfrac{826}{1{,}200}, \\dfrac{840}{1{,}200}, \\dfrac{870}{1{,}200}, \\text{ and } \\dfrac{898}{1{,}200}", "__seed__": "0773"}}, {"seed": 774, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}195}{12{,}000}, \\dfrac{3{,}222}{12{,}000}, \\dfrac{3{,}291}{12{,}000}, \\dfrac{3{,}316}{12{,}000}, \\dfrac{3{,}345}{12{,}000}, \\dfrac{3{,}415}{12{,}000}, \\dfrac{3{,}498}{12{,}000}, \\text{ and } \\dfrac{3{,}716}{12{,}000}", "__seed__": "0774"}}, {"seed": 775, "data": {"p1_how_many": "14", "p1_a": "3.4", "p1_b": "3.5", "p1_numbers": "3.405, 3.41, 3.415, 3.42, 3.425, 3.43, 3.435, 3.44, 3.445, 3.45, 3.46, 3.47, 3.48, and 3.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.4099999999999997", "3.42", "3.4299999999999997", "3.44", "3.4499999999999997", "3.46", "3.4699999999999998", "3.48", "3.4899999999999998"], "p1_2_xs": ["3.405", "3.4149999999999996", "3.425", "3.4349999999999996", "3.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{603}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{645}{4{,}200}, \\dfrac{653}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{662}{4{,}200}, \\text{ and } \\dfrac{686}{4{,}200}", "__seed__": "0775"}}, {"seed": 776, "data": {"p1_how_many": "13", "p1_a": "9.6", "p1_b": "9.7", "p1_numbers": "9.605, 9.61, 9.615, 9.62, 9.625, 9.63, 9.635, 9.64, 9.65, 9.66, 9.67, 9.68, and 9.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.61", "9.62", "9.629999999999999", "9.639999999999999", "9.65", "9.66", "9.67", "9.68", "9.69"], "p1_2_xs": ["9.605", "9.615", "9.625", "9.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{728}{4{,}200}, \\dfrac{742}{4{,}200}, \\dfrac{785}{4{,}200}, \\dfrac{909}{4{,}200}, \\dfrac{944}{4{,}200}, \\dfrac{1{,}020}{4{,}200}, \\dfrac{1{,}034}{4{,}200}, \\dfrac{1{,}037}{4{,}200}, \\dfrac{1{,}048}{4{,}200}, \\text{ and } \\dfrac{1{,}070}{4{,}200}", "__seed__": "0776"}}, {"seed": 777, "data": {"p1_how_many": "13", "p1_a": "5.21", "p1_b": "5.22", "p1_numbers": "5.2105, 5.211, 5.2115, 5.212, 5.2125, 5.213, 5.2135, 5.214, 5.215, 5.216, 5.217, 5.218, and 5.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.211", "5.212", "5.213", "5.2139999999999995", "5.215", "5.216", "5.217", "5.218", "5.219"], "p1_2_xs": ["5.2105", "5.2115", "5.2124999999999995", "5.2135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}093}{35{,}000}, \\dfrac{20{,}177}{35{,}000}, \\dfrac{20{,}987}{35{,}000}, \\dfrac{22{,}382}{35{,}000}, \\dfrac{23{,}404}{35{,}000}, \\dfrac{24{,}069}{35{,}000}, \\dfrac{24{,}934}{35{,}000}, \\dfrac{24{,}956}{35{,}000}, \\dfrac{25{,}887}{35{,}000}, \\dfrac{26{,}326}{35{,}000}, \\text{ and } \\dfrac{27{,}511}{35{,}000}", "__seed__": "0777"}}, {"seed": 778, "data": {"p1_how_many": "10", "p1_a": "6.71", "p1_b": "6.72", "p1_numbers": "6.7105, 6.711, 6.712, 6.713, 6.714, 6.715, 6.716, 6.717, 6.718, and 6.719", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.711", "6.712", "6.713", "6.7139999999999995", "6.715", "6.716", "6.717", "6.718", "6.719"], "p1_2_xs": ["6.7105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}016}{42{,}000}, \\dfrac{7{,}587}{42{,}000}, \\dfrac{8{,}288}{42{,}000}, \\dfrac{8{,}944}{42{,}000}, \\dfrac{9{,}217}{42{,}000}, \\dfrac{10{,}983}{42{,}000}, \\dfrac{11{,}334}{42{,}000}, \\text{ and } \\dfrac{11{,}829}{42{,}000}", "__seed__": "0778"}}, {"seed": 779, "data": {"p1_how_many": "14", "p1_a": "7.27", "p1_b": "7.28", "p1_numbers": "7.2705, 7.271, 7.2715, 7.272, 7.2725, 7.273, 7.2735, 7.274, 7.2745, 7.275, 7.276, 7.277, 7.278, and 7.279", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.271", "7.271999999999999", "7.273", "7.273999999999999", "7.2749999999999995", "7.276", "7.276999999999999", "7.278", "7.279"], "p1_2_xs": ["7.270499999999999", "7.2715", "7.272499999999999", "7.273499999999999", "7.274499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}372}{15{,}000}, \\dfrac{7{,}412}{15{,}000}, \\dfrac{7{,}662}{15{,}000}, \\dfrac{7{,}772}{15{,}000}, \\dfrac{7{,}885}{15{,}000}, \\dfrac{9{,}046}{15{,}000}, \\text{ and } \\dfrac{9{,}409}{15{,}000}", "__seed__": "0779"}}, {"seed": 780, "data": {"p1_how_many": "10", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{123}{200}, \\dfrac{128}{200}, \\dfrac{133}{200}, \\dfrac{135}{200}, \\dfrac{139}{200}, \\dfrac{145}{200}, \\text{ and } \\dfrac{148}{200}", "__seed__": "0780"}}, {"seed": 781, "data": {"p1_how_many": "11", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{2{,}958}{6{,}300}, \\dfrac{3{,}000}{6{,}300}, \\dfrac{3{,}032}{6{,}300}, \\dfrac{3{,}087}{6{,}300}, \\dfrac{3{,}318}{6{,}300}, \\dfrac{3{,}433}{6{,}300}, \\text{ and } \\dfrac{3{,}516}{6{,}300}", "__seed__": "0781"}}, {"seed": 782, "data": {"p1_how_many": "11", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{53}{200}, \\dfrac{55}{200}, \\dfrac{56}{200}, \\dfrac{61}{200}, \\dfrac{65}{200}, \\dfrac{72}{200}, \\dfrac{74}{200}, \\dfrac{75}{200}, \\text{ and } \\dfrac{76}{200}", "__seed__": "0782"}}, {"seed": 783, "data": {"p1_how_many": "13", "p1_a": "4.86", "p1_b": "4.87", "p1_numbers": "4.8605, 4.861, 4.8615, 4.862, 4.8625, 4.863, 4.8635, 4.864, 4.865, 4.866, 4.867, 4.868, and 4.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.861000000000001", "4.862", "4.863", "4.864", "4.865", "4.8660000000000005", "4.867", "4.868", "4.869000000000001"], "p1_2_xs": ["4.8605", "4.8615", "4.8625", "4.8635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{531}{2{,}000}, \\dfrac{543}{2{,}000}, \\dfrac{550}{2{,}000}, \\dfrac{558}{2{,}000}, \\dfrac{562}{2{,}000}, \\dfrac{568}{2{,}000}, \\dfrac{604}{2{,}000}, \\dfrac{730}{2{,}000}, \\dfrac{734}{2{,}000}, \\dfrac{743}{2{,}000}, \\text{ and } \\dfrac{747}{2{,}000}", "__seed__": "0783"}}, {"seed": 784, "data": {"p1_how_many": "14", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.215, 1.22, 1.225, 1.23, 1.235, 1.24, 1.245, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", "1.25", "1.26", "1.27", "1.28", "1.29"], "p1_2_xs": ["1.2049999999999998", "1.2149999999999999", "1.2249999999999999", "1.2349999999999999", "1.2449999999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}261}{12{,}000}, \\dfrac{8{,}329}{12{,}000}, \\dfrac{8{,}519}{12{,}000}, \\dfrac{8{,}574}{12{,}000}, \\dfrac{8{,}592}{12{,}000}, \\dfrac{8{,}632}{12{,}000}, \\dfrac{8{,}646}{12{,}000}, \\dfrac{8{,}784}{12{,}000}, \\dfrac{8{,}823}{12{,}000}, \\dfrac{8{,}857}{12{,}000}, \\dfrac{8{,}900}{12{,}000}, \\text{ and } \\dfrac{8{,}993}{12{,}000}", "__seed__": "0784"}}, {"seed": 785, "data": {"p1_how_many": "13", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.015, 8.02, 8.025, 8.03, 8.035, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005", "8.015", "8.025", "8.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}034}{77{,}000}, \\dfrac{42{,}063}{77{,}000}, \\dfrac{42{,}129}{77{,}000}, \\dfrac{44{,}411}{77{,}000}, \\dfrac{48{,}457}{77{,}000}, \\dfrac{49{,}080}{77{,}000}, \\dfrac{49{,}214}{77{,}000}, \\text{ and } \\dfrac{54{,}791}{77{,}000}", "__seed__": "0785"}}, {"seed": 786, "data": {"p1_how_many": "11", "p1_a": "5.1", "p1_b": "5.2", "p1_numbers": "5.1005, 5.101, 5.1015, 5.102, 5.103, 5.104, 5.105, 5.106, 5.107, 5.108, and 5.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.101", "5.101999999999999", "5.103", "5.103999999999999", "5.1049999999999995", "5.106", "5.106999999999999", "5.108", "5.109"], "p1_2_xs": ["5.100499999999999", "5.1015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{331}{560}, \\dfrac{335}{560}, \\dfrac{339}{560}, \\dfrac{341}{560}, \\dfrac{343}{560}, \\dfrac{344}{560}, \\text{ and } \\dfrac{348}{560}", "__seed__": "0786"}}, {"seed": 787, "data": {"p1_how_many": "12", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.425, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001", "8.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}187}{3{,}500}, \\dfrac{2{,}205}{3{,}500}, \\dfrac{2{,}260}{3{,}500}, \\dfrac{2{,}261}{3{,}500}, \\dfrac{2{,}440}{3{,}500}, \\dfrac{2{,}464}{3{,}500}, \\dfrac{2{,}540}{3{,}500}, \\dfrac{2{,}545}{3{,}500}, \\dfrac{2{,}631}{3{,}500}, \\text{ and } \\dfrac{2{,}653}{3{,}500}", "__seed__": "0787"}}, {"seed": 788, "data": {"p1_how_many": "12", "p1_a": "1.2", "p1_b": "1.3", "p1_numbers": "1.205, 1.21, 1.215, 1.22, 1.225, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, and 1.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.21", "1.22", "1.23", "1.24", 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"4.918", "4.9190000000000005"], "p1_2_xs": ["4.9105", "4.9115", "4.9125", "4.9135", "4.914499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{501}{3{,}000}, \\dfrac{519}{3{,}000}, \\dfrac{528}{3{,}000}, \\dfrac{530}{3{,}000}, \\dfrac{542}{3{,}000}, \\dfrac{547}{3{,}000}, \\dfrac{566}{3{,}000}, \\dfrac{570}{3{,}000}, \\dfrac{587}{3{,}000}, \\dfrac{590}{3{,}000}, \\dfrac{593}{3{,}000}, \\text{ and } \\dfrac{596}{3{,}000}", "__seed__": "0789"}}, {"seed": 790, "data": {"p1_how_many": "13", "p1_a": "5.87", "p1_b": "5.88", "p1_numbers": "5.8705, 5.871, 5.8715, 5.872, 5.8725, 5.873, 5.8735, 5.874, 5.875, 5.876, 5.877, 5.878, and 5.879", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.871", "5.872", "5.873", "5.874", "5.875", "5.876", "5.877", "5.878", "5.8790000000000004"], "p1_2_xs": ["5.8705", "5.8715", "5.8725", "5.8735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{506}{3{,}000}, \\dfrac{554}{3{,}000}, \\dfrac{555}{3{,}000}, \\dfrac{576}{3{,}000}, \\dfrac{586}{3{,}000}, \\dfrac{590}{3{,}000}, \\text{ and } \\dfrac{591}{3{,}000}", "__seed__": "0790"}}, {"seed": 791, "data": {"p1_how_many": "14", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.445, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998", "1.4449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}116}{20{,}000}, \\dfrac{4{,}240}{20{,}000}, \\dfrac{4{,}249}{20{,}000}, \\dfrac{4{,}266}{20{,}000}, \\dfrac{4{,}292}{20{,}000}, \\dfrac{4{,}316}{20{,}000}, \\dfrac{4{,}550}{20{,}000}, \\dfrac{4{,}591}{20{,}000}, \\dfrac{4{,}713}{20{,}000}, \\dfrac{4{,}729}{20{,}000}, \\text{ and } \\dfrac{4{,}796}{20{,}000}", "__seed__": "0791"}}, {"seed": 792, "data": {"p1_how_many": "14", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.535, 4.54, 4.545, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995", "4.535", "4.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{621}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{644}{4{,}200}, \\dfrac{655}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{665}{4{,}200}, \\dfrac{688}{4{,}200}, \\dfrac{698}{4{,}200}, \\text{ and } \\dfrac{699}{4{,}200}", "__seed__": "0792"}}, {"seed": 793, "data": {"p1_how_many": "14", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.0005, 9.001, 9.0015, 9.002, 9.0025, 9.003, 9.0035, 9.004, 9.0045, 9.005, 9.006, 9.007, 9.008, and 9.009", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.001", "9.002", "9.003", "9.004", "9.005", "9.006", "9.007", "9.008", "9.009"], "p1_2_xs": ["9.0005", "9.0015", "9.002500000000001", "9.0035", "9.0045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{32}{120}, \\dfrac{33}{120}, \\dfrac{34}{120}, \\dfrac{35}{120}, \\dfrac{36}{120}, \\dfrac{37}{120}, \\text{ and } \\dfrac{38}{120}", "__seed__": "0793"}}, {"seed": 794, "data": {"p1_how_many": "11", "p1_a": "5.4", "p1_b": "5.5", "p1_numbers": "5.405, 5.41, 5.415, 5.42, 5.43, 5.44, 5.45, 5.46, 5.47, 5.48, and 5.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.41", "5.42", "5.430000000000001", "5.44", "5.45", "5.46", "5.470000000000001", "5.48", "5.49"], "p1_2_xs": ["5.405", "5.415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{413}{2{,}000}, \\dfrac{433}{2{,}000}, \\dfrac{437}{2{,}000}, \\dfrac{448}{2{,}000}, \\dfrac{451}{2{,}000}, \\dfrac{456}{2{,}000}, \\dfrac{464}{2{,}000}, \\dfrac{465}{2{,}000}, \\dfrac{480}{2{,}000}, \\dfrac{492}{2{,}000}, \\dfrac{493}{2{,}000}, \\text{ and } \\dfrac{499}{2{,}000}", "__seed__": "0794"}}, {"seed": 795, "data": {"p1_how_many": "11", "p1_a": "6.1", "p1_b": "6.2", "p1_numbers": "6.105, 6.11, 6.115, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17, 6.18, and 6.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.109999999999999", "6.119999999999999", "6.13", "6.14", "6.1499999999999995", "6.159999999999999", "6.17", "6.18", "6.1899999999999995"], "p1_2_xs": ["6.1049999999999995", "6.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{407}{2{,}000}, \\dfrac{411}{2{,}000}, \\dfrac{415}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{423}{2{,}000}, \\dfrac{438}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{464}{2{,}000}, \\dfrac{466}{2{,}000}, \\dfrac{472}{2{,}000}, \\dfrac{483}{2{,}000}, \\text{ and } \\dfrac{484}{2{,}000}", "__seed__": "0795"}}, {"seed": 796, "data": {"p1_how_many": "10", "p1_a": "8.84", "p1_b": "8.85", "p1_numbers": "8.8405, 8.841, 8.842, 8.843, 8.844, 8.845, 8.846, 8.847, 8.848, and 8.849", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.841", "8.842", "8.843", "8.844", "8.845", "8.846", "8.847", "8.847999999999999", "8.849"], "p1_2_xs": ["8.8405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{320}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{334}{1{,}200}, \\dfrac{363}{1{,}200}, \\dfrac{369}{1{,}200}, \\dfrac{386}{1{,}200}, \\dfrac{387}{1{,}200}, \\text{ and } \\dfrac{395}{1{,}200}", "__seed__": "0796"}}, {"seed": 797, "data": {"p1_how_many": "11", "p1_a": "3.92", "p1_b": "3.93", "p1_numbers": "3.9205, 3.921, 3.9215, 3.922, 3.923, 3.924, 3.925, 3.926, 3.927, 3.928, and 3.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.921", "3.9219999999999997", "3.923", "3.924", "3.925", "3.9259999999999997", "3.927", "3.928", "3.929"], "p1_2_xs": ["3.9205", "3.9215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}033}{12{,}000}, \\dfrac{8{,}078}{12{,}000}, \\dfrac{8{,}313}{12{,}000}, \\dfrac{8{,}388}{12{,}000}, \\dfrac{8{,}431}{12{,}000}, \\dfrac{8{,}509}{12{,}000}, \\dfrac{8{,}616}{12{,}000}, \\dfrac{8{,}739}{12{,}000}, \\dfrac{8{,}794}{12{,}000}, \\dfrac{8{,}829}{12{,}000}, \\dfrac{8{,}868}{12{,}000}, \\text{ and } \\dfrac{8{,}905}{12{,}000}", "__seed__": "0797"}}, {"seed": 798, "data": {"p1_how_many": "13", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.735, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725", "8.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{151}{200}, \\dfrac{152}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0798"}}, {"seed": 799, "data": {"p1_how_many": "12", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.525, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515", "7.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{928}{6{,}300}, \\dfrac{998}{6{,}300}, \\dfrac{1{,}107}{6{,}300}, \\dfrac{1{,}165}{6{,}300}, \\dfrac{1{,}291}{6{,}300}, \\dfrac{1{,}351}{6{,}300}, \\text{ and } \\dfrac{1{,}360}{6{,}300}", "__seed__": "0799"}}, {"seed": 800, "data": {"p1_how_many": "14", "p1_a": "5.72", "p1_b": "5.73", "p1_numbers": "5.7205, 5.721, 5.7215, 5.722, 5.7225, 5.723, 5.7235, 5.724, 5.7245, 5.725, 5.726, 5.727, 5.728, and 5.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.721", "5.7219999999999995", "5.723", "5.723999999999999", "5.725", "5.726", "5.726999999999999", "5.728", "5.729"], "p1_2_xs": ["5.7204999999999995", "5.7215", "5.722499999999999", "5.7235", "5.724499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}067}{15{,}000}, \\dfrac{6{,}122}{15{,}000}, \\dfrac{6{,}384}{15{,}000}, \\dfrac{7{,}251}{15{,}000}, \\dfrac{7{,}951}{15{,}000}, \\dfrac{7{,}990}{15{,}000}, \\dfrac{8{,}189}{15{,}000}, \\dfrac{8{,}261}{15{,}000}, \\dfrac{9{,}219}{15{,}000}, \\text{ and } \\dfrac{9{,}526}{15{,}000}", "__seed__": "0800"}}, {"seed": 801, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}775}{77{,}000}, \\dfrac{44{,}956}{77{,}000}, \\dfrac{46{,}803}{77{,}000}, \\dfrac{46{,}877}{77{,}000}, \\dfrac{47{,}749}{77{,}000}, \\dfrac{49{,}413}{77{,}000}, \\dfrac{49{,}696}{77{,}000}, \\text{ and } \\dfrac{52{,}104}{77{,}000}", "__seed__": "0801"}}, {"seed": 802, "data": {"p1_how_many": "11", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{432}{770}, \\dfrac{446}{770}, \\dfrac{457}{770}, \\dfrac{493}{770}, \\dfrac{507}{770}, \\dfrac{508}{770}, \\dfrac{511}{770}, \\text{ and } \\dfrac{539}{770}", "__seed__": "0802"}}, {"seed": 803, "data": {"p1_how_many": "12", "p1_a": "4.26", "p1_b": "4.27", "p1_numbers": "4.2605, 4.261, 4.2615, 4.262, 4.2625, 4.263, 4.264, 4.265, 4.266, 4.267, 4.268, and 4.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.261", "4.262", "4.263", "4.263999999999999", "4.265", "4.266", "4.2669999999999995", "4.268", "4.269"], "p1_2_xs": ["4.2604999999999995", "4.2615", "4.262499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}106}{20{,}000}, \\dfrac{4{,}135}{20{,}000}, \\dfrac{4{,}326}{20{,}000}, \\dfrac{4{,}360}{20{,}000}, \\dfrac{4{,}509}{20{,}000}, \\dfrac{4{,}806}{20{,}000}, \\text{ and } \\dfrac{4{,}853}{20{,}000}", "__seed__": "0803"}}, {"seed": 804, "data": {"p1_how_many": "11", "p1_a": "9.31", "p1_b": "9.32", "p1_numbers": "9.3105, 9.311, 9.3115, 9.312, 9.313, 9.314, 9.315, 9.316, 9.317, 9.318, and 9.319", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.311", "9.312000000000001", "9.313", "9.314", "9.315000000000001", "9.316", "9.317", "9.318", "9.319"], "p1_2_xs": ["9.310500000000001", "9.3115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{351}{560}, \\dfrac{353}{560}, \\dfrac{360}{560}, \\dfrac{373}{560}, \\dfrac{377}{560}, \\dfrac{385}{560}, \\dfrac{396}{560}, \\text{ and } \\dfrac{397}{560}", "__seed__": "0804"}}, {"seed": 805, "data": {"p1_how_many": "14", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.525, 6.53, 6.535, 6.54, 6.545, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515", "6.5249999999999995", "6.535", "6.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{713}{4{,}200}, \\dfrac{731}{4{,}200}, \\dfrac{746}{4{,}200}, \\dfrac{858}{4{,}200}, \\dfrac{910}{4{,}200}, \\dfrac{959}{4{,}200}, \\dfrac{990}{4{,}200}, \\dfrac{1{,}010}{4{,}200}, \\dfrac{1{,}015}{4{,}200}, \\dfrac{1{,}032}{4{,}200}, \\dfrac{1{,}054}{4{,}200}, \\text{ and } \\dfrac{1{,}149}{4{,}200}", "__seed__": "0805"}}, {"seed": 806, "data": {"p1_how_many": "14", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.515, 8.52, 8.525, 8.53, 8.535, 8.54, 8.545, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505", "8.515", "8.525", "8.535", "8.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{810}{1{,}200}, \\dfrac{818}{1{,}200}, \\dfrac{822}{1{,}200}, \\dfrac{829}{1{,}200}, \\dfrac{834}{1{,}200}, \\dfrac{883}{1{,}200}, \\dfrac{884}{1{,}200}, \\dfrac{890}{1{,}200}, \\text{ and } \\dfrac{895}{1{,}200}", "__seed__": "0806"}}, {"seed": 807, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}004}{35{,}000}, \\dfrac{20{,}356}{35{,}000}, \\dfrac{20{,}530}{35{,}000}, \\dfrac{20{,}654}{35{,}000}, \\dfrac{20{,}730}{35{,}000}, \\dfrac{20{,}756}{35{,}000}, \\dfrac{20{,}866}{35{,}000}, \\dfrac{20{,}926}{35{,}000}, \\text{ and } \\dfrac{20{,}969}{35{,}000}", "__seed__": "0807"}}, {"seed": 808, "data": {"p1_how_many": "10", "p1_a": "3.82", "p1_b": "3.83", "p1_numbers": "3.8205, 3.821, 3.822, 3.823, 3.824, 3.825, 3.826, 3.827, 3.828, and 3.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.8209999999999997", "3.8219999999999996", "3.823", "3.824", "3.8249999999999997", "3.8259999999999996", "3.827", "3.828", "3.8289999999999997"], "p1_2_xs": ["3.8205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}331}{15{,}000}, \\dfrac{6{,}409}{15{,}000}, \\dfrac{7{,}026}{15{,}000}, \\dfrac{8{,}264}{15{,}000}, \\dfrac{8{,}334}{15{,}000}, \\dfrac{8{,}752}{15{,}000}, \\dfrac{8{,}938}{15{,}000}, \\dfrac{9{,}220}{15{,}000}, \\dfrac{9{,}253}{15{,}000}, \\dfrac{9{,}625}{15{,}000}, \\text{ and } \\dfrac{9{,}908}{15{,}000}", "__seed__": "0808"}}, {"seed": 809, "data": {"p1_how_many": "10", "p1_a": "2.91", "p1_b": "2.92", "p1_numbers": "2.9105, 2.911, 2.912, 2.913, 2.914, 2.915, 2.916, 2.917, 2.918, and 2.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.911", "2.912", "2.9130000000000003", "2.914", "2.915", "2.916", "2.9170000000000003", "2.918", "2.919"], "p1_2_xs": ["2.9105000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{48}{200}", "__seed__": "0809"}}, {"seed": 810, "data": {"p1_how_many": "10", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{804}{1{,}200}, \\dfrac{809}{1{,}200}, \\dfrac{813}{1{,}200}, \\dfrac{821}{1{,}200}, \\dfrac{839}{1{,}200}, \\dfrac{841}{1{,}200}, \\dfrac{848}{1{,}200}, \\dfrac{852}{1{,}200}, \\dfrac{857}{1{,}200}, \\dfrac{861}{1{,}200}, \\dfrac{874}{1{,}200}, \\text{ and } \\dfrac{893}{1{,}200}", "__seed__": "0810"}}, {"seed": 811, "data": {"p1_how_many": "14", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.015, 9.02, 9.025, 9.03, 9.035, 9.04, 9.045, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005", "9.015", "9.025", "9.035", "9.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}188}{12{,}000}, \\dfrac{3{,}211}{12{,}000}, \\dfrac{3{,}462}{12{,}000}, \\dfrac{3{,}593}{12{,}000}, \\dfrac{3{,}619}{12{,}000}, \\dfrac{3{,}875}{12{,}000}, \\dfrac{3{,}940}{12{,}000}, \\text{ and } \\dfrac{3{,}983}{12{,}000}", "__seed__": "0811"}}, {"seed": 812, "data": {"p1_how_many": "10", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.02, 7.03, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{307}{1{,}200}, \\dfrac{331}{1{,}200}, \\dfrac{332}{1{,}200}, \\dfrac{345}{1{,}200}, \\dfrac{361}{1{,}200}, \\dfrac{378}{1{,}200}, \\dfrac{380}{1{,}200}, \\dfrac{382}{1{,}200}, \\dfrac{391}{1{,}200}, \\text{ and } \\dfrac{392}{1{,}200}", "__seed__": "0812"}}, {"seed": 813, "data": {"p1_how_many": "10", "p1_a": "3.66", "p1_b": "3.67", "p1_numbers": "3.6605, 3.661, 3.662, 3.663, 3.664, 3.665, 3.666, 3.667, 3.668, and 3.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.661", "3.662", "3.6630000000000003", "3.664", "3.665", "3.666", "3.6670000000000003", "3.668", "3.669"], "p1_2_xs": ["3.6605000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}103}{35{,}000}, \\dfrac{20{,}190}{35{,}000}, \\dfrac{20{,}212}{35{,}000}, \\dfrac{20{,}477}{35{,}000}, \\dfrac{20{,}504}{35{,}000}, \\dfrac{20{,}801}{35{,}000}, \\text{ and } \\dfrac{20{,}863}{35{,}000}", "__seed__": "0813"}}, {"seed": 814, "data": {"p1_how_many": "11", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.515, 6.52, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505", "6.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}028}{20{,}000}, \\dfrac{5{,}781}{20{,}000}, \\dfrac{5{,}976}{20{,}000}, \\dfrac{6{,}376}{20{,}000}, \\dfrac{6{,}760}{20{,}000}, \\dfrac{6{,}931}{20{,}000}, \\text{ and } \\dfrac{7{,}004}{20{,}000}", "__seed__": "0814"}}, {"seed": 815, "data": {"p1_how_many": "11", "p1_a": "1.7", "p1_b": "1.8", "p1_numbers": "1.705, 1.71, 1.715, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, and 1.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.71", "1.72", "1.73", "1.74", "1.75", "1.76", "1.77", "1.78", "1.79"], "p1_2_xs": ["1.7049999999999998", "1.7149999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{43{,}005}{77{,}000}, \\dfrac{45{,}928}{77{,}000}, \\dfrac{48{,}373}{77{,}000}, \\dfrac{48{,}445}{77{,}000}, \\dfrac{49{,}386}{77{,}000}, \\dfrac{49{,}892}{77{,}000}, \\dfrac{50{,}794}{77{,}000}, \\text{ and } \\dfrac{53{,}268}{77{,}000}", "__seed__": "0815"}}, {"seed": 816, "data": {"p1_how_many": "12", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}043}{12{,}000}, \\dfrac{3{,}196}{12{,}000}, \\dfrac{3{,}203}{12{,}000}, \\dfrac{3{,}342}{12{,}000}, \\dfrac{3{,}346}{12{,}000}, \\dfrac{3{,}580}{12{,}000}, \\dfrac{3{,}674}{12{,}000}, \\dfrac{3{,}763}{12{,}000}, \\dfrac{3{,}810}{12{,}000}, \\dfrac{3{,}858}{12{,}000}, \\text{ and } \\dfrac{3{,}889}{12{,}000}", "__seed__": "0816"}}, {"seed": 817, "data": {"p1_how_many": "14", "p1_a": "6.05", "p1_b": "6.06", "p1_numbers": "6.0505, 6.051, 6.0515, 6.052, 6.0525, 6.053, 6.0535, 6.054, 6.0545, 6.055, 6.056, 6.057, 6.058, and 6.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.051", "6.052", "6.053", "6.053999999999999", "6.055", "6.056", "6.0569999999999995", "6.058", "6.059"], "p1_2_xs": ["6.0504999999999995", "6.0515", "6.052499999999999", "6.0535", "6.054499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{32{,}318}{56{,}000}, \\dfrac{32{,}512}{56{,}000}, \\dfrac{32{,}590}{56{,}000}, \\dfrac{32{,}940}{56{,}000}, \\dfrac{33{,}358}{56{,}000}, \\dfrac{33{,}482}{56{,}000}, \\dfrac{33{,}722}{56{,}000}, \\dfrac{33{,}871}{56{,}000}, \\dfrac{33{,}888}{56{,}000}, \\dfrac{33{,}953}{56{,}000}, \\text{ and } \\dfrac{34{,}619}{56{,}000}", "__seed__": "0817"}}, {"seed": 818, "data": {"p1_how_many": "11", "p1_a": "8.26", "p1_b": "8.27", "p1_numbers": "8.2605, 8.261, 8.2615, 8.262, 8.263, 8.264, 8.265, 8.266, 8.267, 8.268, and 8.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.261", "8.262", "8.263", "8.264", "8.265", "8.266", "8.267", "8.267999999999999", "8.269"], "p1_2_xs": ["8.2605", "8.2615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}137}{35{,}000}, \\dfrac{14{,}157}{35{,}000}, \\dfrac{14{,}193}{35{,}000}, \\dfrac{14{,}412}{35{,}000}, \\dfrac{14{,}414}{35{,}000}, \\dfrac{14{,}522}{35{,}000}, \\text{ and } \\dfrac{14{,}762}{35{,}000}", "__seed__": "0818"}}, {"seed": 819, "data": {"p1_how_many": "14", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.325, 9.33, 9.335, 9.34, 9.345, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001", "9.325000000000001", "9.335", "9.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}467}{42{,}000}, \\dfrac{30{,}764}{42{,}000}, \\dfrac{31{,}700}{42{,}000}, \\dfrac{32{,}150}{42{,}000}, \\dfrac{32{,}864}{42{,}000}, \\dfrac{33{,}017}{42{,}000}, \\dfrac{33{,}954}{42{,}000}, \\text{ and } \\dfrac{34{,}435}{42{,}000}", "__seed__": "0819"}}, {"seed": 820, "data": {"p1_how_many": "10", "p1_a": "6.5", "p1_b": "6.6", "p1_numbers": "6.505, 6.51, 6.52, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, and 6.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.51", "6.52", "6.53", "6.54", "6.55", "6.56", "6.57", "6.58", "6.59"], "p1_2_xs": ["6.505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{30{,}525}{42{,}000}, \\dfrac{31{,}708}{42{,}000}, \\dfrac{31{,}796}{42{,}000}, \\dfrac{33{,}263}{42{,}000}, \\dfrac{33{,}546}{42{,}000}, \\dfrac{34{,}610}{42{,}000}, \\text{ and } \\dfrac{34{,}994}{42{,}000}", "__seed__": "0820"}}, {"seed": 821, "data": {"p1_how_many": "10", "p1_a": "5.92", "p1_b": "5.93", "p1_numbers": "5.9205, 5.921, 5.922, 5.923, 5.924, 5.925, 5.926, 5.927, 5.928, and 5.929", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.921", "5.922", "5.923", "5.9239999999999995", "5.925", "5.926", "5.927", "5.928", "5.929"], "p1_2_xs": ["5.9205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0821"}}, {"seed": 822, "data": {"p1_how_many": "13", "p1_a": "2.85", "p1_b": "2.86", "p1_numbers": "2.8505, 2.851, 2.8515, 2.852, 2.8525, 2.853, 2.8535, 2.854, 2.855, 2.856, 2.857, 2.858, and 2.859", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.851", "2.852", "2.853", "2.854", "2.855", "2.856", "2.857", "2.858", "2.859"], "p1_2_xs": ["2.8505000000000003", "2.8515", "2.8525", "2.8535000000000004"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}159}{20{,}000}, \\dfrac{12{,}216}{20{,}000}, \\dfrac{12{,}442}{20{,}000}, \\dfrac{12{,}852}{20{,}000}, \\dfrac{13{,}143}{20{,}000}, \\dfrac{13{,}273}{20{,}000}, \\dfrac{13{,}963}{20{,}000}, \\dfrac{14{,}534}{20{,}000}, \\text{ and } \\dfrac{14{,}546}{20{,}000}", "__seed__": "0822"}}, {"seed": 823, "data": {"p1_how_many": "12", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.315, 2.32, 2.325, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997", "2.3149999999999995", "2.3249999999999997"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}311}{15{,}000}, \\dfrac{5{,}413}{15{,}000}, \\dfrac{5{,}537}{15{,}000}, \\dfrac{5{,}542}{15{,}000}, \\dfrac{5{,}560}{15{,}000}, \\dfrac{5{,}637}{15{,}000}, \\dfrac{5{,}707}{15{,}000}, \\dfrac{5{,}838}{15{,}000}, \\text{ and } \\dfrac{5{,}990}{15{,}000}", "__seed__": "0823"}}, {"seed": 824, "data": {"p1_how_many": "12", "p1_a": "4.44", "p1_b": "4.45", "p1_numbers": "4.4405, 4.441, 4.4415, 4.442, 4.4425, 4.443, 4.444, 4.445, 4.446, 4.447, 4.448, and 4.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.441000000000001", "4.442", "4.4430000000000005", "4.444", "4.445", "4.446000000000001", "4.447", "4.448", "4.449000000000001"], "p1_2_xs": ["4.4405", "4.4415000000000004", "4.4425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}044}{20{,}000}, \\dfrac{5{,}264}{20{,}000}, \\dfrac{6{,}105}{20{,}000}, \\dfrac{6{,}228}{20{,}000}, \\dfrac{6{,}566}{20{,}000}, \\dfrac{6{,}721}{20{,}000}, \\dfrac{6{,}785}{20{,}000}, \\text{ and } \\dfrac{7{,}484}{20{,}000}", "__seed__": "0824"}}, {"seed": 825, "data": {"p1_how_many": "11", "p1_a": "9.23", "p1_b": "9.24", "p1_numbers": "9.2305, 9.231, 9.2315, 9.232, 9.233, 9.234, 9.235, 9.236, 9.237, 9.238, and 9.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.231", "9.232000000000001", "9.233", "9.234", "9.235000000000001", "9.236", "9.237", "9.238", "9.239"], "p1_2_xs": ["9.230500000000001", "9.2315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{4{,}809}{5{,}600}, \\dfrac{4{,}817}{5{,}600}, \\dfrac{4{,}827}{5{,}600}, \\dfrac{4{,}844}{5{,}600}, \\dfrac{4{,}845}{5{,}600}, \\dfrac{4{,}865}{5{,}600}, \\dfrac{4{,}878}{5{,}600}, \\dfrac{4{,}882}{5{,}600}, \\dfrac{4{,}884}{5{,}600}, \\text{ and } \\dfrac{4{,}889}{5{,}600}", "__seed__": "0825"}}, {"seed": 826, "data": {"p1_how_many": "11", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{402}{2{,}000}, \\dfrac{407}{2{,}000}, \\dfrac{412}{2{,}000}, \\dfrac{417}{2{,}000}, \\dfrac{432}{2{,}000}, \\dfrac{438}{2{,}000}, \\dfrac{443}{2{,}000}, \\dfrac{457}{2{,}000}, \\dfrac{468}{2{,}000}, \\dfrac{482}{2{,}000}, \\dfrac{488}{2{,}000}, \\text{ and } \\dfrac{491}{2{,}000}", "__seed__": "0826"}}, {"seed": 827, "data": {"p1_how_many": "11", "p1_a": "9.14", "p1_b": "9.15", "p1_numbers": "9.1405, 9.141, 9.1415, 9.142, 9.143, 9.144, 9.145, 9.146, 9.147, 9.148, and 9.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.141", "9.142000000000001", "9.143", "9.144", "9.145000000000001", "9.146", "9.147", "9.148", "9.149000000000001"], "p1_2_xs": ["9.140500000000001", "9.1415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}100}{42{,}000}, \\dfrac{7{,}526}{42{,}000}, \\dfrac{7{,}665}{42{,}000}, \\dfrac{8{,}492}{42{,}000}, \\dfrac{8{,}742}{42{,}000}, \\dfrac{8{,}801}{42{,}000}, \\dfrac{8{,}850}{42{,}000}, \\dfrac{11{,}102}{42{,}000}, \\dfrac{11{,}342}{42{,}000}, \\text{ and } \\dfrac{11{,}399}{42{,}000}", "__seed__": "0827"}}, {"seed": 828, "data": {"p1_how_many": "10", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.42, 9.43, 9.44, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}387}{42{,}000}, \\dfrac{7{,}468}{42{,}000}, \\dfrac{8{,}833}{42{,}000}, \\dfrac{8{,}939}{42{,}000}, \\dfrac{9{,}293}{42{,}000}, \\dfrac{9{,}553}{42{,}000}, \\dfrac{9{,}671}{42{,}000}, \\text{ and } \\dfrac{11{,}796}{42{,}000}", "__seed__": "0828"}}, {"seed": 829, "data": {"p1_how_many": "12", "p1_a": "4.77", "p1_b": "4.78", "p1_numbers": "4.7705, 4.771, 4.7715, 4.772, 4.7725, 4.773, 4.774, 4.775, 4.776, 4.777, 4.778, and 4.779", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.771", "4.771999999999999", "4.773", "4.773999999999999", "4.7749999999999995", "4.776", "4.776999999999999", "4.778", "4.779"], "p1_2_xs": ["4.770499999999999", "4.7715", "4.772499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{716}{3{,}500}, \\dfrac{822}{3{,}500}, \\dfrac{870}{3{,}500}, \\dfrac{883}{3{,}500}, \\dfrac{977}{3{,}500}, \\dfrac{996}{3{,}500}, \\dfrac{997}{3{,}500}, \\text{ and } \\dfrac{999}{3{,}500}", "__seed__": "0829"}}, {"seed": 830, "data": {"p1_how_many": "11", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.73, 4.74, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{602}{4{,}200}, \\dfrac{603}{4{,}200}, \\dfrac{633}{4{,}200}, \\dfrac{634}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{674}{4{,}200}, \\dfrac{675}{4{,}200}, \\dfrac{684}{4{,}200}, \\dfrac{691}{4{,}200}, \\text{ and } \\dfrac{699}{4{,}200}", "__seed__": "0830"}}, {"seed": 831, "data": {"p1_how_many": "11", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.6005, 8.601, 8.6015, 8.602, 8.603, 8.604, 8.605, 8.606, 8.607, 8.608, and 8.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.600999999999999", "8.602", "8.603", "8.604", "8.605", "8.606", "8.607", "8.607999999999999", "8.609"], "p1_2_xs": ["8.6005", "8.6015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}003}{12{,}000}, \\dfrac{8{,}043}{12{,}000}, \\dfrac{8{,}213}{12{,}000}, \\dfrac{8{,}300}{12{,}000}, \\dfrac{8{,}530}{12{,}000}, \\dfrac{8{,}653}{12{,}000}, \\dfrac{8{,}674}{12{,}000}, \\dfrac{8{,}749}{12{,}000}, \\dfrac{8{,}763}{12{,}000}, \\dfrac{8{,}833}{12{,}000}, \\text{ and } \\dfrac{8{,}933}{12{,}000}", "__seed__": "0831"}}, {"seed": 832, "data": {"p1_how_many": "14", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.515, 8.52, 8.525, 8.53, 8.535, 8.54, 8.545, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505", "8.515", "8.525", "8.535", "8.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}505}{2{,}000}, \\dfrac{1{,}508}{2{,}000}, \\dfrac{1{,}519}{2{,}000}, \\dfrac{1{,}522}{2{,}000}, \\dfrac{1{,}527}{2{,}000}, \\dfrac{1{,}534}{2{,}000}, \\dfrac{1{,}544}{2{,}000}, \\dfrac{1{,}551}{2{,}000}, \\dfrac{1{,}557}{2{,}000}, \\dfrac{1{,}571}{2{,}000}, \\dfrac{1{,}577}{2{,}000}, \\text{ and } \\dfrac{1{,}595}{2{,}000}", "__seed__": "0832"}}, {"seed": 833, "data": {"p1_how_many": "13", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.325, 6.33, 6.335, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995", "6.324999999999999", "6.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}508}{4{,}200}, \\dfrac{3{,}515}{4{,}200}, \\dfrac{3{,}524}{4{,}200}, \\dfrac{3{,}547}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}558}{4{,}200}, \\dfrac{3{,}563}{4{,}200}, \\dfrac{3{,}590}{4{,}200}, \\text{ and } \\dfrac{3{,}592}{4{,}200}", "__seed__": "0833"}}, {"seed": 834, "data": {"p1_how_many": "11", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}707}{6{,}300}, \\dfrac{2{,}709}{6{,}300}, \\dfrac{2{,}717}{6{,}300}, \\dfrac{2{,}719}{6{,}300}, \\dfrac{2{,}728}{6{,}300}, \\dfrac{2{,}735}{6{,}300}, \\dfrac{2{,}747}{6{,}300}, \\dfrac{2{,}776}{6{,}300}, \\text{ and } \\dfrac{2{,}791}{6{,}300}", "__seed__": "0834"}}, {"seed": 835, "data": {"p1_how_many": "11", "p1_a": "8.3", "p1_b": "8.4", "p1_numbers": "8.305, 8.31, 8.315, 8.32, 8.33, 8.34, 8.35, 8.36, 8.37, 8.38, and 8.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.31", "8.32", "8.33", "8.34", "8.350000000000001", "8.360000000000001", "8.370000000000001", "8.38", "8.39"], "p1_2_xs": ["8.305000000000001", "8.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}415}{56{,}000}, \\dfrac{36{,}686}{56{,}000}, \\dfrac{36{,}826}{56{,}000}, \\dfrac{38{,}031}{56{,}000}, \\dfrac{38{,}523}{56{,}000}, \\dfrac{39{,}117}{56{,}000}, \\dfrac{39{,}216}{56{,}000}, \\dfrac{39{,}471}{56{,}000}, \\dfrac{39{,}558}{56{,}000}, \\text{ and } \\dfrac{39{,}716}{56{,}000}", "__seed__": "0835"}}, {"seed": 836, "data": {"p1_how_many": "11", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{22{,}023}{35{,}000}, \\dfrac{22{,}124}{35{,}000}, \\dfrac{22{,}440}{35{,}000}, \\dfrac{22{,}883}{35{,}000}, \\dfrac{23{,}034}{35{,}000}, \\dfrac{23{,}726}{35{,}000}, \\dfrac{25{,}084}{35{,}000}, \\text{ and } \\dfrac{25{,}907}{35{,}000}", "__seed__": "0836"}}, {"seed": 837, "data": {"p1_how_many": "12", "p1_a": "8.7", "p1_b": "8.8", "p1_numbers": "8.705, 8.71, 8.715, 8.72, 8.725, 8.73, 8.74, 8.75, 8.76, 8.77, 8.78, and 8.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.709999999999999", "8.719999999999999", "8.729999999999999", "8.739999999999998", "8.75", "8.76", "8.77", "8.78", "8.79"], "p1_2_xs": ["8.705", "8.715", "8.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}454}{35{,}000}, \\dfrac{7{,}652}{35{,}000}, \\dfrac{8{,}679}{35{,}000}, \\dfrac{9{,}204}{35{,}000}, \\dfrac{9{,}311}{35{,}000}, \\dfrac{9{,}332}{35{,}000}, \\dfrac{9{,}439}{35{,}000}, \\dfrac{9{,}605}{35{,}000}, \\text{ and } \\dfrac{9{,}709}{35{,}000}", "__seed__": "0837"}}, {"seed": 838, "data": {"p1_how_many": "13", "p1_a": "2.81", "p1_b": "2.82", "p1_numbers": "2.8105, 2.811, 2.8115, 2.812, 2.8125, 2.813, 2.8135, 2.814, 2.815, 2.816, 2.817, 2.818, and 2.819", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.811", "2.812", "2.813", "2.814", "2.815", "2.816", "2.817", "2.818", "2.819"], "p1_2_xs": ["2.8105", "2.8115", "2.8125", "2.8135000000000003"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{624}{4{,}200}, \\dfrac{627}{4{,}200}, \\dfrac{633}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{663}{4{,}200}, \\dfrac{664}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0838"}}, {"seed": 839, "data": {"p1_how_many": "10", "p1_a": "9.72", "p1_b": "9.73", "p1_numbers": "9.7205, 9.721, 9.722, 9.723, 9.724, 9.725, 9.726, 9.727, 9.728, and 9.729", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.721", "9.722000000000001", "9.723", "9.724", "9.725000000000001", "9.726", "9.727", "9.728", "9.729000000000001"], "p1_2_xs": ["9.720500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}144}{42{,}000}, \\dfrac{7{,}364}{42{,}000}, \\dfrac{7{,}479}{42{,}000}, \\dfrac{8{,}037}{42{,}000}, \\dfrac{8{,}132}{42{,}000}, \\dfrac{8{,}306}{42{,}000}, \\dfrac{9{,}190}{42{,}000}, \\dfrac{10{,}866}{42{,}000}, \\dfrac{11{,}185}{42{,}000}, \\dfrac{11{,}307}{42{,}000}, \\dfrac{11{,}322}{42{,}000}, \\text{ and } \\dfrac{11{,}697}{42{,}000}", "__seed__": "0839"}}, {"seed": 840, "data": {"p1_how_many": "10", "p1_a": "9.06", "p1_b": "9.07", "p1_numbers": "9.0605, 9.061, 9.062, 9.063, 9.064, 9.065, 9.066, 9.067, 9.068, and 9.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.061", "9.062000000000001", "9.063", "9.064", "9.065000000000001", "9.066", "9.067", "9.068", "9.069"], "p1_2_xs": ["9.060500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{202}{350}, \\dfrac{203}{350}, \\dfrac{204}{350}, \\dfrac{205}{350}, \\dfrac{206}{350}, \\dfrac{207}{350}, \\dfrac{208}{350}, \\text{ and } \\dfrac{209}{350}", "__seed__": "0840"}}, {"seed": 841, "data": {"p1_how_many": "11", "p1_a": "7.5", "p1_b": "7.6", "p1_numbers": "7.505, 7.51, 7.515, 7.52, 7.53, 7.54, 7.55, 7.56, 7.57, 7.58, and 7.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.51", "7.52", "7.53", "7.54", "7.55", "7.56", "7.57", "7.58", "7.59"], "p1_2_xs": ["7.505", "7.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}410}{3{,}500}, \\dfrac{1{,}415}{3{,}500}, \\dfrac{1{,}424}{3{,}500}, \\dfrac{1{,}440}{3{,}500}, \\dfrac{1{,}452}{3{,}500}, \\dfrac{1{,}453}{3{,}500}, \\dfrac{1{,}456}{3{,}500}, \\dfrac{1{,}468}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}476}{3{,}500}, \\text{ and } \\dfrac{1{,}491}{3{,}500}", "__seed__": "0841"}}, {"seed": 842, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}051}{63{,}000}, \\dfrac{27{,}226}{63{,}000}, \\dfrac{27{,}229}{63{,}000}, \\dfrac{27{,}322}{63{,}000}, \\dfrac{27{,}381}{63{,}000}, \\dfrac{27{,}506}{63{,}000}, \\dfrac{27{,}537}{63{,}000}, \\dfrac{27{,}625}{63{,}000}, \\dfrac{27{,}628}{63{,}000}, \\dfrac{27{,}693}{63{,}000}, \\dfrac{27{,}823}{63{,}000}, \\text{ and } \\dfrac{27{,}986}{63{,}000}", "__seed__": "0842"}}, {"seed": 843, "data": {"p1_how_many": "14", "p1_a": "3.3", "p1_b": "3.4", "p1_numbers": "3.305, 3.31, 3.315, 3.32, 3.325, 3.33, 3.335, 3.34, 3.345, 3.35, 3.36, 3.37, 3.38, and 3.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.3099999999999996", "3.32", "3.3299999999999996", "3.34", "3.3499999999999996", "3.36", "3.3699999999999997", "3.38", "3.3899999999999997"], "p1_2_xs": ["3.3049999999999997", "3.3149999999999995", "3.3249999999999997", "3.3349999999999995", "3.3449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{3{,}242}{5{,}600}, \\dfrac{3{,}244}{5{,}600}, \\dfrac{3{,}271}{5{,}600}, \\dfrac{3{,}304}{5{,}600}, \\dfrac{3{,}352}{5{,}600}, \\dfrac{3{,}371}{5{,}600}, \\dfrac{3{,}373}{5{,}600}, \\text{ and } \\dfrac{3{,}400}{5{,}600}", "__seed__": "0843"}}, {"seed": 844, "data": {"p1_how_many": "12", "p1_a": "4.5", "p1_b": "4.6", "p1_numbers": "4.505, 4.51, 4.515, 4.52, 4.525, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, and 4.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.51", "4.52", "4.53", "4.54", "4.55", "4.56", "4.57", "4.58", "4.59"], "p1_2_xs": ["4.505", "4.515", "4.5249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}025}{3{,}500}, \\dfrac{1{,}050}{3{,}500}, \\dfrac{1{,}146}{3{,}500}, \\dfrac{1{,}159}{3{,}500}, \\dfrac{1{,}193}{3{,}500}, \\dfrac{1{,}208}{3{,}500}, \\dfrac{1{,}225}{3{,}500}, \\dfrac{1{,}248}{3{,}500}, \\dfrac{1{,}255}{3{,}500}, \\text{ and } \\dfrac{1{,}332}{3{,}500}", "__seed__": "0844"}}, {"seed": 845, "data": {"p1_how_many": "10", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997"], 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"\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{201}{350}, \\dfrac{207}{350}, \\dfrac{210}{350}, \\dfrac{211}{350}, \\dfrac{216}{350}, \\dfrac{230}{350}, \\dfrac{232}{350}, \\dfrac{235}{350}, \\text{ and } \\dfrac{263}{350}", "__seed__": "0846"}}, {"seed": 847, "data": {"p1_how_many": "12", "p1_a": "4.21", "p1_b": "4.22", "p1_numbers": "4.2105, 4.211, 4.2115, 4.212, 4.2125, 4.213, 4.214, 4.215, 4.216, 4.217, 4.218, and 4.219", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.211", "4.212", "4.213", "4.2139999999999995", "4.215", "4.216", "4.217", "4.218", "4.219"], "p1_2_xs": ["4.2105", "4.2115", "4.2124999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{20{,}123}{35{,}000}, \\dfrac{20{,}173}{35{,}000}, \\dfrac{20{,}253}{35{,}000}, \\dfrac{20{,}316}{35{,}000}, \\dfrac{20{,}351}{35{,}000}, \\dfrac{20{,}444}{35{,}000}, \\dfrac{20{,}638}{35{,}000}, \\dfrac{20{,}644}{35{,}000}, \\dfrac{20{,}660}{35{,}000}, \\text{ and } \\dfrac{20{,}781}{35{,}000}", "__seed__": "0847"}}, {"seed": 848, "data": {"p1_how_many": "11", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.615, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995", "7.614999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{2{,}160}{3{,}500}, \\dfrac{2{,}311}{3{,}500}, \\dfrac{2{,}536}{3{,}500}, \\dfrac{2{,}663}{3{,}500}, \\dfrac{2{,}673}{3{,}500}, \\dfrac{2{,}692}{3{,}500}, \\dfrac{2{,}717}{3{,}500}, \\text{ and } \\dfrac{2{,}727}{3{,}500}", "__seed__": "0848"}}, {"seed": 849, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}545}{20{,}000}, \\dfrac{5{,}630}{20{,}000}, \\dfrac{5{,}687}{20{,}000}, \\dfrac{6{,}888}{20{,}000}, \\dfrac{6{,}974}{20{,}000}, \\dfrac{7{,}133}{20{,}000}, \\dfrac{7{,}186}{20{,}000}, \\dfrac{7{,}204}{20{,}000}, \\dfrac{7{,}902}{20{,}000}, \\text{ and } \\dfrac{7{,}920}{20{,}000}", "__seed__": "0849"}}, {"seed": 850, "data": {"p1_how_many": "10", "p1_a": "4.3", "p1_b": "4.4", "p1_numbers": "4.305, 4.31, 4.32, 4.33, 4.34, 4.35, 4.36, 4.37, 4.38, and 4.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.31", "4.319999999999999", "4.33", "4.34", "4.35", "4.359999999999999", "4.37", "4.38", "4.39"], "p1_2_xs": ["4.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{616}{4{,}200}, \\dfrac{621}{4{,}200}, \\dfrac{625}{4{,}200}, \\dfrac{627}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{675}{4{,}200}, \\text{ and } \\dfrac{689}{4{,}200}", "__seed__": "0850"}}, {"seed": 851, "data": {"p1_how_many": "12", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.3005, 5.301, 5.3015, 5.302, 5.3025, 5.303, 5.304, 5.305, 5.306, 5.307, 5.308, and 5.309", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.301", "5.302", "5.303", "5.303999999999999", "5.305", "5.306", "5.3069999999999995", "5.308", "5.309"], "p1_2_xs": ["5.3004999999999995", "5.3015", "5.302499999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{632}{1{,}500}, \\dfrac{653}{1{,}500}, \\dfrac{709}{1{,}500}, \\dfrac{861}{1{,}500}, \\dfrac{883}{1{,}500}, \\dfrac{888}{1{,}500}, \\dfrac{917}{1{,}500}, \\dfrac{922}{1{,}500}, \\dfrac{933}{1{,}500}, \\text{ and } \\dfrac{996}{1{,}500}", "__seed__": "0851"}}, {"seed": 852, "data": {"p1_how_many": "11", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{42{,}846}{77{,}000}, \\dfrac{42{,}872}{77{,}000}, \\dfrac{49{,}102}{77{,}000}, \\dfrac{50{,}816}{77{,}000}, \\dfrac{55{,}449}{77{,}000}, \\dfrac{60{,}418}{77{,}000}, \\dfrac{60{,}755}{77{,}000}, \\text{ and } \\dfrac{63{,}153}{77{,}000}", "__seed__": "0852"}}, {"seed": 853, "data": {"p1_how_many": "13", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}045}{4{,}200}, \\dfrac{3{,}183}{4{,}200}, \\dfrac{3{,}192}{4{,}200}, \\dfrac{3{,}229}{4{,}200}, \\dfrac{3{,}246}{4{,}200}, \\dfrac{3{,}311}{4{,}200}, \\dfrac{3{,}313}{4{,}200}, \\text{ and } \\dfrac{3{,}474}{4{,}200}", "__seed__": "0853"}}, {"seed": 854, "data": {"p1_how_many": "11", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}055}{56{,}000}, \\dfrac{35{,}095}{56{,}000}, \\dfrac{35{,}212}{56{,}000}, \\dfrac{35{,}759}{56{,}000}, \\dfrac{37{,}116}{56{,}000}, \\dfrac{37{,}274}{56{,}000}, \\dfrac{38{,}796}{56{,}000}, \\dfrac{38{,}816}{56{,}000}, \\text{ and } \\dfrac{39{,}757}{56{,}000}", "__seed__": "0854"}}, {"seed": 855, "data": {"p1_how_many": "12", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{163}{560}, \\dfrac{166}{560}, \\dfrac{169}{560}, 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\\dfrac{6{,}583}{42{,}000}, \\dfrac{6{,}771}{42{,}000}, \\dfrac{6{,}812}{42{,}000}, \\text{ and } \\dfrac{6{,}943}{42{,}000}", "__seed__": "0856"}}, {"seed": 857, "data": {"p1_how_many": "13", "p1_a": "7.1", "p1_b": "7.2", "p1_numbers": "7.105, 7.11, 7.115, 7.12, 7.125, 7.13, 7.135, 7.14, 7.15, 7.16, 7.17, 7.18, and 7.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.109999999999999", "7.119999999999999", "7.13", "7.14", "7.1499999999999995", "7.159999999999999", "7.17", "7.18", "7.1899999999999995"], "p1_2_xs": ["7.1049999999999995", "7.114999999999999", "7.124999999999999", "7.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{502}{1{,}500}, \\dfrac{520}{1{,}500}, \\dfrac{525}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{537}{1{,}500}, \\dfrac{552}{1{,}500}, \\dfrac{562}{1{,}500}, \\dfrac{564}{1{,}500}, \\dfrac{582}{1{,}500}, \\text{ and } \\dfrac{599}{1{,}500}", "__seed__": "0857"}}, {"seed": 858, "data": {"p1_how_many": "13", "p1_a": "7.91", "p1_b": "7.92", "p1_numbers": "7.9105, 7.911, 7.9115, 7.912, 7.9125, 7.913, 7.9135, 7.914, 7.915, 7.916, 7.917, 7.918, and 7.919", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.9110000000000005", "7.912", "7.913", "7.914", "7.915", "7.916", "7.917", "7.918", "7.9190000000000005"], "p1_2_xs": ["7.9105", "7.9115", "7.9125", "7.9135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}516}{42{,}000}, \\dfrac{7{,}523}{42{,}000}, \\dfrac{7{,}705}{42{,}000}, \\dfrac{7{,}845}{42{,}000}, \\dfrac{8{,}182}{42{,}000}, \\dfrac{8{,}202}{42{,}000}, \\dfrac{9{,}091}{42{,}000}, \\dfrac{9{,}464}{42{,}000}, \\dfrac{10{,}488}{42{,}000}, \\dfrac{10{,}663}{42{,}000}, \\text{ and } \\dfrac{10{,}982}{42{,}000}", "__seed__": "0858"}}, {"seed": 859, "data": {"p1_how_many": "13", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.11", "2.12", "2.13", "2.14", "2.15", "2.16", "2.17", "2.18", "2.19"], "p1_2_xs": ["2.105", "2.1149999999999998", "2.125", "2.135"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}043}{15{,}000}, \\dfrac{5{,}088}{15{,}000}, \\dfrac{5{,}090}{15{,}000}, \\dfrac{5{,}182}{15{,}000}, \\dfrac{5{,}213}{15{,}000}, \\dfrac{5{,}360}{15{,}000}, \\dfrac{5{,}366}{15{,}000}, \\dfrac{5{,}505}{15{,}000}, \\dfrac{5{,}670}{15{,}000}, \\dfrac{5{,}680}{15{,}000}, \\text{ and } \\dfrac{5{,}899}{15{,}000}", "__seed__": "0859"}}, {"seed": 860, "data": 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"7.502", "7.503", "7.504", "7.505", "7.506", "7.507", "7.508", "7.509"], "p1_2_xs": ["7.5005", "7.5015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}106}{20{,}000}, \\dfrac{4{,}184}{20{,}000}, \\dfrac{4{,}226}{20{,}000}, \\dfrac{4{,}329}{20{,}000}, \\dfrac{4{,}413}{20{,}000}, \\dfrac{4{,}428}{20{,}000}, \\dfrac{4{,}541}{20{,}000}, \\dfrac{4{,}878}{20{,}000}, \\dfrac{4{,}959}{20{,}000}, \\text{ and } \\dfrac{4{,}963}{20{,}000}", "__seed__": "0861"}}, {"seed": 862, "data": {"p1_how_many": "12", "p1_a": "1.17", "p1_b": "1.18", "p1_numbers": "1.1705, 1.171, 1.1715, 1.172, 1.1725, 1.173, 1.174, 1.175, 1.176, 1.177, 1.178, and 1.179", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.1709999999999998", "1.172", "1.1729999999999998", "1.174", "1.1749999999999998", "1.176", "1.1769999999999998", "1.178", 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"5.6899999999999995"], "p1_2_xs": ["5.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}078}{20{,}000}, \\dfrac{4{,}140}{20{,}000}, \\dfrac{4{,}510}{20{,}000}, \\dfrac{4{,}519}{20{,}000}, \\dfrac{4{,}617}{20{,}000}, \\dfrac{4{,}641}{20{,}000}, \\dfrac{4{,}667}{20{,}000}, \\dfrac{4{,}673}{20{,}000}, \\dfrac{4{,}830}{20{,}000}, \\dfrac{4{,}893}{20{,}000}, \\text{ and } \\dfrac{4{,}910}{20{,}000}", "__seed__": "0863"}}, {"seed": 864, "data": {"p1_how_many": "10", "p1_a": "9.82", "p1_b": "9.83", "p1_numbers": "9.8205, 9.821, 9.822, 9.823, 9.824, 9.825, 9.826, 9.827, 9.828, and 9.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.821", "9.822000000000001", "9.823", "9.824", "9.825000000000001", "9.826", "9.827", "9.828", "9.829"], "p1_2_xs": ["9.820500000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{212}{560}, \\dfrac{216}{560}, \\dfrac{218}{560}, \\dfrac{226}{560}, \\dfrac{228}{560}, \\dfrac{232}{560}, \\text{ and } \\dfrac{236}{560}", "__seed__": "0864"}}, {"seed": 865, "data": {"p1_how_many": "14", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.545, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997", "2.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{241}{300}, \\dfrac{242}{300}, 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\\dfrac{5{,}640}{30{,}000}", "__seed__": "0866"}}, {"seed": 867, "data": {"p1_how_many": "11", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{20{,}169}{35{,}000}, \\dfrac{20{,}949}{35{,}000}, \\dfrac{21{,}081}{35{,}000}, \\dfrac{21{,}714}{35{,}000}, \\dfrac{22{,}481}{35{,}000}, \\dfrac{22{,}575}{35{,}000}, \\dfrac{23{,}365}{35{,}000}, \\dfrac{25{,}548}{35{,}000}, \\dfrac{25{,}857}{35{,}000}, \\text{ and } \\dfrac{26{,}329}{35{,}000}", "__seed__": "0867"}}, {"seed": 868, "data": {"p1_how_many": "10", "p1_a": "1.3", "p1_b": "1.4", "p1_numbers": 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"7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}520}{4{,}200}, \\dfrac{3{,}522}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}543}{4{,}200}, \\dfrac{3{,}549}{4{,}200}, \\dfrac{3{,}550}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}579}{4{,}200}, \\dfrac{3{,}583}{4{,}200}, \\text{ and } \\dfrac{3{,}588}{4{,}200}", "__seed__": "0869"}}, {"seed": 870, "data": {"p1_how_many": "10", "p1_a": "9.36", "p1_b": "9.37", "p1_numbers": "9.3605, 9.361, 9.362, 9.363, 9.364, 9.365, 9.366, 9.367, 9.368, and 9.369", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.360999999999999", "9.362", "9.363", "9.363999999999999", "9.365", "9.366", "9.366999999999999", "9.367999999999999", "9.369"], "p1_2_xs": ["9.3605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}653}{5{,}600}, \\dfrac{1{,}688}{5{,}600}, \\dfrac{1{,}698}{5{,}600}, \\dfrac{1{,}749}{5{,}600}, \\dfrac{1{,}921}{5{,}600}, \\dfrac{2{,}083}{5{,}600}, \\dfrac{2{,}086}{5{,}600}, \\dfrac{2{,}090}{5{,}600}, \\dfrac{2{,}091}{5{,}600}, \\text{ and } \\dfrac{2{,}098}{5{,}600}", "__seed__": "0870"}}, {"seed": 871, "data": {"p1_how_many": "10", "p1_a": "2.3", "p1_b": "2.4", "p1_numbers": "2.305, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, and 2.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.3099999999999996", "2.32", "2.3299999999999996", "2.34", "2.3499999999999996", "2.36", "2.3699999999999997", "2.38", "2.3899999999999997"], "p1_2_xs": ["2.3049999999999997"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}409}{3{,}500}, \\dfrac{1{,}418}{3{,}500}, \\dfrac{1{,}427}{3{,}500}, \\dfrac{1{,}430}{3{,}500}, \\dfrac{1{,}432}{3{,}500}, \\dfrac{1{,}433}{3{,}500}, \\dfrac{1{,}464}{3{,}500}, \\dfrac{1{,}467}{3{,}500}, \\dfrac{1{,}469}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}481}{3{,}500}, \\text{ and } \\dfrac{1{,}482}{3{,}500}", "__seed__": "0871"}}, {"seed": 872, "data": {"p1_how_many": "14", "p1_a": "2.96", "p1_b": "2.97", "p1_numbers": "2.9605, 2.961, 2.9615, 2.962, 2.9625, 2.963, 2.9635, 2.964, 2.9645, 2.965, 2.966, 2.967, 2.968, and 2.969", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.961", "2.9619999999999997", "2.963", "2.964", "2.965", "2.9659999999999997", "2.967", "2.968", "2.969"], "p1_2_xs": ["2.9605", "2.9615", "2.9625", "2.9635000000000002", "2.9645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{607}{4{,}200}, \\dfrac{626}{4{,}200}, \\dfrac{632}{4{,}200}, \\dfrac{647}{4{,}200}, \\dfrac{650}{4{,}200}, \\dfrac{657}{4{,}200}, \\dfrac{675}{4{,}200}, \\dfrac{688}{4{,}200}, \\text{ and } \\dfrac{692}{4{,}200}", "__seed__": "0872"}}, {"seed": 873, "data": {"p1_how_many": "13", "p1_a": "3.25", "p1_b": "3.26", "p1_numbers": "3.2505, 3.251, 3.2515, 3.252, 3.2525, 3.253, 3.2535, 3.254, 3.255, 3.256, 3.257, 3.258, and 3.259", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.251", "3.252", "3.253", "3.254", "3.255", "3.256", "3.257", "3.258", "3.259"], "p1_2_xs": ["3.2505", "3.2515", "3.2525", "3.2535000000000003"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{76}{420}, \\dfrac{79}{420}, \\dfrac{80}{420}, \\dfrac{84}{420}, \\dfrac{90}{420}, \\dfrac{92}{420}, \\dfrac{101}{420}, \\dfrac{104}{420}, \\text{ and } \\dfrac{119}{420}", "__seed__": "0873"}}, {"seed": 874, "data": {"p1_how_many": "13", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.235, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225", "5.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{506}{1{,}500}, \\dfrac{511}{1{,}500}, \\dfrac{518}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{534}{1{,}500}, \\dfrac{543}{1{,}500}, \\dfrac{551}{1{,}500}, 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\\dfrac{1{,}579}{2{,}000}, \\text{ and } \\dfrac{1{,}581}{2{,}000}", "__seed__": "0875"}}, {"seed": 876, "data": {"p1_how_many": "10", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{481}{560}, \\dfrac{483}{560}, \\dfrac{484}{560}, \\dfrac{485}{560}, \\dfrac{487}{560}, \\dfrac{488}{560}, \\text{ and } \\dfrac{489}{560}", "__seed__": "0876"}}, {"seed": 877, "data": {"p1_how_many": "13", "p1_a": "1.42", "p1_b": "1.43", "p1_numbers": "1.4205, 1.421, 1.4215, 1.422, 1.4225, 1.423, 1.4235, 1.424, 1.425, 1.426, 1.427, 1.428, and 1.429", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4209999999999998", "1.422", "1.4229999999999998", "1.424", "1.4249999999999998", "1.426", "1.4269999999999998", "1.428", "1.4289999999999998"], "p1_2_xs": ["1.4204999999999999", "1.4214999999999998", "1.4224999999999999", "1.4234999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{717}{3{,}500}, \\dfrac{721}{3{,}500}, \\dfrac{731}{3{,}500}, \\dfrac{759}{3{,}500}, \\dfrac{769}{3{,}500}, \\dfrac{794}{3{,}500}, \\dfrac{796}{3{,}500}, \\dfrac{802}{3{,}500}, \\dfrac{818}{3{,}500}, \\dfrac{839}{3{,}500}, \\dfrac{854}{3{,}500}, \\text{ and } \\dfrac{946}{3{,}500}", "__seed__": "0877"}}, {"seed": 878, "data": {"p1_how_many": "11", "p1_a": "8.5", "p1_b": "8.6", "p1_numbers": "8.505, 8.51, 8.515, 8.52, 8.53, 8.54, 8.55, 8.56, 8.57, 8.58, and 8.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.51", "8.52", "8.53", "8.54", "8.55", "8.56", "8.57", "8.58", "8.59"], "p1_2_xs": ["8.505", "8.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{22{,}458}{35{,}000}, \\dfrac{23{,}084}{35{,}000}, \\dfrac{23{,}552}{35{,}000}, \\dfrac{24{,}001}{35{,}000}, \\dfrac{24{,}288}{35{,}000}, \\dfrac{24{,}962}{35{,}000}, \\dfrac{25{,}123}{35{,}000}, \\dfrac{25{,}592}{35{,}000}, \\dfrac{25{,}664}{35{,}000}, \\dfrac{25{,}706}{35{,}000}, \\dfrac{27{,}718}{35{,}000}, \\text{ and } \\dfrac{27{,}741}{35{,}000}", "__seed__": "0878"}}, {"seed": 879, "data": {"p1_how_many": "14", "p1_a": "8.35", "p1_b": "8.36", "p1_numbers": "8.3505, 8.351, 8.3515, 8.352, 8.3525, 8.353, 8.3535, 8.354, 8.3545, 8.355, 8.356, 8.357, 8.358, and 8.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.350999999999999", "8.352", "8.353", "8.354", "8.355", "8.356", "8.357", "8.357999999999999", "8.359"], "p1_2_xs": ["8.3505", "8.3515", "8.352500000000001", "8.3535", "8.3545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}018}{20{,}000}, \\dfrac{12{,}356}{20{,}000}, \\dfrac{13{,}276}{20{,}000}, \\dfrac{13{,}355}{20{,}000}, \\dfrac{13{,}421}{20{,}000}, \\dfrac{13{,}558}{20{,}000}, \\dfrac{13{,}946}{20{,}000}, \\dfrac{14{,}150}{20{,}000}, \\dfrac{14{,}245}{20{,}000}, \\dfrac{14{,}352}{20{,}000}, \\dfrac{14{,}442}{20{,}000}, \\text{ and } \\dfrac{14{,}797}{20{,}000}", "__seed__": "0879"}}, {"seed": 880, "data": {"p1_how_many": "11", "p1_a": "7.06", "p1_b": "7.07", "p1_numbers": "7.0605, 7.061, 7.0615, 7.062, 7.063, 7.064, 7.065, 7.066, 7.067, 7.068, and 7.069", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.061", "7.061999999999999", "7.063", "7.063999999999999", "7.0649999999999995", "7.066", "7.066999999999999", "7.068", "7.069"], "p1_2_xs": ["7.060499999999999", "7.0615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}262}{56{,}000}, \\dfrac{21{,}461}{56{,}000}, \\dfrac{21{,}471}{56{,}000}, \\dfrac{21{,}536}{56{,}000}, \\dfrac{21{,}799}{56{,}000}, \\dfrac{21{,}926}{56{,}000}, \\dfrac{22{,}359}{56{,}000}, \\text{ and } \\dfrac{23{,}756}{56{,}000}", "__seed__": "0880"}}, {"seed": 881, "data": {"p1_how_many": "11", "p1_a": "5.34", "p1_b": "5.35", "p1_numbers": "5.3405, 5.341, 5.3415, 5.342, 5.343, 5.344, 5.345, 5.346, 5.347, 5.348, and 5.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.341", "5.342", "5.343", "5.343999999999999", "5.345", "5.346", "5.3469999999999995", "5.348", "5.349"], "p1_2_xs": ["5.3405", "5.3415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{61}{420}, \\dfrac{62}{420}, \\dfrac{63}{420}, \\dfrac{64}{420}, \\dfrac{65}{420}, \\dfrac{66}{420}, \\dfrac{67}{420}, \\dfrac{68}{420}, \\text{ and } \\dfrac{69}{420}", "__seed__": "0881"}}, {"seed": 882, "data": {"p1_how_many": "13", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.735, 6.74, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725", "6.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{16{,}112}{35{,}000}, \\dfrac{16{,}449}{35{,}000}, \\dfrac{17{,}040}{35{,}000}, \\dfrac{17{,}820}{35{,}000}, \\dfrac{18{,}470}{35{,}000}, \\dfrac{18{,}695}{35{,}000}, \\dfrac{19{,}500}{35{,}000}, \\text{ and } \\dfrac{19{,}946}{35{,}000}", "__seed__": "0882"}}, {"seed": 883, "data": {"p1_how_many": "12", "p1_a": "1.67", "p1_b": "1.68", "p1_numbers": "1.6705, 1.671, 1.6715, 1.672, 1.6725, 1.673, 1.674, 1.675, 1.676, 1.677, 1.678, and 1.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.6709999999999998", "1.672", "1.6729999999999998", "1.674", "1.6749999999999998", "1.676", "1.6769999999999998", "1.678", "1.6789999999999998"], "p1_2_xs": ["1.6704999999999999", "1.6714999999999998", "1.6724999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{506}{3{,}000}, \\dfrac{516}{3{,}000}, \\dfrac{531}{3{,}000}, \\dfrac{556}{3{,}000}, \\dfrac{558}{3{,}000}, \\dfrac{566}{3{,}000}, \\dfrac{574}{3{,}000}, \\dfrac{578}{3{,}000}, \\dfrac{579}{3{,}000}, \\dfrac{585}{3{,}000}, \\dfrac{588}{3{,}000}, \\text{ and } \\dfrac{591}{3{,}000}", "__seed__": "0883"}}, {"seed": 884, "data": {"p1_how_many": "13", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.225, 3.23, 3.235, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215", "3.225", "3.235"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}423}{3{,}500}, \\dfrac{1{,}441}{3{,}500}, \\dfrac{1{,}450}{3{,}500}, \\dfrac{1{,}452}{3{,}500}, \\dfrac{1{,}459}{3{,}500}, \\dfrac{1{,}482}{3{,}500}, \\dfrac{1{,}485}{3{,}500}, \\text{ and } \\dfrac{1{,}487}{3{,}500}", "__seed__": "0884"}}, {"seed": 885, "data": {"p1_how_many": "12", "p1_a": "3.7", "p1_b": "3.8", "p1_numbers": "3.705, 3.71, 3.715, 3.72, 3.725, 3.73, 3.74, 3.75, 3.76, 3.77, 3.78, and 3.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.71", "3.72", "3.73", "3.74", "3.75", "3.7600000000000002", "3.77", "3.7800000000000002", "3.79"], "p1_2_xs": ["3.705", "3.715", "3.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}257}{20{,}000}, \\dfrac{5{,}343}{20{,}000}, \\dfrac{6{,}058}{20{,}000}, \\dfrac{6{,}600}{20{,}000}, \\dfrac{6{,}674}{20{,}000}, \\dfrac{6{,}825}{20{,}000}, \\dfrac{6{,}852}{20{,}000}, \\text{ and } \\dfrac{7{,}492}{20{,}000}", "__seed__": "0885"}}, {"seed": 886, "data": {"p1_how_many": "13", "p1_a": "7.0", "p1_b": "7.1", "p1_numbers": "7.005, 7.01, 7.015, 7.02, 7.025, 7.03, 7.035, 7.04, 7.05, 7.06, 7.07, 7.08, and 7.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.01", "7.02", "7.03", "7.04", "7.05", "7.06", "7.07", "7.08", "7.09"], "p1_2_xs": ["7.005", "7.015", "7.0249999999999995", "7.035"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{3{,}164}{6{,}300}, \\dfrac{3{,}191}{6{,}300}, \\dfrac{3{,}222}{6{,}300}, \\dfrac{3{,}231}{6{,}300}, \\dfrac{3{,}243}{6{,}300}, \\dfrac{3{,}268}{6{,}300}, \\dfrac{3{,}271}{6{,}300}, \\dfrac{3{,}299}{6{,}300}, \\dfrac{3{,}305}{6{,}300}, \\dfrac{3{,}415}{6{,}300}, \\text{ and } \\dfrac{3{,}516}{6{,}300}", "__seed__": "0886"}}, {"seed": 887, "data": {"p1_how_many": "10", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}057}{35{,}000}, \\dfrac{7{,}643}{35{,}000}, \\dfrac{8{,}260}{35{,}000}, \\dfrac{9{,}068}{35{,}000}, \\dfrac{9{,}139}{35{,}000}, \\dfrac{9{,}277}{35{,}000}, \\dfrac{9{,}597}{35{,}000}, \\dfrac{9{,}614}{35{,}000}, \\dfrac{9{,}729}{35{,}000}, \\text{ and } \\dfrac{9{,}902}{35{,}000}", "__seed__": "0887"}}, {"seed": 888, "data": {"p1_how_many": "13", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.625, 5.63, 5.635, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999", "5.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}020}{20{,}000}, \\dfrac{4{,}139}{20{,}000}, \\dfrac{4{,}179}{20{,}000}, \\dfrac{4{,}283}{20{,}000}, \\dfrac{4{,}354}{20{,}000}, \\dfrac{4{,}517}{20{,}000}, \\dfrac{4{,}604}{20{,}000}, \\dfrac{4{,}718}{20{,}000}, \\text{ and } \\dfrac{4{,}761}{20{,}000}", "__seed__": "0888"}}, {"seed": 889, "data": {"p1_how_many": "12", "p1_a": "6.53", "p1_b": "6.54", "p1_numbers": "6.5305, 6.531, 6.5315, 6.532, 6.5325, 6.533, 6.534, 6.535, 6.536, 6.537, 6.538, and 6.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.531000000000001", "6.532", "6.533", "6.534", "6.535", "6.5360000000000005", "6.537", "6.538", "6.539000000000001"], "p1_2_xs": ["6.5305", "6.5315", "6.5325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{7{,}586}{42{,}000}, \\dfrac{7{,}651}{42{,}000}, \\dfrac{7{,}926}{42{,}000}, \\dfrac{8{,}101}{42{,}000}, \\dfrac{8{,}481}{42{,}000}, \\dfrac{9{,}147}{42{,}000}, \\dfrac{9{,}330}{42{,}000}, \\dfrac{9{,}443}{42{,}000}, \\dfrac{11{,}438}{42{,}000}, \\text{ and } \\dfrac{11{,}942}{42{,}000}", "__seed__": "0889"}}, {"seed": 890, "data": {"p1_how_many": "10", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.6005, 2.601, 2.602, 2.603, 2.604, 2.605, 2.606, 2.607, 2.608, and 2.609", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.601", "2.602", "2.603", "2.604", "2.605", "2.606", "2.607", "2.608", "2.609"], "p1_2_xs": ["2.6005000000000003"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{35{,}244}{56{,}000}, \\dfrac{35{,}917}{56{,}000}, \\dfrac{36{,}841}{56{,}000}, \\dfrac{37{,}914}{56{,}000}, \\dfrac{38{,}611}{56{,}000}, \\dfrac{39{,}580}{56{,}000}, \\dfrac{39{,}612}{56{,}000}, \\text{ and } \\dfrac{39{,}921}{56{,}000}", "__seed__": "0890"}}, {"seed": 891, "data": {"p1_how_many": "14", "p1_a": "4.23", "p1_b": "4.24", "p1_numbers": "4.2305, 4.231, 4.2315, 4.232, 4.2325, 4.233, 4.2335, 4.234, 4.2345, 4.235, 4.236, 4.237, 4.238, and 4.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.231000000000001", "4.232", "4.2330000000000005", "4.234", "4.235", "4.236000000000001", "4.237", "4.238", "4.239000000000001"], "p1_2_xs": ["4.2305", "4.2315000000000005", "4.2325", "4.2335", "4.2345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{624}{4{,}200}, \\dfrac{626}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{641}{4{,}200}, \\dfrac{649}{4{,}200}, \\dfrac{658}{4{,}200}, \\dfrac{659}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{677}{4{,}200}, \\text{ and } \\dfrac{696}{4{,}200}", "__seed__": "0891"}}, {"seed": 892, "data": {"p1_how_many": "10", "p1_a": "7.54", "p1_b": "7.55", "p1_numbers": "7.5405, 7.541, 7.542, 7.543, 7.544, 7.545, 7.546, 7.547, 7.548, and 7.549", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.541", "7.542", "7.543", "7.544", "7.545", "7.546", "7.547", "7.548", "7.549"], "p1_2_xs": ["7.5405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}051}{15{,}000}, \\dfrac{5{,}124}{15{,}000}, \\dfrac{5{,}248}{15{,}000}, \\dfrac{5{,}451}{15{,}000}, \\dfrac{5{,}464}{15{,}000}, \\dfrac{5{,}467}{15{,}000}, \\dfrac{5{,}480}{15{,}000}, \\dfrac{5{,}564}{15{,}000}, \\dfrac{5{,}636}{15{,}000}, \\text{ and } \\dfrac{5{,}742}{15{,}000}", "__seed__": "0892"}}, {"seed": 893, "data": {"p1_how_many": "14", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.345, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335", "5.345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{1{,}406}{3{,}500}, \\dfrac{1{,}409}{3{,}500}, \\dfrac{1{,}414}{3{,}500}, \\dfrac{1{,}416}{3{,}500}, \\dfrac{1{,}432}{3{,}500}, \\dfrac{1{,}434}{3{,}500}, \\dfrac{1{,}459}{3{,}500}, \\dfrac{1{,}464}{3{,}500}, \\dfrac{1{,}470}{3{,}500}, \\dfrac{1{,}472}{3{,}500}, \\text{ and } \\dfrac{1{,}477}{3{,}500}", "__seed__": "0893"}}, {"seed": 894, "data": {"p1_how_many": "11", "p1_a": "6.3", "p1_b": "6.4", "p1_numbers": "6.305, 6.31, 6.315, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.31", "6.319999999999999", "6.33", "6.34", "6.35", "6.359999999999999", "6.37", "6.38", "6.39"], "p1_2_xs": ["6.305", "6.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}160}{5{,}600}, \\dfrac{2{,}177}{5{,}600}, \\dfrac{2{,}188}{5{,}600}, \\dfrac{2{,}191}{5{,}600}, \\dfrac{2{,}220}{5{,}600}, \\dfrac{2{,}226}{5{,}600}, \\dfrac{2{,}233}{5{,}600}, \\dfrac{2{,}245}{5{,}600}, \\dfrac{2{,}326}{5{,}600}, \\dfrac{2{,}342}{5{,}600}, \\text{ and } \\dfrac{2{,}394}{5{,}600}", "__seed__": "0894"}}, {"seed": 895, "data": {"p1_how_many": "10", "p1_a": "1.75", "p1_b": "1.76", "p1_numbers": "1.7505, 1.751, 1.752, 1.753, 1.754, 1.755, 1.756, 1.757, 1.758, and 1.759", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.751", "1.752", "1.753", "1.754", "1.755", "1.756", "1.757", "1.758", "1.759"], "p1_2_xs": ["1.7505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{9{,}280}{63{,}000}, \\dfrac{9{,}508}{63{,}000}, \\dfrac{9{,}822}{63{,}000}, \\dfrac{10{,}529}{63{,}000}, \\dfrac{10{,}596}{63{,}000}, \\dfrac{10{,}904}{63{,}000}, \\dfrac{12{,}510}{63{,}000}, \\dfrac{13{,}213}{63{,}000}, \\dfrac{13{,}698}{63{,}000}, \\text{ and } \\dfrac{13{,}742}{63{,}000}", "__seed__": "0895"}}, {"seed": 896, "data": {"p1_how_many": "10", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{3{,}008}{12{,}000}, \\dfrac{3{,}227}{12{,}000}, \\dfrac{3{,}299}{12{,}000}, \\dfrac{3{,}417}{12{,}000}, \\dfrac{3{,}436}{12{,}000}, \\dfrac{3{,}445}{12{,}000}, \\dfrac{3{,}572}{12{,}000}, \\dfrac{3{,}586}{12{,}000}, \\dfrac{3{,}627}{12{,}000}, \\dfrac{3{,}901}{12{,}000}, \\text{ and } \\dfrac{3{,}946}{12{,}000}", "__seed__": "0896"}}, {"seed": 897, "data": {"p1_how_many": "10", "p1_a": "6.6", "p1_b": "6.7", "p1_numbers": "6.605, 6.61, 6.62, 6.63, 6.64, 6.65, 6.66, 6.67, 6.68, and 6.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.609999999999999", "6.619999999999999", "6.63", "6.64", "6.6499999999999995", "6.659999999999999", "6.67", "6.68", "6.6899999999999995"], "p1_2_xs": ["6.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{152}{200}, \\dfrac{153}{200}, \\dfrac{154}{200}, \\dfrac{155}{200}, \\dfrac{156}{200}, \\dfrac{157}{200}, \\dfrac{158}{200}, \\text{ and } \\dfrac{159}{200}", "__seed__": "0897"}}, {"seed": 898, "data": {"p1_how_many": "12", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.125, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115", "1.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}036}{20{,}000}, \\dfrac{5{,}373}{20{,}000}, \\dfrac{5{,}586}{20{,}000}, \\dfrac{5{,}751}{20{,}000}, \\dfrac{5{,}833}{20{,}000}, \\dfrac{6{,}149}{20{,}000}, \\dfrac{6{,}313}{20{,}000}, \\dfrac{6{,}813}{20{,}000}, \\dfrac{7{,}668}{20{,}000}, \\text{ and } \\dfrac{7{,}751}{20{,}000}", "__seed__": "0898"}}, {"seed": 899, "data": {"p1_how_many": "10", "p1_a": "5.97", "p1_b": "5.98", "p1_numbers": "5.9705, 5.971, 5.972, 5.973, 5.974, 5.975, 5.976, 5.977, 5.978, and 5.979", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.971", "5.9719999999999995", "5.973", "5.973999999999999", "5.975", "5.976", "5.976999999999999", "5.978", "5.979"], "p1_2_xs": ["5.9704999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{128}{200}, \\dfrac{132}{200}, \\dfrac{133}{200}, \\dfrac{136}{200}, \\dfrac{140}{200}, \\dfrac{145}{200}, \\dfrac{147}{200}, \\text{ and } \\dfrac{148}{200}", "__seed__": "0899"}}, {"seed": 900, "data": {"p1_how_many": "11", "p1_a": "8.43", "p1_b": "8.44", "p1_numbers": "8.4305, 8.431, 8.4315, 8.432, 8.433, 8.434, 8.435, 8.436, 8.437, 8.438, and 8.439", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.431", "8.432", "8.433", "8.434", "8.435", "8.436", "8.437", "8.437999999999999", "8.439"], "p1_2_xs": ["8.4305", "8.4315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}016}{63{,}000}, \\dfrac{27{,}080}{63{,}000}, \\dfrac{27{,}227}{63{,}000}, \\dfrac{27{,}423}{63{,}000}, \\dfrac{27{,}449}{63{,}000}, \\dfrac{27{,}741}{63{,}000}, \\dfrac{27{,}754}{63{,}000}, \\dfrac{27{,}846}{63{,}000}, \\dfrac{27{,}873}{63{,}000}, \\dfrac{27{,}949}{63{,}000}, \\text{ and } \\dfrac{27{,}990}{63{,}000}", "__seed__": "0900"}}, {"seed": 901, "data": {"p1_how_many": "12", "p1_a": "4.33", "p1_b": "4.34", "p1_numbers": "4.3305, 4.331, 4.3315, 4.332, 4.3325, 4.333, 4.334, 4.335, 4.336, 4.337, 4.338, and 4.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.331", "4.332", "4.333", "4.334", "4.335", "4.336", "4.337", "4.338", "4.339"], "p1_2_xs": ["4.3305", "4.3315", "4.3325"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{507}{3{,}000}, \\dfrac{528}{3{,}000}, \\dfrac{560}{3{,}000}, \\dfrac{575}{3{,}000}, \\dfrac{581}{3{,}000}, \\dfrac{582}{3{,}000}, \\dfrac{588}{3{,}000}, \\text{ and } \\dfrac{594}{3{,}000}", "__seed__": "0901"}}, {"seed": 902, "data": {"p1_how_many": "13", "p1_a": "2.34", "p1_b": "2.35", "p1_numbers": "2.3405, 2.341, 2.3415, 2.342, 2.3425, 2.343, 2.3435, 2.344, 2.345, 2.346, 2.347, 2.348, and 2.349", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.3409999999999997", "2.3419999999999996", "2.343", "2.344", "2.3449999999999998", "2.3459999999999996", "2.347", "2.348", "2.3489999999999998"], "p1_2_xs": ["2.3405", "2.3415", "2.3425", "2.3435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{505}{1{,}500}, \\dfrac{516}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{541}{1{,}500}, \\dfrac{542}{1{,}500}, \\dfrac{570}{1{,}500}, 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"9.6", "p1_numbers": "9.505, 9.51, 9.515, 9.52, 9.525, 9.53, 9.535, 9.54, 9.545, 9.55, 9.56, 9.57, 9.58, and 9.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.51", "9.52", "9.53", "9.54", "9.55", "9.56", "9.57", "9.58", "9.59"], "p1_2_xs": ["9.505", "9.515", "9.525", "9.535", "9.545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{613}{4{,}200}, \\dfrac{621}{4{,}200}, \\dfrac{628}{4{,}200}, \\dfrac{631}{4{,}200}, \\dfrac{653}{4{,}200}, \\dfrac{691}{4{,}200}, \\text{ and } \\dfrac{694}{4{,}200}", "__seed__": "0904"}}, {"seed": 905, "data": {"p1_how_many": "11", "p1_a": "5.14", "p1_b": "5.15", "p1_numbers": "5.1405, 5.141, 5.1415, 5.142, 5.143, 5.144, 5.145, 5.146, 5.147, 5.148, and 5.149", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.141", "5.1419999999999995", "5.143", "5.143999999999999", "5.145", "5.146", "5.146999999999999", "5.148", "5.149"], "p1_2_xs": ["5.140499999999999", "5.1415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}029}{4{,}200}, \\dfrac{3{,}061}{4{,}200}, \\dfrac{3{,}138}{4{,}200}, \\dfrac{3{,}297}{4{,}200}, \\dfrac{3{,}311}{4{,}200}, \\dfrac{3{,}429}{4{,}200}, \\dfrac{3{,}432}{4{,}200}, \\text{ and } \\dfrac{3{,}448}{4{,}200}", "__seed__": "0905"}}, {"seed": 906, "data": {"p1_how_many": "14", "p1_a": "3.1", "p1_b": "3.2", "p1_numbers": "3.105, 3.11, 3.115, 3.12, 3.125, 3.13, 3.135, 3.14, 3.145, 3.15, 3.16, 3.17, 3.18, and 3.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.11", "3.12", "3.13", "3.14", "3.15", "3.16", "3.17", "3.18", "3.19"], "p1_2_xs": ["3.105", "3.1149999999999998", "3.125", "3.135", "3.145"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}017}{15{,}000}, \\dfrac{5{,}064}{15{,}000}, \\dfrac{5{,}169}{15{,}000}, \\dfrac{5{,}386}{15{,}000}, \\dfrac{5{,}440}{15{,}000}, \\dfrac{5{,}551}{15{,}000}, \\dfrac{5{,}735}{15{,}000}, \\dfrac{5{,}865}{15{,}000}, \\dfrac{5{,}915}{15{,}000}, \\text{ and } \\dfrac{5{,}935}{15{,}000}", "__seed__": "0906"}}, {"seed": 907, "data": {"p1_how_many": "13", "p1_a": "2.22", "p1_b": "2.23", "p1_numbers": "2.2205, 2.221, 2.2215, 2.222, 2.2225, 2.223, 2.2235, 2.224, 2.225, 2.226, 2.227, 2.228, and 2.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.221", "2.222", "2.2230000000000003", "2.224", "2.225", "2.226", "2.2270000000000003", "2.228", "2.229"], "p1_2_xs": ["2.2205000000000004", "2.2215000000000003", "2.2225", "2.2235000000000005"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}230}{15{,}000}, \\dfrac{5{,}275}{15{,}000}, \\dfrac{5{,}291}{15{,}000}, \\dfrac{5{,}607}{15{,}000}, \\dfrac{5{,}793}{15{,}000}, \\dfrac{5{,}802}{15{,}000}, \\dfrac{5{,}823}{15{,}000}, \\dfrac{5{,}883}{15{,}000}, \\dfrac{5{,}932}{15{,}000}, \\dfrac{5{,}979}{15{,}000}, \\text{ and } \\dfrac{5{,}988}{15{,}000}", "__seed__": "0907"}}, {"seed": 908, "data": {"p1_how_many": "10", "p1_a": "8.44", "p1_b": "8.45", "p1_numbers": "8.4405, 8.441, 8.442, 8.443, 8.444, 8.445, 8.446, 8.447, 8.448, and 8.449", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.440999999999999", "8.442", "8.443", "8.443999999999999", "8.445", "8.446", "8.447", "8.447999999999999", "8.449"], "p1_2_xs": ["8.4405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{628}{4{,}200}, \\dfrac{630}{4{,}200}, \\dfrac{634}{4{,}200}, \\dfrac{647}{4{,}200}, \\dfrac{670}{4{,}200}, \\dfrac{679}{4{,}200}, \\text{ and } \\dfrac{687}{4{,}200}", "__seed__": "0908"}}, {"seed": 909, "data": {"p1_how_many": "14", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.225, 3.23, 3.235, 3.24, 3.245, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215", "3.225", "3.235", "3.245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{15{,}003}{20{,}000}, \\dfrac{15{,}030}{20{,}000}, \\dfrac{15{,}051}{20{,}000}, \\dfrac{15{,}314}{20{,}000}, \\dfrac{15{,}441}{20{,}000}, \\dfrac{15{,}518}{20{,}000}, \\dfrac{15{,}573}{20{,}000}, \\dfrac{15{,}614}{20{,}000}, \\dfrac{15{,}725}{20{,}000}, \\dfrac{15{,}902}{20{,}000}, \\text{ and } \\dfrac{15{,}904}{20{,}000}", "__seed__": "0909"}}, {"seed": 910, "data": {"p1_how_many": "11", "p1_a": "4.1", "p1_b": "4.2", "p1_numbers": "4.105, 4.11, 4.115, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.109999999999999", "4.119999999999999", "4.13", "4.14", "4.1499999999999995", "4.159999999999999", "4.17", "4.18", "4.1899999999999995"], "p1_2_xs": ["4.1049999999999995", "4.114999999999999"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{44}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\dfrac{48}{200}, \\text{ and } \\dfrac{49}{200}", "__seed__": "0910"}}, {"seed": 911, "data": {"p1_how_many": "13", "p1_a": "9.45", "p1_b": "9.46", "p1_numbers": "9.4505, 9.451, 9.4515, 9.452, 9.4525, 9.453, 9.4535, 9.454, 9.455, 9.456, 9.457, 9.458, and 9.459", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.450999999999999", "9.452", "9.453", "9.453999999999999", "9.455", "9.456", "9.456999999999999", "9.457999999999998", "9.459"], "p1_2_xs": ["9.4505", "9.4515", "9.4525", "9.4535"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}044}{15{,}000}, \\dfrac{5{,}080}{15{,}000}, \\dfrac{5{,}240}{15{,}000}, \\dfrac{5{,}263}{15{,}000}, \\dfrac{5{,}369}{15{,}000}, \\dfrac{5{,}438}{15{,}000}, \\dfrac{5{,}574}{15{,}000}, \\dfrac{5{,}831}{15{,}000}, \\dfrac{5{,}881}{15{,}000}, \\dfrac{5{,}925}{15{,}000}, \\dfrac{5{,}976}{15{,}000}, \\text{ and } \\dfrac{5{,}986}{15{,}000}", "__seed__": "0911"}}, {"seed": 912, "data": {"p1_how_many": "13", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.735, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725", "2.735"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{4{,}250}{7{,}700}, \\dfrac{4{,}363}{7{,}700}, \\dfrac{4{,}431}{7{,}700}, \\dfrac{5{,}003}{7{,}700}, \\dfrac{5{,}089}{7{,}700}, \\dfrac{5{,}120}{7{,}700}, \\dfrac{5{,}217}{7{,}700}, \\text{ and } \\dfrac{5{,}430}{7{,}700}", "__seed__": "0912"}}, {"seed": 913, "data": {"p1_how_many": "11", "p1_a": "9.0", "p1_b": "9.1", "p1_numbers": "9.005, 9.01, 9.015, 9.02, 9.03, 9.04, 9.05, 9.06, 9.07, 9.08, and 9.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.01", "9.02", "9.03", "9.04", "9.05", "9.06", "9.07", "9.08", "9.09"], "p1_2_xs": ["9.005", "9.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{1}{3}", "p2_numbers": "\\dfrac{301}{1{,}200}, \\dfrac{332}{1{,}200}, \\dfrac{340}{1{,}200}, \\dfrac{360}{1{,}200}, \\dfrac{394}{1{,}200}, \\dfrac{395}{1{,}200}, \\dfrac{397}{1{,}200}, \\text{ and } \\dfrac{399}{1{,}200}", "__seed__": "0913"}}, {"seed": 914, "data": {"p1_how_many": "12", "p1_a": "2.6", "p1_b": "2.7", "p1_numbers": "2.605, 2.61, 2.615, 2.62, 2.625, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, and 2.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.61", "2.62", "2.63", "2.64", "2.65", "2.66", "2.67", "2.68", "2.69"], "p1_2_xs": ["2.605", "2.6149999999999998", "2.625"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}197}{56{,}000}, \\dfrac{21{,}242}{56{,}000}, \\dfrac{21{,}524}{56{,}000}, \\dfrac{21{,}932}{56{,}000}, \\dfrac{22{,}200}{56{,}000}, \\dfrac{22{,}908}{56{,}000}, \\dfrac{23{,}113}{56{,}000}, \\dfrac{23{,}154}{56{,}000}, \\dfrac{23{,}703}{56{,}000}, \\text{ and } \\dfrac{23{,}745}{56{,}000}", "__seed__": "0914"}}, {"seed": 915, "data": {"p1_how_many": "11", "p1_a": "8.64", "p1_b": "8.65", "p1_numbers": "8.6405, 8.641, 8.6415, 8.642, 8.643, 8.644, 8.645, 8.646, 8.647, 8.648, and 8.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.641", "8.642000000000001", "8.643", "8.644", "8.645000000000001", "8.646", "8.647", "8.648", "8.649000000000001"], "p1_2_xs": ["8.640500000000001", "8.6415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{152}{350}, \\dfrac{157}{350}, \\dfrac{170}{350}, \\dfrac{171}{350}, \\dfrac{176}{350}, \\dfrac{181}{350}, \\dfrac{184}{350}, \\text{ and } \\dfrac{193}{350}", "__seed__": "0915"}}, {"seed": 916, "data": {"p1_how_many": "13", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.635, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625", "3.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{5}{8}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{3{,}509}{5{,}600}, \\dfrac{3{,}521}{5{,}600}, \\dfrac{3{,}544}{5{,}600}, \\dfrac{3{,}554}{5{,}600}, \\dfrac{3{,}602}{5{,}600}, \\dfrac{3{,}613}{5{,}600}, \\dfrac{3{,}687}{5{,}600}, \\dfrac{3{,}703}{5{,}600}, \\dfrac{3{,}788}{5{,}600}, \\dfrac{3{,}881}{5{,}600}, \\dfrac{3{,}906}{5{,}600}, \\text{ and } \\dfrac{3{,}967}{5{,}600}", "__seed__": "0916"}}, {"seed": 917, "data": {"p1_how_many": "12", "p1_a": "2.1", "p1_b": "2.2", "p1_numbers": "2.1005, 2.101, 2.1015, 2.102, 2.1025, 2.103, 2.104, 2.105, 2.106, 2.107, 2.108, and 2.109", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.101", "2.102", "2.103", "2.104", "2.105", "2.106", "2.107", "2.108", "2.109"], "p1_2_xs": ["2.1005000000000003", "2.1015", "2.1025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{415}{2{,}000}, \\dfrac{418}{2{,}000}, \\dfrac{427}{2{,}000}, \\dfrac{445}{2{,}000}, \\dfrac{450}{2{,}000}, \\dfrac{489}{2{,}000}, \\text{ and } \\dfrac{499}{2{,}000}", "__seed__": "0917"}}, {"seed": 918, "data": {"p1_how_many": "10", "p1_a": "5.74", "p1_b": "5.75", "p1_numbers": "5.7405, 5.741, 5.742, 5.743, 5.744, 5.745, 5.746, 5.747, 5.748, and 5.749", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.7410000000000005", "5.742", "5.743", "5.744", "5.745", "5.746", "5.747", "5.748", "5.7490000000000006"], "p1_2_xs": ["5.7405"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{14{,}048}{63{,}000}, \\dfrac{14{,}137}{63{,}000}, \\dfrac{14{,}257}{63{,}000}, \\dfrac{14{,}488}{63{,}000}, \\dfrac{14{,}680}{63{,}000}, \\dfrac{14{,}995}{63{,}000}, \\dfrac{15{,}854}{63{,}000}, \\dfrac{16{,}274}{63{,}000}, \\dfrac{16{,}724}{63{,}000}, \\dfrac{16{,}849}{63{,}000}, \\dfrac{17{,}468}{63{,}000}, \\text{ and } \\dfrac{17{,}901}{63{,}000}", "__seed__": "0918"}}, {"seed": 919, "data": {"p1_how_many": "11", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.63, 8.64, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{9}", "p2_b": "\\dfrac{4}{7}", "p2_numbers": "\\dfrac{281}{630}, \\dfrac{287}{630}, \\dfrac{288}{630}, \\dfrac{290}{630}, \\dfrac{326}{630}, \\dfrac{338}{630}, \\text{ and } \\dfrac{346}{630}", "__seed__": "0919"}}, {"seed": 920, "data": {"p1_how_many": "11", "p1_a": "3.01", "p1_b": "3.02", "p1_numbers": "3.0105, 3.011, 3.0115, 3.012, 3.013, 3.014, 3.015, 3.016, 3.017, 3.018, and 3.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.0109999999999997", "3.0119999999999996", "3.013", "3.014", "3.0149999999999997", "3.0159999999999996", "3.017", "3.018", "3.0189999999999997"], "p1_2_xs": ["3.0105", "3.0115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}897}{20{,}000}, \\dfrac{5{,}978}{20{,}000}, \\dfrac{6{,}636}{20{,}000}, \\dfrac{6{,}655}{20{,}000}, \\dfrac{6{,}912}{20{,}000}, \\dfrac{7{,}152}{20{,}000}, \\dfrac{7{,}410}{20{,}000}, \\dfrac{7{,}528}{20{,}000}, \\dfrac{7{,}947}{20{,}000}, \\text{ and } \\dfrac{7{,}997}{20{,}000}", "__seed__": "0920"}}, {"seed": 921, "data": {"p1_how_many": "11", "p1_a": "1.97", "p1_b": "1.98", "p1_numbers": "1.9705, 1.971, 1.9715, 1.972, 1.973, 1.974, 1.975, 1.976, 1.977, 1.978, and 1.979", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.9709999999999999", "1.972", "1.9729999999999999", "1.974", "1.9749999999999999", "1.976", "1.9769999999999999", "1.978", "1.9789999999999999"], "p1_2_xs": ["1.9705", "1.9714999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{2{,}101}{5{,}600}, \\dfrac{2{,}102}{5{,}600}, \\dfrac{2{,}121}{5{,}600}, \\dfrac{2{,}232}{5{,}600}, \\dfrac{2{,}235}{5{,}600}, \\dfrac{2{,}247}{5{,}600}, \\dfrac{2{,}277}{5{,}600}, \\dfrac{2{,}286}{5{,}600}, \\dfrac{2{,}303}{5{,}600}, \\dfrac{2{,}325}{5{,}600}, \\text{ and } \\dfrac{2{,}345}{5{,}600}", "__seed__": "0921"}}, {"seed": 922, "data": {"p1_how_many": "13", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.405, 2.41, 2.415, 2.42, 2.425, 2.43, 2.435, 2.44, 2.45, 2.46, 2.47, 2.48, and 2.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.4099999999999997", "2.42", "2.4299999999999997", "2.44", "2.4499999999999997", "2.46", "2.4699999999999998", "2.48", "2.4899999999999998"], "p1_2_xs": ["2.405", "2.4149999999999996", "2.425", "2.4349999999999996"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{720}{4{,}200}, \\dfrac{744}{4{,}200}, \\dfrac{779}{4{,}200}, \\dfrac{791}{4{,}200}, \\dfrac{856}{4{,}200}, \\dfrac{875}{4{,}200}, \\dfrac{940}{4{,}200}, \\dfrac{994}{4{,}200}, \\dfrac{1{,}013}{4{,}200}, \\dfrac{1{,}022}{4{,}200}, \\text{ and } \\dfrac{1{,}041}{4{,}200}", "__seed__": "0922"}}, {"seed": 923, "data": {"p1_how_many": "10", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{505}{1{,}500}, \\dfrac{514}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{532}{1{,}500}, \\dfrac{544}{1{,}500}, \\dfrac{559}{1{,}500}, \\dfrac{566}{1{,}500}, \\dfrac{567}{1{,}500}, \\dfrac{578}{1{,}500}, \\text{ and } \\dfrac{597}{1{,}500}", "__seed__": "0923"}}, {"seed": 924, "data": {"p1_how_many": "10", "p1_a": "8.01", "p1_b": "8.02", "p1_numbers": "8.0105, 8.011, 8.012, 8.013, 8.014, 8.015, 8.016, 8.017, 8.018, and 8.019", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.011", "8.012", "8.013", "8.014", "8.015", "8.016", "8.017", "8.017999999999999", "8.019"], "p1_2_xs": ["8.0105"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}605}{5{,}600}, \\dfrac{1{,}625}{5{,}600}, \\dfrac{1{,}702}{5{,}600}, \\dfrac{1{,}712}{5{,}600}, \\dfrac{1{,}755}{5{,}600}, \\dfrac{1{,}757}{5{,}600}, \\dfrac{1{,}838}{5{,}600}, \\dfrac{1{,}959}{5{,}600}, \\text{ and } \\dfrac{1{,}997}{5{,}600}", "__seed__": "0924"}}, {"seed": 925, "data": {"p1_how_many": "11", "p1_a": "1.1", "p1_b": "1.2", "p1_numbers": "1.105, 1.11, 1.115, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, and 1.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.11", "1.12", "1.1300000000000001", "1.1400000000000001", "1.1500000000000001", "1.1600000000000001", "1.1700000000000002", "1.1800000000000002", "1.1900000000000002"], "p1_2_xs": ["1.105", "1.115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{2{,}009}{3{,}500}, \\dfrac{2{,}018}{3{,}500}, \\dfrac{2{,}028}{3{,}500}, \\dfrac{2{,}042}{3{,}500}, \\dfrac{2{,}046}{3{,}500}, \\dfrac{2{,}047}{3{,}500}, \\dfrac{2{,}052}{3{,}500}, \\dfrac{2{,}078}{3{,}500}, \\dfrac{2{,}079}{3{,}500}, \\text{ and } \\dfrac{2{,}095}{3{,}500}", "__seed__": "0925"}}, {"seed": 926, "data": {"p1_how_many": "13", "p1_a": "9.3", "p1_b": "9.4", "p1_numbers": "9.305, 9.31, 9.315, 9.32, 9.325, 9.33, 9.335, 9.34, 9.35, 9.36, 9.37, 9.38, and 9.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.31", "9.32", "9.33", "9.34", "9.350000000000001", "9.360000000000001", "9.370000000000001", "9.38", "9.39"], "p1_2_xs": ["9.305000000000001", "9.315000000000001", "9.325000000000001", "9.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}419}{6{,}300}, \\dfrac{1{,}466}{6{,}300}, \\dfrac{1{,}533}{6{,}300}, \\dfrac{1{,}541}{6{,}300}, \\dfrac{1{,}591}{6{,}300}, \\dfrac{1{,}661}{6{,}300}, \\dfrac{1{,}766}{6{,}300}, \\text{ and } \\dfrac{1{,}781}{6{,}300}", "__seed__": "0926"}}, {"seed": 927, "data": {"p1_how_many": "11", "p1_a": "5.5", "p1_b": "5.6", "p1_numbers": "5.505, 5.51, 5.515, 5.52, 5.53, 5.54, 5.55, 5.56, 5.57, 5.58, and 5.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.51", "5.52", "5.53", "5.54", "5.55", "5.56", "5.57", "5.58", "5.59"], "p1_2_xs": ["5.505", "5.515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{96}{630}, \\dfrac{100}{630}, \\dfrac{105}{630}, \\dfrac{110}{630}, \\dfrac{120}{630}, \\dfrac{122}{630}, \\dfrac{125}{630}, \\text{ and } \\dfrac{128}{630}", "__seed__": "0927"}}, {"seed": 928, "data": {"p1_how_many": "11", "p1_a": "7.64", "p1_b": "7.65", "p1_numbers": "7.6405, 7.641, 7.6415, 7.642, 7.643, 7.644, 7.645, 7.646, 7.647, 7.648, and 7.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.641", "7.6419999999999995", "7.643", "7.643999999999999", "7.645", "7.646", "7.646999999999999", "7.648", "7.649"], "p1_2_xs": ["7.640499999999999", "7.6415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{761}{4{,}200}, \\dfrac{815}{4{,}200}, \\dfrac{866}{4{,}200}, \\dfrac{888}{4{,}200}, \\dfrac{932}{4{,}200}, \\dfrac{966}{4{,}200}, \\dfrac{981}{4{,}200}, \\dfrac{1{,}128}{4{,}200}, \\dfrac{1{,}153}{4{,}200}, \\text{ and } \\dfrac{1{,}181}{4{,}200}", "__seed__": "0928"}}, {"seed": 929, "data": {"p1_how_many": "12", "p1_a": "5.2", "p1_b": "5.3", "p1_numbers": "5.205, 5.21, 5.215, 5.22, 5.225, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, and 5.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.21", "5.22", "5.23", "5.24", "5.25", "5.26", "5.2700000000000005", "5.28", "5.29"], "p1_2_xs": ["5.205", "5.215", "5.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{823}{1{,}200}, \\dfrac{837}{1{,}200}, \\dfrac{843}{1{,}200}, \\dfrac{853}{1{,}200}, \\dfrac{864}{1{,}200}, \\dfrac{872}{1{,}200}, \\dfrac{881}{1{,}200}, \\dfrac{887}{1{,}200}, \\text{ and } \\dfrac{894}{1{,}200}", "__seed__": "0929"}}, {"seed": 930, "data": {"p1_how_many": "11", "p1_a": "5.7", "p1_b": "5.8", "p1_numbers": "5.705, 5.71, 5.715, 5.72, 5.73, 5.74, 5.75, 5.76, 5.77, 5.78, and 5.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.71", "5.72", "5.73", "5.74", "5.75", "5.76", "5.7700000000000005", "5.78", "5.79"], "p1_2_xs": ["5.705", "5.715"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}006}{3{,}500}, \\dfrac{1{,}055}{3{,}500}, \\dfrac{1{,}063}{3{,}500}, \\dfrac{1{,}099}{3{,}500}, \\dfrac{1{,}131}{3{,}500}, \\dfrac{1{,}143}{3{,}500}, \\dfrac{1{,}170}{3{,}500}, \\dfrac{1{,}178}{3{,}500}, \\dfrac{1{,}258}{3{,}500}, \\dfrac{1{,}284}{3{,}500}, \\dfrac{1{,}371}{3{,}500}, \\text{ and } \\dfrac{1{,}395}{3{,}500}", "__seed__": "0930"}}, {"seed": 931, "data": {"p1_how_many": "10", "p1_a": "7.2", "p1_b": "7.3", "p1_numbers": "7.205, 7.21, 7.22, 7.23, 7.24, 7.25, 7.26, 7.27, 7.28, and 7.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.21", "7.22", "7.23", "7.24", "7.25", "7.26", "7.2700000000000005", "7.28", "7.29"], "p1_2_xs": ["7.205"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}238}{12{,}000}, \\dfrac{8{,}273}{12{,}000}, \\dfrac{8{,}309}{12{,}000}, \\dfrac{8{,}357}{12{,}000}, \\dfrac{8{,}600}{12{,}000}, \\dfrac{8{,}747}{12{,}000}, \\dfrac{8{,}756}{12{,}000}, \\text{ and } \\dfrac{8{,}930}{12{,}000}", "__seed__": "0931"}}, {"seed": 932, "data": {"p1_how_many": "13", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.425, 8.43, 8.435, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001", "8.425", "8.435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}114}{20{,}000}, \\dfrac{5{,}433}{20{,}000}, \\dfrac{5{,}562}{20{,}000}, \\dfrac{5{,}713}{20{,}000}, \\dfrac{5{,}869}{20{,}000}, \\dfrac{6{,}046}{20{,}000}, \\dfrac{6{,}117}{20{,}000}, \\dfrac{6{,}265}{20{,}000}, \\dfrac{6{,}686}{20{,}000}, \\dfrac{7{,}156}{20{,}000}, \\dfrac{7{,}271}{20{,}000}, \\text{ and } \\dfrac{7{,}496}{20{,}000}", "__seed__": "0932"}}, {"seed": 933, "data": {"p1_how_many": "13", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.615, 7.62, 7.625, 7.63, 7.635, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995", "7.614999999999999", "7.624999999999999", "7.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{45}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{48}{200}", "__seed__": "0933"}}, {"seed": 934, "data": {"p1_how_many": "13", "p1_a": "2.04", "p1_b": "2.05", "p1_numbers": "2.0405, 2.041, 2.0415, 2.042, 2.0425, 2.043, 2.0435, 2.044, 2.045, 2.046, 2.047, 2.048, and 2.049", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.041", "2.042", "2.043", "2.044", "2.045", "2.046", "2.047", "2.048", "2.049"], "p1_2_xs": ["2.0405", "2.0415", "2.0425", "2.0435000000000003"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{627}{1{,}500}, \\dfrac{631}{1{,}500}, \\dfrac{713}{1{,}500}, \\dfrac{756}{1{,}500}, \\dfrac{802}{1{,}500}, \\dfrac{819}{1{,}500}, \\dfrac{856}{1{,}500}, \\dfrac{945}{1{,}500}, \\dfrac{964}{1{,}500}, \\text{ and } \\dfrac{986}{1{,}500}", "__seed__": "0934"}}, {"seed": 935, "data": {"p1_how_many": "13", "p1_a": "3.5", "p1_b": "3.6", "p1_numbers": "3.505, 3.51, 3.515, 3.52, 3.525, 3.53, 3.535, 3.54, 3.55, 3.56, 3.57, 3.58, and 3.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.51", "3.52", "3.53", "3.54", "3.55", "3.56", "3.57", "3.58", "3.59"], "p1_2_xs": ["3.505", "3.5149999999999997", "3.525", "3.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{27{,}002}{63{,}000}, \\dfrac{27{,}105}{63{,}000}, \\dfrac{27{,}114}{63{,}000}, \\dfrac{27{,}184}{63{,}000}, \\dfrac{27{,}250}{63{,}000}, \\dfrac{27{,}475}{63{,}000}, \\dfrac{27{,}589}{63{,}000}, \\dfrac{27{,}835}{63{,}000}, \\text{ and } \\dfrac{27{,}945}{63{,}000}", "__seed__": "0935"}}, {"seed": 936, "data": {"p1_how_many": "14", "p1_a": "8.6", "p1_b": "8.7", "p1_numbers": "8.605, 8.61, 8.615, 8.62, 8.625, 8.63, 8.635, 8.64, 8.645, 8.65, 8.66, 8.67, 8.68, and 8.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.61", "8.62", "8.629999999999999", "8.639999999999999", "8.65", "8.66", "8.67", "8.68", "8.69"], "p1_2_xs": ["8.605", "8.615", "8.625", "8.635", "8.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{31{,}357}{42{,}000}, \\dfrac{32{,}180}{42{,}000}, \\dfrac{32{,}599}{42{,}000}, \\dfrac{32{,}733}{42{,}000}, \\dfrac{33{,}448}{42{,}000}, \\dfrac{33{,}589}{42{,}000}, \\dfrac{33{,}712}{42{,}000}, \\dfrac{34{,}150}{42{,}000}, \\text{ and } \\dfrac{34{,}516}{42{,}000}", "__seed__": "0936"}}, {"seed": 937, "data": {"p1_how_many": "13", "p1_a": "1.67", "p1_b": "1.68", "p1_numbers": "1.6705, 1.671, 1.6715, 1.672, 1.6725, 1.673, 1.6735, 1.674, 1.675, 1.676, 1.677, 1.678, and 1.679", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.6709999999999998", "1.672", "1.6729999999999998", "1.674", "1.6749999999999998", "1.676", "1.6769999999999998", "1.678", "1.6789999999999998"], "p1_2_xs": ["1.6704999999999999", "1.6714999999999998", "1.6724999999999999", "1.6734999999999998"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{1{,}203}{2{,}000}, \\dfrac{1{,}224}{2{,}000}, \\dfrac{1{,}248}{2{,}000}, \\dfrac{1{,}278}{2{,}000}, \\dfrac{1{,}311}{2{,}000}, \\dfrac{1{,}360}{2{,}000}, \\dfrac{1{,}370}{2{,}000}, \\dfrac{1{,}464}{2{,}000}, \\text{ and } \\dfrac{1{,}488}{2{,}000}", "__seed__": "0937"}}, {"seed": 938, "data": {"p1_how_many": "12", "p1_a": "6.2", "p1_b": "6.3", "p1_numbers": "6.2005, 6.201, 6.2015, 6.202, 6.2025, 6.203, 6.204, 6.205, 6.206, 6.207, 6.208, and 6.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.2010000000000005", "6.202", "6.203", "6.204", "6.205", "6.206", "6.207", "6.208", "6.2090000000000005"], "p1_2_xs": ["6.2005", "6.2015", "6.2025"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}364}{7{,}700}, \\dfrac{4{,}476}{7{,}700}, \\dfrac{4{,}846}{7{,}700}, \\dfrac{4{,}863}{7{,}700}, \\dfrac{4{,}918}{7{,}700}, \\dfrac{5{,}078}{7{,}700}, \\dfrac{5{,}207}{7{,}700}, \\dfrac{5{,}372}{7{,}700}, \\dfrac{5{,}725}{7{,}700}, \\dfrac{5{,}780}{7{,}700}, \\text{ and } \\dfrac{6{,}556}{7{,}700}", "__seed__": "0938"}}, {"seed": 939, "data": {"p1_how_many": "13", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.525, 2.53, 2.535, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997", "2.525", "2.5349999999999997"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{44{,}562}{77{,}000}, \\dfrac{46{,}118}{77{,}000}, \\dfrac{48{,}566}{77{,}000}, \\dfrac{54{,}929}{77{,}000}, \\dfrac{55{,}240}{77{,}000}, \\dfrac{55{,}424}{77{,}000}, \\dfrac{56{,}339}{77{,}000}, \\dfrac{57{,}547}{77{,}000}, \\dfrac{58{,}264}{77{,}000}, \\text{ and } \\dfrac{58{,}553}{77{,}000}", "__seed__": "0939"}}, {"seed": 940, "data": {"p1_how_many": "10", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.62, 5.63, 5.64, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{2}{9}", "p2_numbers": "\\dfrac{96}{630}, \\dfrac{101}{630}, \\dfrac{105}{630}, \\dfrac{111}{630}, \\dfrac{119}{630}, \\dfrac{130}{630}, \\dfrac{131}{630}, \\dfrac{136}{630}, \\text{ and } \\dfrac{138}{630}", "__seed__": "0940"}}, {"seed": 941, "data": {"p1_how_many": "14", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.705, 6.71, 6.715, 6.72, 6.725, 6.73, 6.735, 6.74, 6.745, 6.75, 6.76, 6.77, 6.78, and 6.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.71", "6.72", "6.73", "6.74", "6.75", "6.76", "6.7700000000000005", "6.78", "6.79"], "p1_2_xs": ["6.705", "6.715", "6.725", "6.735", "6.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}515}{4{,}200}, \\dfrac{3{,}537}{4{,}200}, \\dfrac{3{,}544}{4{,}200}, \\dfrac{3{,}547}{4{,}200}, \\dfrac{3{,}551}{4{,}200}, \\dfrac{3{,}553}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}570}{4{,}200}, \\dfrac{3{,}588}{4{,}200}, \\text{ and } \\dfrac{3{,}599}{4{,}200}", "__seed__": "0941"}}, {"seed": 942, "data": {"p1_how_many": "11", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}046}{15{,}000}, \\dfrac{6{,}708}{15{,}000}, \\dfrac{6{,}747}{15{,}000}, \\dfrac{6{,}936}{15{,}000}, \\dfrac{7{,}633}{15{,}000}, \\dfrac{7{,}719}{15{,}000}, \\dfrac{7{,}957}{15{,}000}, \\dfrac{8{,}449}{15{,}000}, \\dfrac{8{,}621}{15{,}000}, \\dfrac{9{,}577}{15{,}000}, \\text{ and } \\dfrac{9{,}592}{15{,}000}", "__seed__": "0942"}}, {"seed": 943, "data": {"p1_how_many": "10", "p1_a": "6.26", "p1_b": "6.27", "p1_numbers": "6.2605, 6.261, 6.262, 6.263, 6.264, 6.265, 6.266, 6.267, 6.268, and 6.269", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.261", "6.262", "6.263", "6.263999999999999", "6.265", "6.266", "6.2669999999999995", "6.268", "6.269"], "p1_2_xs": ["6.2604999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{6{,}157}{42{,}000}, \\dfrac{6{,}329}{42{,}000}, \\dfrac{6{,}361}{42{,}000}, \\dfrac{6{,}545}{42{,}000}, \\dfrac{6{,}581}{42{,}000}, \\dfrac{6{,}813}{42{,}000}, \\text{ and } \\dfrac{6{,}815}{42{,}000}", "__seed__": "0943"}}, {"seed": 944, "data": {"p1_how_many": "10", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.62, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{8{,}097}{12{,}000}, \\dfrac{8{,}162}{12{,}000}, \\dfrac{8{,}179}{12{,}000}, \\dfrac{8{,}204}{12{,}000}, \\dfrac{8{,}234}{12{,}000}, \\dfrac{8{,}385}{12{,}000}, \\dfrac{8{,}427}{12{,}000}, \\dfrac{8{,}680}{12{,}000}, \\dfrac{8{,}815}{12{,}000}, \\dfrac{8{,}855}{12{,}000}, \\text{ and } \\dfrac{8{,}948}{12{,}000}", "__seed__": "0944"}}, {"seed": 945, "data": {"p1_how_many": "12", "p1_a": "8.1", "p1_b": "8.2", "p1_numbers": "8.105, 8.11, 8.115, 8.12, 8.125, 8.13, 8.14, 8.15, 8.16, 8.17, 8.18, and 8.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.11", "8.12", "8.129999999999999", "8.139999999999999", "8.15", "8.16", "8.17", "8.18", "8.19"], "p1_2_xs": ["8.105", "8.115", "8.125"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}019}{15{,}000}, \\dfrac{5{,}034}{15{,}000}, \\dfrac{5{,}072}{15{,}000}, \\dfrac{5{,}144}{15{,}000}, \\dfrac{5{,}375}{15{,}000}, \\dfrac{5{,}440}{15{,}000}, \\dfrac{5{,}463}{15{,}000}, \\dfrac{5{,}566}{15{,}000}, \\dfrac{5{,}664}{15{,}000}, \\dfrac{5{,}819}{15{,}000}, \\text{ and } \\dfrac{5{,}874}{15{,}000}", "__seed__": "0945"}}, {"seed": 946, "data": {"p1_how_many": "14", "p1_a": "4.23", "p1_b": "4.24", "p1_numbers": "4.2305, 4.231, 4.2315, 4.232, 4.2325, 4.233, 4.2335, 4.234, 4.2345, 4.235, 4.236, 4.237, 4.238, and 4.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.231000000000001", "4.232", "4.2330000000000005", "4.234", "4.235", "4.236000000000001", "4.237", "4.238", "4.239000000000001"], "p1_2_xs": ["4.2305", "4.2315000000000005", "4.2325", "4.2335", "4.2345"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{71}{350}, \\dfrac{73}{350}, \\dfrac{74}{350}, \\dfrac{79}{350}, \\dfrac{81}{350}, \\dfrac{84}{350}, \\text{ and } \\dfrac{90}{350}", "__seed__": "0946"}}, {"seed": 947, "data": {"p1_how_many": "14", "p1_a": "4.7", "p1_b": "4.8", "p1_numbers": "4.705, 4.71, 4.715, 4.72, 4.725, 4.73, 4.735, 4.74, 4.745, 4.75, 4.76, 4.77, 4.78, and 4.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.71", "4.72", "4.73", "4.74", "4.75", "4.76", "4.7700000000000005", "4.78", "4.79"], "p1_2_xs": ["4.705", "4.715", "4.725", "4.735", "4.745"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{7}", "p2_b": "\\dfrac{7}{8}", "p2_numbers": "\\dfrac{48{,}078}{56{,}000}, \\dfrac{48{,}299}{56{,}000}, \\dfrac{48{,}322}{56{,}000}, \\dfrac{48{,}379}{56{,}000}, \\dfrac{48{,}453}{56{,}000}, \\dfrac{48{,}522}{56{,}000}, \\dfrac{48{,}552}{56{,}000}, \\dfrac{48{,}637}{56{,}000}, \\dfrac{48{,}727}{56{,}000}, \\dfrac{48{,}729}{56{,}000}, \\dfrac{48{,}764}{56{,}000}, \\text{ and } \\dfrac{48{,}792}{56{,}000}", "__seed__": "0947"}}, {"seed": 948, "data": {"p1_how_many": "13", "p1_a": "6.23", "p1_b": "6.24", "p1_numbers": "6.2305, 6.231, 6.2315, 6.232, 6.2325, 6.233, 6.2335, 6.234, 6.235, 6.236, 6.237, 6.238, and 6.239", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.231000000000001", "6.232", "6.2330000000000005", "6.234", "6.235", "6.236000000000001", "6.237", "6.238", "6.239000000000001"], "p1_2_xs": ["6.2305", "6.2315000000000005", "6.2325", "6.2335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}514}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}535}{4{,}200}, \\dfrac{3{,}538}{4{,}200}, \\dfrac{3{,}552}{4{,}200}, \\dfrac{3{,}584}{4{,}200}, \\text{ and } \\dfrac{3{,}594}{4{,}200}", "__seed__": "0948"}}, {"seed": 949, "data": {"p1_how_many": "11", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.415, 8.42, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001", "8.415000000000001"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{3{,}514}{4{,}200}, \\dfrac{3{,}533}{4{,}200}, \\dfrac{3{,}542}{4{,}200}, \\dfrac{3{,}562}{4{,}200}, \\dfrac{3{,}566}{4{,}200}, \\dfrac{3{,}573}{4{,}200}, \\dfrac{3{,}579}{4{,}200}, \\dfrac{3{,}584}{4{,}200}, \\dfrac{3{,}589}{4{,}200}, \\dfrac{3{,}595}{4{,}200}, \\text{ and } \\dfrac{3{,}598}{4{,}200}", "__seed__": "0949"}}, {"seed": 950, "data": {"p1_how_many": "10", "p1_a": "8.0", "p1_b": "8.1", "p1_numbers": "8.005, 8.01, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08, and 8.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.01", "8.02", "8.03", "8.04", "8.05", "8.06", "8.07", "8.08", "8.09"], "p1_2_xs": ["8.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}010}{20{,}000}, \\dfrac{4{,}015}{20{,}000}, \\dfrac{4{,}085}{20{,}000}, \\dfrac{4{,}118}{20{,}000}, \\dfrac{4{,}176}{20{,}000}, \\dfrac{4{,}482}{20{,}000}, \\dfrac{4{,}612}{20{,}000}, \\dfrac{4{,}621}{20{,}000}, \\dfrac{4{,}851}{20{,}000}, \\text{ and } \\dfrac{4{,}853}{20{,}000}", "__seed__": "0950"}}, {"seed": 951, "data": {"p1_how_many": "11", "p1_a": "1.16", "p1_b": "1.17", "p1_numbers": "1.1605, 1.161, 1.1615, 1.162, 1.163, 1.164, 1.165, 1.166, 1.167, 1.168, and 1.169", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.1609999999999998", "1.162", "1.1629999999999998", "1.164", "1.1649999999999998", "1.166", "1.1669999999999998", "1.168", "1.1689999999999998"], "p1_2_xs": ["1.1604999999999999", "1.1614999999999998"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{82}{420}, \\dfrac{89}{420}, \\dfrac{97}{420}, \\dfrac{104}{420}, \\dfrac{105}{420}, \\dfrac{109}{420}, \\dfrac{112}{420}, \\text{ and } \\dfrac{116}{420}", "__seed__": "0951"}}, {"seed": 952, "data": {"p1_how_many": "14", "p1_a": "4.82", "p1_b": "4.83", "p1_numbers": "4.8205, 4.821, 4.8215, 4.822, 4.8225, 4.823, 4.8235, 4.824, 4.8245, 4.825, 4.826, 4.827, 4.828, and 4.829", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.821000000000001", "4.822", "4.823", "4.824", "4.825", "4.8260000000000005", "4.827", "4.828", "4.829000000000001"], "p1_2_xs": ["4.8205", "4.8215", "4.8225", "4.8235", "4.8245"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{3}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{819}{1{,}200}, \\dfrac{833}{1{,}200}, \\dfrac{854}{1{,}200}, \\dfrac{863}{1{,}200}, \\dfrac{878}{1{,}200}, \\dfrac{888}{1{,}200}, \\text{ and } \\dfrac{893}{1{,}200}", "__seed__": "0952"}}, {"seed": 953, "data": {"p1_how_many": "13", "p1_a": "5.3", "p1_b": "5.4", "p1_numbers": "5.305, 5.31, 5.315, 5.32, 5.325, 5.33, 5.335, 5.34, 5.35, 5.36, 5.37, 5.38, and 5.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.31", "5.319999999999999", "5.33", "5.34", "5.35", "5.359999999999999", "5.37", "5.38", "5.39"], "p1_2_xs": ["5.305", "5.3149999999999995", "5.324999999999999", "5.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{1{,}638}{5{,}600}, \\dfrac{1{,}644}{5{,}600}, \\dfrac{1{,}652}{5{,}600}, \\dfrac{1{,}680}{5{,}600}, \\dfrac{1{,}721}{5{,}600}, \\dfrac{1{,}800}{5{,}600}, \\dfrac{1{,}844}{5{,}600}, \\dfrac{1{,}889}{5{,}600}, \\dfrac{1{,}892}{5{,}600}, \\dfrac{1{,}991}{5{,}600}, \\text{ and } \\dfrac{2{,}084}{5{,}600}", "__seed__": "0953"}}, {"seed": 954, "data": {"p1_how_many": "11", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{5}{6}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{351}{420}, \\dfrac{352}{420}, \\dfrac{353}{420}, \\dfrac{354}{420}, \\dfrac{355}{420}, \\dfrac{356}{420}, \\dfrac{357}{420}, \\dfrac{358}{420}, \\text{ and } \\dfrac{359}{420}", "__seed__": "0954"}}, {"seed": 955, "data": {"p1_how_many": "11", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.2005, 3.201, 3.2015, 3.202, 3.203, 3.204, 3.205, 3.206, 3.207, 3.208, and 3.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.201", "3.202", "3.2030000000000003", "3.204", "3.205", "3.206", "3.2070000000000003", "3.208", "3.209"], "p1_2_xs": ["3.2005000000000003", "3.2015000000000002"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}385}{20{,}000}, \\dfrac{12{,}859}{20{,}000}, \\dfrac{12{,}882}{20{,}000}, \\dfrac{12{,}889}{20{,}000}, \\dfrac{13{,}292}{20{,}000}, \\dfrac{13{,}624}{20{,}000}, \\dfrac{14{,}349}{20{,}000}, \\dfrac{14{,}428}{20{,}000}, \\text{ and } \\dfrac{14{,}559}{20{,}000}", "__seed__": "0955"}}, {"seed": 956, "data": {"p1_how_many": "11", "p1_a": "6.7", "p1_b": "6.8", "p1_numbers": "6.7005, 6.701, 6.7015, 6.702, 6.703, 6.704, 6.705, 6.706, 6.707, 6.708, and 6.709", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.7010000000000005", "6.702", "6.703", "6.704", "6.705", "6.706", "6.707", "6.708", "6.7090000000000005"], "p1_2_xs": ["6.7005", "6.7015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}134}{15{,}000}, \\dfrac{6{,}769}{15{,}000}, \\dfrac{7{,}129}{15{,}000}, \\dfrac{7{,}774}{15{,}000}, \\dfrac{9{,}096}{15{,}000}, \\dfrac{9{,}149}{15{,}000}, \\dfrac{9{,}306}{15{,}000}, \\dfrac{9{,}330}{15{,}000}, \\dfrac{9{,}335}{15{,}000}, \\dfrac{9{,}812}{15{,}000}, \\dfrac{9{,}900}{15{,}000}, \\text{ and } \\dfrac{9{,}992}{15{,}000}", "__seed__": "0956"}}, {"seed": 957, "data": {"p1_how_many": "13", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.335, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999", "7.335"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{644}{1{,}500}, \\dfrac{678}{1{,}500}, \\dfrac{696}{1{,}500}, \\dfrac{714}{1{,}500}, \\dfrac{741}{1{,}500}, \\dfrac{770}{1{,}500}, \\dfrac{784}{1{,}500}, \\dfrac{871}{1{,}500}, \\text{ and } \\dfrac{904}{1{,}500}", "__seed__": "0957"}}, {"seed": 958, "data": {"p1_how_many": "11", "p1_a": "7.05", "p1_b": "7.06", "p1_numbers": "7.0505, 7.051, 7.0515, 7.052, 7.053, 7.054, 7.055, 7.056, 7.057, 7.058, and 7.059", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.051", "7.052", "7.053", "7.053999999999999", "7.055", "7.056", "7.0569999999999995", "7.058", "7.059"], "p1_2_xs": ["7.0504999999999995", "7.0515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}418}{3{,}000}, \\dfrac{2{,}426}{3{,}000}, \\dfrac{2{,}453}{3{,}000}, \\dfrac{2{,}468}{3{,}000}, \\dfrac{2{,}474}{3{,}000}, \\dfrac{2{,}476}{3{,}000}, \\text{ and } \\dfrac{2{,}497}{3{,}000}", "__seed__": "0958"}}, {"seed": 959, "data": {"p1_how_many": "10", "p1_a": "1.46", "p1_b": "1.47", "p1_numbers": "1.4605, 1.461, 1.462, 1.463, 1.464, 1.465, 1.466, 1.467, 1.468, and 1.469", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["1.4609999999999999", "1.462", "1.4629999999999999", "1.464", "1.4649999999999999", "1.466", "1.4669999999999999", "1.468", "1.4689999999999999"], "p1_2_xs": ["1.4605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{628}{1{,}500}, \\dfrac{643}{1{,}500}, \\dfrac{646}{1{,}500}, \\dfrac{658}{1{,}500}, \\dfrac{735}{1{,}500}, \\dfrac{810}{1{,}500}, \\dfrac{825}{1{,}500}, \\dfrac{850}{1{,}500}, \\dfrac{894}{1{,}500}, \\dfrac{897}{1{,}500}, \\text{ and } \\dfrac{907}{1{,}500}", "__seed__": "0959"}}, {"seed": 960, "data": {"p1_how_many": "14", "p1_a": "4.65", "p1_b": "4.66", "p1_numbers": "4.6505, 4.651, 4.6515, 4.652, 4.6525, 4.653, 4.6535, 4.654, 4.6545, 4.655, 4.656, 4.657, 4.658, and 4.659", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.651000000000001", "4.652", "4.6530000000000005", "4.654", "4.655", "4.656000000000001", "4.657", "4.658", "4.659000000000001"], "p1_2_xs": ["4.6505", "4.6515", "4.6525", "4.6535", "4.6545"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{3}{8}", "p2_numbers": "\\dfrac{16{,}647}{56{,}000}, \\dfrac{16{,}717}{56{,}000}, \\dfrac{17{,}224}{56{,}000}, \\dfrac{18{,}421}{56{,}000}, \\dfrac{19{,}042}{56{,}000}, \\dfrac{20{,}360}{56{,}000}, \\text{ and } \\dfrac{20{,}671}{56{,}000}", "__seed__": "0960"}}, {"seed": 961, "data": {"p1_how_many": "11", "p1_a": "8.41", "p1_b": "8.42", "p1_numbers": "8.4105, 8.411, 8.4115, 8.412, 8.413, 8.414, 8.415, 8.416, 8.417, 8.418, and 8.419", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.411", "8.412", "8.413", "8.414", "8.415000000000001", "8.416", "8.417", "8.418", "8.419"], "p1_2_xs": ["8.4105", "8.4115"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{610}{4{,}200}, \\dfrac{611}{4{,}200}, \\dfrac{613}{4{,}200}, \\dfrac{618}{4{,}200}, \\dfrac{635}{4{,}200}, \\dfrac{660}{4{,}200}, \\dfrac{668}{4{,}200}, \\dfrac{669}{4{,}200}, \\dfrac{671}{4{,}200}, \\dfrac{682}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0961"}}, {"seed": 962, "data": {"p1_how_many": "11", "p1_a": "5.33", "p1_b": "5.34", "p1_numbers": "5.3305, 5.331, 5.3315, 5.332, 5.333, 5.334, 5.335, 5.336, 5.337, 5.338, and 5.339", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.331", "5.332", "5.333", "5.334", "5.335", "5.336", "5.337", "5.338", "5.339"], "p1_2_xs": ["5.3305", "5.3315"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}712}{6{,}300}, \\dfrac{2{,}713}{6{,}300}, \\dfrac{2{,}726}{6{,}300}, \\dfrac{2{,}728}{6{,}300}, \\dfrac{2{,}729}{6{,}300}, \\dfrac{2{,}757}{6{,}300}, \\dfrac{2{,}763}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}765}{6{,}300}, \\dfrac{2{,}770}{6{,}300}, \\dfrac{2{,}775}{6{,}300}, \\text{ and } \\dfrac{2{,}777}{6{,}300}", "__seed__": "0962"}}, {"seed": 963, "data": {"p1_how_many": "11", "p1_a": "2.0", "p1_b": "2.1", "p1_numbers": "2.005, 2.01, 2.015, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, and 2.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.01", "2.02", "2.03", "2.04", "2.05", "2.06", "2.07", "2.08", "2.09"], "p1_2_xs": ["2.005", "2.0149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}158}{15{,}000}, \\dfrac{6{,}423}{15{,}000}, \\dfrac{6{,}979}{15{,}000}, \\dfrac{7{,}263}{15{,}000}, \\dfrac{8{,}003}{15{,}000}, \\dfrac{8{,}033}{15{,}000}, \\dfrac{8{,}219}{15{,}000}, \\dfrac{8{,}540}{15{,}000}, \\dfrac{8{,}982}{15{,}000}, \\text{ and } \\dfrac{9{,}535}{15{,}000}", "__seed__": "0963"}}, {"seed": 964, "data": {"p1_how_many": "10", "p1_a": "5.8", "p1_b": "5.9", "p1_numbers": "5.8005, 5.801, 5.802, 5.803, 5.804, 5.805, 5.806, 5.807, 5.808, and 5.809", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.801", "5.802", "5.803", "5.803999999999999", "5.805", "5.806", "5.8069999999999995", "5.808", "5.809"], "p1_2_xs": ["5.8004999999999995"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}060}{35{,}000}, \\dfrac{14{,}146}{35{,}000}, \\dfrac{14{,}311}{35{,}000}, \\dfrac{14{,}327}{35{,}000}, \\dfrac{14{,}558}{35{,}000}, \\dfrac{14{,}642}{35{,}000}, \\dfrac{14{,}701}{35{,}000}, \\dfrac{14{,}920}{35{,}000}, \\text{ and } \\dfrac{14{,}936}{35{,}000}", "__seed__": "0964"}}, {"seed": 965, "data": {"p1_how_many": "14", "p1_a": "2.4", "p1_b": "2.5", "p1_numbers": "2.4005, 2.401, 2.4015, 2.402, 2.4025, 2.403, 2.4035, 2.404, 2.4045, 2.405, 2.406, 2.407, 2.408, and 2.409", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.401", "2.4019999999999997", "2.403", "2.404", "2.405", "2.4059999999999997", "2.407", "2.408", "2.409"], "p1_2_xs": ["2.4005", "2.4015", "2.4025", "2.4035", "2.4045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{9}", "p2_b": "\\dfrac{2}{7}", "p2_numbers": "\\dfrac{1{,}427}{6{,}300}, \\dfrac{1{,}437}{6{,}300}, \\dfrac{1{,}445}{6{,}300}, \\dfrac{1{,}575}{6{,}300}, \\dfrac{1{,}582}{6{,}300}, \\dfrac{1{,}652}{6{,}300}, \\dfrac{1{,}738}{6{,}300}, \\dfrac{1{,}743}{6{,}300}, \\text{ and } \\dfrac{1{,}784}{6{,}300}", "__seed__": "0965"}}, {"seed": 966, "data": {"p1_how_many": "11", "p1_a": "8.2", "p1_b": "8.3", "p1_numbers": "8.205, 8.21, 8.215, 8.22, 8.23, 8.24, 8.25, 8.26, 8.27, 8.28, and 8.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.209999999999999", "8.219999999999999", "8.229999999999999", "8.239999999999998", "8.25", "8.26", "8.27", "8.28", "8.29"], "p1_2_xs": ["8.205", "8.215"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}066}{4{,}200}, \\dfrac{3{,}106}{4{,}200}, \\dfrac{3{,}173}{4{,}200}, \\dfrac{3{,}201}{4{,}200}, \\dfrac{3{,}277}{4{,}200}, \\dfrac{3{,}366}{4{,}200}, \\text{ and } \\dfrac{3{,}495}{4{,}200}", "__seed__": "0966"}}, {"seed": 967, "data": {"p1_how_many": "13", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}151}{20{,}000}, \\dfrac{12{,}235}{20{,}000}, \\dfrac{12{,}326}{20{,}000}, \\dfrac{12{,}592}{20{,}000}, \\dfrac{12{,}753}{20{,}000}, \\dfrac{12{,}813}{20{,}000}, \\text{ and } \\dfrac{14{,}192}{20{,}000}", "__seed__": "0967"}}, {"seed": 968, "data": {"p1_how_many": "11", "p1_a": "7.66", "p1_b": "7.67", "p1_numbers": "7.6605, 7.661, 7.6615, 7.662, 7.663, 7.664, 7.665, 7.666, 7.667, 7.668, and 7.669", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.6610000000000005", "7.662", "7.663", "7.664", "7.665", "7.666", "7.667", "7.668", "7.6690000000000005"], "p1_2_xs": ["7.6605", "7.6615"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{6}{7}", "p2_numbers": "\\dfrac{4{,}519}{7{,}700}, \\dfrac{4{,}583}{7{,}700}, \\dfrac{4{,}747}{7{,}700}, \\dfrac{4{,}985}{7{,}700}, \\dfrac{5{,}638}{7{,}700}, \\dfrac{5{,}718}{7{,}700}, \\dfrac{5{,}984}{7{,}700}, \\text{ and } \\dfrac{6{,}012}{7{,}700}", "__seed__": "0968"}}, {"seed": 969, "data": {"p1_how_many": "14", "p1_a": "4.4", "p1_b": "4.5", "p1_numbers": "4.405, 4.41, 4.415, 4.42, 4.425, 4.43, 4.435, 4.44, 4.445, 4.45, 4.46, 4.47, 4.48, and 4.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.41", "4.42", "4.430000000000001", "4.44", "4.45", "4.46", "4.470000000000001", "4.48", "4.49"], "p1_2_xs": ["4.405", "4.415", "4.425", "4.4350000000000005", "4.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{501}{3{,}000}, \\dfrac{507}{3{,}000}, \\dfrac{508}{3{,}000}, \\dfrac{509}{3{,}000}, \\dfrac{514}{3{,}000}, \\dfrac{531}{3{,}000}, \\dfrac{537}{3{,}000}, \\dfrac{540}{3{,}000}, \\dfrac{560}{3{,}000}, \\dfrac{561}{3{,}000}, \\dfrac{571}{3{,}000}, \\text{ and } \\dfrac{592}{3{,}000}", "__seed__": "0969"}}, {"seed": 970, "data": {"p1_how_many": "11", "p1_a": "2.5", "p1_b": "2.6", "p1_numbers": "2.505, 2.51, 2.515, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, and 2.59", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.51", "2.52", "2.53", "2.54", "2.55", "2.56", "2.57", "2.58", "2.59"], "p1_2_xs": ["2.505", "2.5149999999999997"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}643}{20{,}000}, \\dfrac{12{,}949}{20{,}000}, \\dfrac{12{,}975}{20{,}000}, \\dfrac{13{,}024}{20{,}000}, \\dfrac{13{,}626}{20{,}000}, \\dfrac{14{,}066}{20{,}000}, \\dfrac{14{,}069}{20{,}000}, \\dfrac{14{,}138}{20{,}000}, \\text{ and } \\dfrac{14{,}738}{20{,}000}", "__seed__": "0970"}}, {"seed": 971, "data": {"p1_how_many": "12", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.325, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995", "7.324999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{3}{5}", "p2_numbers": "\\dfrac{156}{350}, \\dfrac{159}{350}, \\dfrac{164}{350}, \\dfrac{171}{350}, \\dfrac{179}{350}, \\dfrac{186}{350}, \\dfrac{187}{350}, \\dfrac{196}{350}, \\text{ and } \\dfrac{204}{350}", "__seed__": "0971"}}, {"seed": 972, "data": {"p1_how_many": "12", "p1_a": "6.1", "p1_b": "6.2", "p1_numbers": "6.105, 6.11, 6.115, 6.12, 6.125, 6.13, 6.14, 6.15, 6.16, 6.17, 6.18, and 6.19", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["6.109999999999999", "6.119999999999999", "6.13", "6.14", "6.1499999999999995", "6.159999999999999", "6.17", "6.18", "6.1899999999999995"], "p1_2_xs": ["6.1049999999999995", "6.114999999999999", "6.124999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{7}", "p2_b": "\\dfrac{1}{6}", "p2_numbers": "\\dfrac{610}{4{,}200}, \\dfrac{619}{4{,}200}, \\dfrac{637}{4{,}200}, \\dfrac{652}{4{,}200}, \\dfrac{692}{4{,}200}, \\dfrac{695}{4{,}200}, \\text{ and } \\dfrac{697}{4{,}200}", "__seed__": "0972"}}, {"seed": 973, "data": {"p1_how_many": "12", "p1_a": "7.6", "p1_b": "7.7", "p1_numbers": "7.605, 7.61, 7.615, 7.62, 7.625, 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, and 7.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.609999999999999", "7.619999999999999", "7.63", "7.64", "7.6499999999999995", "7.659999999999999", "7.67", "7.68", "7.6899999999999995"], "p1_2_xs": ["7.6049999999999995", "7.614999999999999", "7.624999999999999"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{6}{11}", "p2_b": "\\dfrac{5}{7}", "p2_numbers": "\\dfrac{42{,}513}{77{,}000}, \\dfrac{43{,}001}{77{,}000}, \\dfrac{43{,}151}{77{,}000}, \\dfrac{43{,}514}{77{,}000}, \\dfrac{43{,}639}{77{,}000}, \\dfrac{46{,}601}{77{,}000}, \\dfrac{48{,}056}{77{,}000}, \\dfrac{48{,}311}{77{,}000}, \\dfrac{50{,}374}{77{,}000}, \\dfrac{52{,}650}{77{,}000}, \\dfrac{53{,}303}{77{,}000}, \\text{ and } \\dfrac{54{,}048}{77{,}000}", "__seed__": "0973"}}, {"seed": 974, "data": {"p1_how_many": "14", "p1_a": "1.4", "p1_b": "1.5", "p1_numbers": "1.405, 1.41, 1.415, 1.42, 1.425, 1.43, 1.435, 1.44, 1.445, 1.45, 1.46, 1.47, 1.48, and 1.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.41", "1.42", "1.43", "1.44", "1.45", "1.46", "1.47", "1.48", "1.49"], "p1_2_xs": ["1.4049999999999998", "1.4149999999999998", "1.4249999999999998", "1.4349999999999998", "1.4449999999999998"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{55}{200}, \\dfrac{58}{200}, \\dfrac{63}{200}, \\dfrac{65}{200}, \\dfrac{69}{200}, \\dfrac{72}{200}, \\text{ and } \\dfrac{75}{200}", "__seed__": "0974"}}, {"seed": 975, "data": {"p1_how_many": "14", "p1_a": "6.95", "p1_b": "6.96", "p1_numbers": "6.9505, 6.951, 6.9515, 6.952, 6.9525, 6.953, 6.9535, 6.954, 6.9545, 6.955, 6.956, 6.957, 6.958, and 6.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.9510000000000005", "6.952", "6.953", "6.954", "6.955", "6.956", "6.957", "6.958", "6.9590000000000005"], "p1_2_xs": ["6.9505", "6.9515", "6.9525", "6.9535", "6.9544999999999995"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{213}{560}, \\dfrac{219}{560}, \\dfrac{224}{560}, \\dfrac{227}{560}, \\dfrac{229}{560}, \\dfrac{234}{560}, \\text{ and } \\dfrac{239}{560}", "__seed__": "0975"}}, {"seed": 976, "data": {"p1_how_many": "11", "p1_a": "6.35", "p1_b": "6.36", "p1_numbers": "6.3505, 6.351, 6.3515, 6.352, 6.353, 6.354, 6.355, 6.356, 6.357, 6.358, and 6.359", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.351", "6.351999999999999", "6.353", "6.353999999999999", "6.3549999999999995", "6.356", "6.356999999999999", "6.358", "6.359"], "p1_2_xs": ["6.350499999999999", "6.3515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{1{,}058}{3{,}500}, \\dfrac{1{,}059}{3{,}500}, \\dfrac{1{,}204}{3{,}500}, \\dfrac{1{,}238}{3{,}500}, \\dfrac{1{,}239}{3{,}500}, \\dfrac{1{,}240}{3{,}500}, \\dfrac{1{,}267}{3{,}500}, \\dfrac{1{,}338}{3{,}500}, \\text{ and } \\dfrac{1{,}345}{3{,}500}", "__seed__": "0976"}}, {"seed": 977, "data": {"p1_how_many": "10", "p1_a": "6.15", "p1_b": "6.16", "p1_numbers": "6.1505, 6.151, 6.152, 6.153, 6.154, 6.155, 6.156, 6.157, 6.158, and 6.159", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["6.151000000000001", "6.152", "6.1530000000000005", "6.154", "6.155", "6.156000000000001", "6.157", "6.158", "6.159000000000001"], "p1_2_xs": ["6.1505"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}118}{20{,}000}, \\dfrac{5{,}259}{20{,}000}, \\dfrac{5{,}429}{20{,}000}, \\dfrac{5{,}759}{20{,}000}, \\dfrac{5{,}930}{20{,}000}, \\dfrac{5{,}937}{20{,}000}, \\dfrac{7{,}038}{20{,}000}, \\dfrac{7{,}462}{20{,}000}, \\dfrac{7{,}805}{20{,}000}, \\dfrac{7{,}916}{20{,}000}, \\text{ and } \\dfrac{7{,}928}{20{,}000}", "__seed__": "0977"}}, {"seed": 978, "data": {"p1_how_many": "14", "p1_a": "5.6", "p1_b": "5.7", "p1_numbers": "5.605, 5.61, 5.615, 5.62, 5.625, 5.63, 5.635, 5.64, 5.645, 5.65, 5.66, 5.67, 5.68, and 5.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["5.609999999999999", "5.619999999999999", "5.63", "5.64", "5.6499999999999995", "5.659999999999999", "5.67", "5.68", "5.6899999999999995"], "p1_2_xs": ["5.6049999999999995", "5.614999999999999", "5.624999999999999", "5.635", "5.645"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{1}{6}", "p2_b": "\\dfrac{1}{5}", "p2_numbers": "\\dfrac{5{,}100}{30{,}000}, \\dfrac{5{,}200}{30{,}000}, \\dfrac{5{,}210}{30{,}000}, \\dfrac{5{,}250}{30{,}000}, \\dfrac{5{,}445}{30{,}000}, \\dfrac{5{,}463}{30{,}000}, \\dfrac{5{,}680}{30{,}000}, \\dfrac{5{,}685}{30{,}000}, \\dfrac{5{,}835}{30{,}000}, \\dfrac{5{,}849}{30{,}000}, \\dfrac{5{,}901}{30{,}000}, \\text{ and } \\dfrac{5{,}991}{30{,}000}", "__seed__": "0978"}}, {"seed": 979, "data": {"p1_how_many": "14", "p1_a": "4.54", "p1_b": "4.55", "p1_numbers": "4.5405, 4.541, 4.5415, 4.542, 4.5425, 4.543, 4.5435, 4.544, 4.5445, 4.545, 4.546, 4.547, 4.548, and 4.549", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["4.541", "4.542", "4.543", "4.544", "4.545", "4.546", "4.547", "4.548", "4.549"], "p1_2_xs": ["4.5405", "4.5415", "4.5424999999999995", "4.5435", "4.544499999999999"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{51}{150}, \\dfrac{52}{150}, \\dfrac{53}{150}, \\dfrac{54}{150}, \\dfrac{55}{150}, \\dfrac{56}{150}, \\dfrac{57}{150}, \\dfrac{58}{150}, \\text{ and } \\dfrac{59}{150}", "__seed__": "0979"}}, {"seed": 980, "data": {"p1_how_many": "10", "p1_a": "4.0", "p1_b": "4.1", "p1_numbers": "4.005, 4.01, 4.02, 4.03, 4.04, 4.05, 4.06, 4.07, 4.08, and 4.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.01", "4.02", "4.03", "4.04", "4.05", "4.06", "4.07", "4.08", "4.09"], "p1_2_xs": ["4.005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{4}{5}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{2{,}405}{3{,}000}, \\dfrac{2{,}409}{3{,}000}, \\dfrac{2{,}436}{3{,}000}, \\dfrac{2{,}438}{3{,}000}, \\dfrac{2{,}451}{3{,}000}, \\dfrac{2{,}461}{3{,}000}, \\text{ and } \\dfrac{2{,}488}{3{,}000}", "__seed__": "0980"}}, {"seed": 981, "data": {"p1_how_many": "11", "p1_a": "7.3", "p1_b": "7.4", "p1_numbers": "7.305, 7.31, 7.315, 7.32, 7.33, 7.34, 7.35, 7.36, 7.37, 7.38, and 7.39", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.31", "7.319999999999999", "7.33", "7.34", "7.35", "7.359999999999999", "7.37", "7.38", "7.39"], "p1_2_xs": ["7.305", "7.3149999999999995"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{121}{200}, \\dfrac{123}{200}, \\dfrac{124}{200}, \\dfrac{125}{200}, \\dfrac{130}{200}, \\dfrac{136}{200}, \\dfrac{138}{200}, \\dfrac{143}{200}, \\text{ and } \\dfrac{149}{200}", "__seed__": "0981"}}, {"seed": 982, "data": {"p1_how_many": "14", "p1_a": "4.0", "p1_b": "4.1", "p1_numbers": "4.005, 4.01, 4.015, 4.02, 4.025, 4.03, 4.035, 4.04, 4.045, 4.05, 4.06, 4.07, 4.08, and 4.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["4.01", "4.02", "4.03", "4.04", "4.05", "4.06", "4.07", "4.08", "4.09"], "p1_2_xs": ["4.005", "4.015", "4.0249999999999995", "4.035", "4.045"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{507}{1{,}500}, \\dfrac{515}{1{,}500}, \\dfrac{526}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{531}{1{,}500}, \\dfrac{556}{1{,}500}, \\dfrac{564}{1{,}500}, \\dfrac{572}{1{,}500}, \\dfrac{577}{1{,}500}, \\text{ and } \\dfrac{579}{1{,}500}", "__seed__": "0982"}}, {"seed": 983, "data": {"p1_how_many": "11", "p1_a": "1.0", "p1_b": "1.1", "p1_numbers": "1.005, 1.01, 1.015, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, and 1.09", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.01", "1.02", "1.03", "1.04", "1.05", "1.06", "1.07", "1.08", "1.09"], "p1_2_xs": ["1.005", "1.015"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{5}", "p2_b": "\\dfrac{3}{4}", "p2_numbers": "\\dfrac{12{,}266}{20{,}000}, \\dfrac{12{,}576}{20{,}000}, \\dfrac{12{,}670}{20{,}000}, \\dfrac{12{,}685}{20{,}000}, \\dfrac{13{,}466}{20{,}000}, \\dfrac{13{,}670}{20{,}000}, \\dfrac{13{,}713}{20{,}000}, \\dfrac{13{,}755}{20{,}000}, \\dfrac{13{,}793}{20{,}000}, \\dfrac{14{,}147}{20{,}000}, \\dfrac{14{,}528}{20{,}000}, \\text{ and } \\dfrac{14{,}774}{20{,}000}", "__seed__": "0983"}}, {"seed": 984, "data": {"p1_how_many": "10", "p1_a": "9.2", "p1_b": "9.3", "p1_numbers": "9.2005, 9.201, 9.202, 9.203, 9.204, 9.205, 9.206, 9.207, 9.208, and 9.209", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.200999999999999", "9.202", "9.203", "9.203999999999999", "9.205", "9.206", "9.206999999999999", "9.207999999999998", "9.209"], "p1_2_xs": ["9.2005"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{271}{630}, \\dfrac{272}{630}, \\dfrac{273}{630}, \\dfrac{274}{630}, \\dfrac{275}{630}, \\dfrac{276}{630}, \\dfrac{277}{630}, \\dfrac{278}{630}, \\text{ and } \\dfrac{279}{630}", "__seed__": "0984"}}, {"seed": 985, "data": {"p1_how_many": "14", "p1_a": "9.4", "p1_b": "9.5", "p1_numbers": "9.405, 9.41, 9.415, 9.42, 9.425, 9.43, 9.435, 9.44, 9.445, 9.45, 9.46, 9.47, 9.48, and 9.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["9.41", "9.42", "9.43", "9.44", "9.450000000000001", "9.46", "9.47", "9.48", "9.49"], "p1_2_xs": ["9.405000000000001", "9.415000000000001", "9.425", "9.435", "9.445"], "num_line_directions": "Graph the given numbers and the additional 14 numbers accurately on the number line", "p2_how_many": "8", "p2_a": "\\dfrac{5}{7}", "p2_b": "\\dfrac{5}{6}", "p2_numbers": "\\dfrac{3{,}052}{4{,}200}, \\dfrac{3{,}063}{4{,}200}, \\dfrac{3{,}081}{4{,}200}, \\dfrac{3{,}158}{4{,}200}, \\dfrac{3{,}195}{4{,}200}, \\dfrac{3{,}238}{4{,}200}, \\dfrac{3{,}239}{4{,}200}, \\text{ and } \\dfrac{3{,}267}{4{,}200}", "__seed__": "0985"}}, {"seed": 986, "data": {"p1_how_many": "12", "p1_a": "7.12", "p1_b": "7.13", "p1_numbers": "7.1205, 7.121, 7.1215, 7.122, 7.1225, 7.123, 7.124, 7.125, 7.126, 7.127, 7.128, and 7.129", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.121", "7.122", "7.123", "7.124", "7.125", "7.126", "7.127", "7.128", "7.1290000000000004"], "p1_2_xs": ["7.1205", "7.1215", "7.1225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}450}{20{,}000}, \\dfrac{5{,}548}{20{,}000}, \\dfrac{5{,}991}{20{,}000}, \\dfrac{6{,}176}{20{,}000}, \\dfrac{6{,}335}{20{,}000}, \\dfrac{6{,}454}{20{,}000}, \\dfrac{6{,}996}{20{,}000}, \\dfrac{7{,}324}{20{,}000}, \\dfrac{7{,}716}{20{,}000}, \\text{ and } \\dfrac{7{,}848}{20{,}000}", "__seed__": "0986"}}, {"seed": 987, "data": {"p1_how_many": "13", "p1_a": "1.6", "p1_b": "1.7", "p1_numbers": "1.605, 1.61, 1.615, 1.62, 1.625, 1.63, 1.635, 1.64, 1.65, 1.66, 1.67, 1.68, and 1.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["1.61", "1.62", "1.6300000000000001", "1.6400000000000001", "1.6500000000000001", "1.6600000000000001", "1.6700000000000002", "1.6800000000000002", "1.6900000000000002"], "p1_2_xs": ["1.605", "1.615", "1.625", "1.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{2}{3}", "p2_numbers": "\\dfrac{6{,}318}{15{,}000}, \\dfrac{6{,}918}{15{,}000}, \\dfrac{7{,}708}{15{,}000}, \\dfrac{7{,}886}{15{,}000}, \\dfrac{8{,}229}{15{,}000}, \\dfrac{8{,}604}{15{,}000}, \\text{ and } \\dfrac{8{,}775}{15{,}000}", "__seed__": "0987"}}, {"seed": 988, "data": {"p1_how_many": "12", "p1_a": "2.53", "p1_b": "2.54", "p1_numbers": "2.5305, 2.531, 2.5315, 2.532, 2.5325, 2.533, 2.534, 2.535, 2.536, 2.537, 2.538, and 2.539", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["2.5309999999999997", "2.5319999999999996", "2.533", "2.534", "2.5349999999999997", "2.5359999999999996", "2.537", "2.538", "2.5389999999999997"], "p1_2_xs": ["2.5305", "2.5315", "2.5324999999999998"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "9", "p2_a": "\\dfrac{4}{7}", "p2_b": "\\dfrac{5}{8}", "p2_numbers": "\\dfrac{33{,}130}{56{,}000}, \\dfrac{33{,}254}{56{,}000}, \\dfrac{33{,}798}{56{,}000}, \\dfrac{34{,}065}{56{,}000}, \\dfrac{34{,}094}{56{,}000}, \\dfrac{34{,}145}{56{,}000}, \\dfrac{34{,}180}{56{,}000}, \\dfrac{34{,}301}{56{,}000}, \\text{ and } \\dfrac{34{,}540}{56{,}000}", "__seed__": "0988"}}, {"seed": 989, "data": {"p1_how_many": "10", "p1_a": "9.86", "p1_b": "9.87", "p1_numbers": "9.8605, 9.861, 9.862, 9.863, 9.864, 9.865, 9.866, 9.867, 9.868, and 9.869", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["9.860999999999999", "9.862", "9.863", "9.863999999999999", "9.865", "9.866", "9.866999999999999", "9.867999999999999", "9.869"], "p1_2_xs": ["9.8605"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{7}", "p2_b": "\\dfrac{4}{9}", "p2_numbers": "\\dfrac{2{,}715}{6{,}300}, \\dfrac{2{,}716}{6{,}300}, \\dfrac{2{,}720}{6{,}300}, \\dfrac{2{,}740}{6{,}300}, \\dfrac{2{,}746}{6{,}300}, \\dfrac{2{,}760}{6{,}300}, \\dfrac{2{,}764}{6{,}300}, \\dfrac{2{,}773}{6{,}300}, \\dfrac{2{,}775}{6{,}300}, \\text{ and } \\dfrac{2{,}796}{6{,}300}", "__seed__": "0989"}}, {"seed": 990, "data": {"p1_how_many": "10", "p1_a": "3.22", "p1_b": "3.23", "p1_numbers": "3.2205, 3.221, 3.222, 3.223, 3.224, 3.225, 3.226, 3.227, 3.228, and 3.229", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["3.221", "3.222", 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"5.022499999999999", "5.023499999999999"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{4{,}015}{20{,}000}, \\dfrac{4{,}158}{20{,}000}, \\dfrac{4{,}383}{20{,}000}, \\dfrac{4{,}405}{20{,}000}, \\dfrac{4{,}473}{20{,}000}, \\dfrac{4{,}630}{20{,}000}, \\text{ and } \\dfrac{4{,}792}{20{,}000}", "__seed__": "0991"}}, {"seed": 992, "data": {"p1_how_many": "11", "p1_a": "7.95", "p1_b": "7.96", "p1_numbers": "7.9505, 7.951, 7.9515, 7.952, 7.953, 7.954, 7.955, 7.956, 7.957, 7.958, and 7.959", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["7.9510000000000005", "7.952", "7.953", "7.954", "7.955", "7.956", "7.957", "7.958", "7.9590000000000005"], "p1_2_xs": ["7.9505", "7.9515"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}025}{35{,}000}, \\dfrac{14{,}047}{35{,}000}, \\dfrac{14{,}279}{35{,}000}, \\dfrac{14{,}710}{35{,}000}, \\dfrac{14{,}829}{35{,}000}, \\dfrac{14{,}892}{35{,}000}, \\dfrac{14{,}898}{35{,}000}, \\dfrac{14{,}958}{35{,}000}, \\dfrac{14{,}973}{35{,}000}, \\text{ and } \\dfrac{14{,}995}{35{,}000}", "__seed__": "0992"}}, {"seed": 993, "data": {"p1_how_many": "12", "p1_a": "7.4", "p1_b": "7.5", "p1_numbers": "7.405, 7.41, 7.415, 7.42, 7.425, 7.43, 7.44, 7.45, 7.46, 7.47, 7.48, and 7.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["7.41", "7.42", "7.430000000000001", "7.44", "7.45", "7.46", "7.470000000000001", "7.48", "7.49"], "p1_2_xs": ["7.405", "7.415", "7.425"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{5}", "p2_b": "\\dfrac{1}{4}", "p2_numbers": "\\dfrac{41}{200}, \\dfrac{42}{200}, \\dfrac{43}{200}, \\dfrac{44}{200}, \\dfrac{46}{200}, \\dfrac{47}{200}, \\text{ and } \\dfrac{48}{200}", "__seed__": "0993"}}, {"seed": 994, "data": {"p1_how_many": "12", "p1_a": "3.2", "p1_b": "3.3", "p1_numbers": "3.205, 3.21, 3.215, 3.22, 3.225, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, and 3.29", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.21", "3.22", "3.23", "3.24", "3.25", "3.2600000000000002", "3.27", "3.2800000000000002", "3.29"], "p1_2_xs": ["3.205", "3.215", "3.225"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{2}{7}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{102}{350}, \\dfrac{110}{350}, \\dfrac{111}{350}, \\dfrac{112}{350}, \\dfrac{117}{350}, \\dfrac{119}{350}, \\text{ and } \\dfrac{136}{350}", "__seed__": "0994"}}, {"seed": 995, "data": {"p1_how_many": "10", "p1_a": "8.4", "p1_b": "8.5", "p1_numbers": "8.405, 8.41, 8.42, 8.43, 8.44, 8.45, 8.46, 8.47, 8.48, and 8.49", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["8.41", "8.42", "8.43", "8.44", "8.450000000000001", "8.46", "8.47", "8.48", "8.49"], "p1_2_xs": ["8.405000000000001"], "num_line_directions": "Graph the given numbers and the additional 10 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{2}{5}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{14{,}088}{35{,}000}, \\dfrac{14{,}367}{35{,}000}, \\dfrac{14{,}430}{35{,}000}, \\dfrac{14{,}492}{35{,}000}, \\dfrac{14{,}516}{35{,}000}, \\dfrac{14{,}565}{35{,}000}, \\dfrac{14{,}665}{35{,}000}, \\dfrac{14{,}680}{35{,}000}, \\dfrac{14{,}734}{35{,}000}, \\dfrac{14{,}740}{35{,}000}, \\dfrac{14{,}880}{35{,}000}, \\text{ and } \\dfrac{14{,}949}{35{,}000}", "__seed__": "0995"}}, {"seed": 996, "data": {"p1_how_many": "13", "p1_a": "3.6", "p1_b": "3.7", "p1_numbers": "3.605, 3.61, 3.615, 3.62, 3.625, 3.63, 3.635, 3.64, 3.65, 3.66, 3.67, 3.68, and 3.69", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["3.61", "3.62", "3.63", "3.64", "3.65", "3.66", "3.67", "3.68", "3.69"], "p1_2_xs": ["3.605", "3.6149999999999998", "3.625", "3.635"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "7", "p2_a": "\\dfrac{1}{4}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{5{,}399}{20{,}000}, \\dfrac{5{,}438}{20{,}000}, \\dfrac{5{,}506}{20{,}000}, \\dfrac{6{,}485}{20{,}000}, \\dfrac{6{,}746}{20{,}000}, \\dfrac{7{,}068}{20{,}000}, \\text{ and } \\dfrac{7{,}243}{20{,}000}", "__seed__": "0996"}}, {"seed": 997, "data": {"p1_how_many": "11", "p1_a": "5.24", "p1_b": "5.25", "p1_numbers": "5.2405, 5.241, 5.2415, 5.242, 5.243, 5.244, 5.245, 5.246, 5.247, 5.248, and 5.249", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["5.2410000000000005", "5.242", "5.243", "5.244", "5.245", "5.246", "5.247", "5.248", "5.2490000000000006"], "p1_2_xs": ["5.2405", "5.2415"], "num_line_directions": "Graph the given numbers and the additional 11 numbers accurately on the number line", "p2_how_many": "11", "p2_a": "\\dfrac{1}{3}", "p2_b": "\\dfrac{2}{5}", "p2_numbers": "\\dfrac{503}{1{,}500}, \\dfrac{519}{1{,}500}, \\dfrac{529}{1{,}500}, \\dfrac{530}{1{,}500}, \\dfrac{546}{1{,}500}, \\dfrac{547}{1{,}500}, \\dfrac{550}{1{,}500}, \\dfrac{587}{1{,}500}, \\dfrac{591}{1{,}500}, \\dfrac{592}{1{,}500}, \\text{ and } \\dfrac{595}{1{,}500}", "__seed__": "0997"}}, {"seed": 998, "data": {"p1_how_many": "13", "p1_a": "8.64", "p1_b": "8.65", "p1_numbers": "8.6405, 8.641, 8.6415, 8.642, 8.6425, 8.643, 8.6435, 8.644, 8.645, 8.646, 8.647, 8.648, and 8.649", "p1_decimal_vals": "2", "p1_increment": "\\frac{1}{1000}", "p1_1_xs": ["8.641", "8.642000000000001", "8.643", "8.644", "8.645000000000001", "8.646", "8.647", "8.648", "8.649000000000001"], "p1_2_xs": ["8.640500000000001", "8.6415", "8.642500000000002", "8.643500000000001"], "num_line_directions": "Graph the given numbers and the additional 13 numbers accurately on the number line", "p2_how_many": "12", "p2_a": "\\dfrac{3}{4}", "p2_b": "\\dfrac{4}{5}", "p2_numbers": "\\dfrac{1{,}507}{2{,}000}, \\dfrac{1{,}508}{2{,}000}, \\dfrac{1{,}510}{2{,}000}, \\dfrac{1{,}515}{2{,}000}, \\dfrac{1{,}518}{2{,}000}, \\dfrac{1{,}530}{2{,}000}, \\dfrac{1{,}539}{2{,}000}, \\dfrac{1{,}547}{2{,}000}, \\dfrac{1{,}555}{2{,}000}, \\dfrac{1{,}564}{2{,}000}, \\dfrac{1{,}567}{2{,}000}, \\text{ and } \\dfrac{1{,}584}{2{,}000}", "__seed__": "0998"}}, {"seed": 999, "data": {"p1_how_many": "12", "p1_a": "2.7", "p1_b": "2.8", "p1_numbers": "2.705, 2.71, 2.715, 2.72, 2.725, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, and 2.79", "p1_decimal_vals": "1", "p1_increment": "\\frac{1}{100}", "p1_1_xs": ["2.71", "2.72", "2.73", "2.74", "2.75", "2.7600000000000002", "2.77", "2.7800000000000002", "2.79"], "p1_2_xs": ["2.705", "2.715", "2.725"], "num_line_directions": "Graph the given numbers and the additional 12 numbers accurately on the number line", "p2_how_many": "10", "p2_a": "\\dfrac{3}{8}", "p2_b": "\\dfrac{3}{7}", "p2_numbers": "\\dfrac{21{,}796}{56{,}000}, \\dfrac{22{,}029}{56{,}000}, \\dfrac{22{,}775}{56{,}000}, \\dfrac{22{,}810}{56{,}000}, \\dfrac{22{,}873}{56{,}000}, \\dfrac{23{,}084}{56{,}000}, \\dfrac{23{,}239}{56{,}000}, \\dfrac{23{,}295}{56{,}000}, \\dfrac{23{,}796}{56{,}000}, \\text{ and } \\dfrac{23{,}969}{56{,}000}", "__seed__": "0999"}}]}, {"title": "Decimal Place Values", "slug": "D1", "description": "\n I can identify place values in decimal numbers using both numerical notation and English words, and represent decimal numbers using base-ten blocks.\n ", "template": "\n\n \n \n

Consider the number {{pv_dec_string}}. Identify and name each of the place values used in this number. Write these names using both a numerical label (e.g. ``10s'') and an English-word label (e.g. ``tens'').

\n
\n \n

{{pv_ans_text}}

\n
\n
\n \n \n

Using {{units_block_choice}} to represent the units, draw a base-ten block representation of the number {{blocks_dec}}.

\n
\n \n

{{blocks_ans_text}}

\n
\n
\n
\n", "exercises": [{"seed": 0, "data": {"pv_dec_string": "992,477.06389", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.153", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0000"}}, {"seed": 1, "data": {"pv_dec_string": "407.326049", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0001"}}, {"seed": 2, "data": {"pv_dec_string": "655,514.5852", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 6 small cubes", "__seed__": "0002"}}, {"seed": 3, "data": {"pv_dec_string": "4,587,850.6053", "pv_ans_text": "4 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0003"}}, {"seed": 4, "data": {"pv_dec_string": "97,816.15361", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.21", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 1 longs, and 0 small cubes", "__seed__": "0004"}}, {"seed": 5, "data": {"pv_dec_string": "6,992,669.2169", "pv_ans_text": "6 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 3 small cubes", "__seed__": "0005"}}, {"seed": 6, "data": {"pv_dec_string": "340,774.7684", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0006"}}, {"seed": 7, "data": {"pv_dec_string": "694.001913", "pv_ans_text": "6 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.224", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0007"}}, {"seed": 8, "data": {"pv_dec_string": "16,796.13469", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 5 small cubes", "__seed__": "0008"}}, {"seed": 9, "data": {"pv_dec_string": "674.260836", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 2 small cubes", "__seed__": "0009"}}, {"seed": 10, "data": {"pv_dec_string": "13,886.67734", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.12", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0010"}}, {"seed": 11, "data": {"pv_dec_string": "200,967.34713", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 3 small cubes", "__seed__": "0011"}}, {"seed": 12, "data": {"pv_dec_string": "4,836.450036", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.633", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 3 small cubes", "__seed__": "0012"}}, {"seed": 13, "data": {"pv_dec_string": "8,292.218899", "pv_ans_text": "8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.240", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0013"}}, {"seed": 14, "data": {"pv_dec_string": "9,992.054838", "pv_ans_text": "9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.63", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0014"}}, {"seed": 15, "data": {"pv_dec_string": "429,974.7998", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.451", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0015"}}, {"seed": 16, "data": {"pv_dec_string": "2,964,739.9292", "pv_ans_text": "2 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.015", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 1 longs, and 5 small cubes", "__seed__": "0016"}}, {"seed": 17, "data": {"pv_dec_string": "321.376057", "pv_ans_text": "3 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.14", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0017"}}, {"seed": 18, "data": {"pv_dec_string": "533,698.3724", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0018"}}, {"seed": 19, "data": {"pv_dec_string": "403.393733", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.15", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0019"}}, {"seed": 20, "data": {"pv_dec_string": "7,102.50037", "pv_ans_text": "7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.146", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 4 longs, and 6 small cubes", "__seed__": "0020"}}, {"seed": 21, "data": {"pv_dec_string": "757,776.806", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.134", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0021"}}, {"seed": 22, "data": {"pv_dec_string": "1,875.973392", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 2 small cubes", "__seed__": "0022"}}, {"seed": 23, "data": {"pv_dec_string": "62,079.615021", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.16", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0023"}}, {"seed": 24, "data": {"pv_dec_string": "648,443.4976", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.430", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0024"}}, {"seed": 25, "data": {"pv_dec_string": "518,926.7324", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.564", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 6 longs, and 4 small cubes", "__seed__": "0025"}}, {"seed": 26, "data": {"pv_dec_string": "932,406.3667", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0026"}}, {"seed": 27, "data": {"pv_dec_string": "7,523,929.0946", "pv_ans_text": "7 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.451", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0027"}}, {"seed": 28, "data": {"pv_dec_string": "393.686779", "pv_ans_text": "3 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.234", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0028"}}, {"seed": 29, "data": {"pv_dec_string": "865,762.2975", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.262", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 6 longs, and 2 small cubes", "__seed__": "0029"}}, {"seed": 30, "data": {"pv_dec_string": "26,417.687065", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0030"}}, {"seed": 31, "data": {"pv_dec_string": "22,341.288174", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.26", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0031"}}, {"seed": 32, "data": {"pv_dec_string": "19,278.04694", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.31", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0032"}}, {"seed": 33, "data": {"pv_dec_string": "473.688155", "pv_ans_text": "4 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0033"}}, {"seed": 34, "data": {"pv_dec_string": "87,402.01659", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.113", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0034"}}, {"seed": 35, "data": {"pv_dec_string": "1,647.31928", "pv_ans_text": "1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0035"}}, {"seed": 36, "data": {"pv_dec_string": "30,516.27952", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 2 small cubes", "__seed__": "0036"}}, {"seed": 37, "data": {"pv_dec_string": "4,832.889082", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0037"}}, {"seed": 38, "data": {"pv_dec_string": "1,772.8065", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 3 small cubes", "__seed__": "0038"}}, {"seed": 39, "data": {"pv_dec_string": "53,264.993479", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.126", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 2 longs, and 6 small cubes", "__seed__": "0039"}}, {"seed": 40, "data": {"pv_dec_string": "4,365,297.7812", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.241", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0040"}}, {"seed": 41, "data": {"pv_dec_string": "1,627,100.3801", "pv_ans_text": "1 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.265", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 6 longs, and 5 small cubes", "__seed__": "0041"}}, {"seed": 42, "data": {"pv_dec_string": "46,964.342", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 1 small cubes", "__seed__": "0042"}}, {"seed": 43, "data": {"pv_dec_string": "90,651.17785", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 4 small cubes", "__seed__": "0043"}}, {"seed": 44, "data": {"pv_dec_string": "4,338.44775", "pv_ans_text": "4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0044"}}, {"seed": 45, "data": {"pv_dec_string": "29,941.92678", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 2 small cubes", "__seed__": "0045"}}, {"seed": 46, "data": {"pv_dec_string": "584.98676", "pv_ans_text": "5 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0046"}}, {"seed": 47, "data": {"pv_dec_string": "72,433.651132", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0047"}}, {"seed": 48, "data": {"pv_dec_string": "31,395.34096", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 3 small cubes", "__seed__": "0048"}}, {"seed": 49, "data": {"pv_dec_string": "28,014.611323", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0049"}}, {"seed": 50, "data": {"pv_dec_string": "561,464.9278", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0050"}}, {"seed": 51, "data": {"pv_dec_string": "607,373.5177", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0051"}}, {"seed": 52, "data": {"pv_dec_string": "677.960078", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.013", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 1 longs, and 3 small cubes", "__seed__": "0052"}}, {"seed": 53, "data": {"pv_dec_string": "2,306.097075", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.362", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 6 longs, and 2 small cubes", "__seed__": "0053"}}, {"seed": 54, "data": {"pv_dec_string": "4,583,257.7742", "pv_ans_text": "4 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0054"}}, {"seed": 55, "data": {"pv_dec_string": "8,493,583.9491", "pv_ans_text": "8 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 6 small cubes", "__seed__": "0055"}}, {"seed": 56, "data": {"pv_dec_string": "2,824.80616", "pv_ans_text": "2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.31", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0056"}}, {"seed": 57, "data": {"pv_dec_string": "1,996.503918", "pv_ans_text": "1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.56", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0057"}}, {"seed": 58, "data": {"pv_dec_string": "29,343.38975", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.603", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 0 longs, and 3 small cubes", "__seed__": "0058"}}, {"seed": 59, "data": {"pv_dec_string": "500.83225", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.44", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0059"}}, {"seed": 60, "data": {"pv_dec_string": "53,268.40304", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.35", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0060"}}, {"seed": 61, "data": {"pv_dec_string": "39,264.05101", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.311", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0061"}}, {"seed": 62, "data": {"pv_dec_string": "39,576.04037", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0062"}}, {"seed": 63, "data": {"pv_dec_string": "42,364.61019", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.04", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0063"}}, {"seed": 64, "data": {"pv_dec_string": "88,652.682255", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.20", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0064"}}, {"seed": 65, "data": {"pv_dec_string": "4,318,513.329", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.22", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0065"}}, {"seed": 66, "data": {"pv_dec_string": "7,608.50823", "pv_ans_text": "7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0066"}}, {"seed": 67, "data": {"pv_dec_string": "402,497.43346", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 4 small cubes", "__seed__": "0067"}}, {"seed": 68, "data": {"pv_dec_string": "81,717.0742", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.62", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0068"}}, {"seed": 69, "data": {"pv_dec_string": "11,777.7422", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.344", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 4 longs, and 4 small cubes", "__seed__": "0069"}}, {"seed": 70, "data": {"pv_dec_string": "198.476117", "pv_ans_text": "1 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0070"}}, {"seed": 71, "data": {"pv_dec_string": "5,762.167245", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.05", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0071"}}, {"seed": 72, "data": {"pv_dec_string": "9,985.07097", "pv_ans_text": "9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.24", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0072"}}, {"seed": 73, "data": {"pv_dec_string": "838.930614", "pv_ans_text": "8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 1 small cubes", "__seed__": "0073"}}, {"seed": 74, "data": {"pv_dec_string": "12,380.0968", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 1 small cubes", "__seed__": "0074"}}, {"seed": 75, "data": {"pv_dec_string": "317,095.06179", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.306", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 0 longs, and 6 small cubes", "__seed__": "0075"}}, {"seed": 76, "data": {"pv_dec_string": "963,711.43543", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.32", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0076"}}, {"seed": 77, "data": {"pv_dec_string": "538,227.05194", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.453", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 3 small cubes", "__seed__": "0077"}}, {"seed": 78, "data": {"pv_dec_string": "895,304.3003", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0078"}}, {"seed": 79, "data": {"pv_dec_string": "238,893.14091", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 2 small cubes", "__seed__": "0079"}}, {"seed": 80, "data": {"pv_dec_string": "598.858435", "pv_ans_text": "5 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.11", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0080"}}, {"seed": 81, "data": {"pv_dec_string": "691,126.56081", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0081"}}, {"seed": 82, "data": {"pv_dec_string": "1,349.94995", "pv_ans_text": "1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.63", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0082"}}, {"seed": 83, "data": {"pv_dec_string": "16,436.00905", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0083"}}, {"seed": 84, "data": {"pv_dec_string": "9,922,335.7236", "pv_ans_text": "9 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.515", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 1 longs, and 5 small cubes", "__seed__": "0084"}}, {"seed": 85, "data": {"pv_dec_string": "40,408.248368", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.66", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0085"}}, {"seed": 86, "data": {"pv_dec_string": "7,394,699.9594", "pv_ans_text": "7 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 3 small cubes", "__seed__": "0086"}}, {"seed": 87, "data": {"pv_dec_string": "38,101.34148", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.24", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0087"}}, {"seed": 88, "data": {"pv_dec_string": "730,383.1446", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.16", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0088"}}, {"seed": 89, "data": {"pv_dec_string": "3,684,109.2976", "pv_ans_text": "3 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.233", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 3 small cubes", "__seed__": "0089"}}, {"seed": 90, "data": {"pv_dec_string": "361.330321", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.604", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0090"}}, {"seed": 91, "data": {"pv_dec_string": "1,784.76868", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0091"}}, {"seed": 92, "data": {"pv_dec_string": "1,741.448746", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0092"}}, {"seed": 93, "data": {"pv_dec_string": "19,117.6684", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.161", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0093"}}, {"seed": 94, "data": {"pv_dec_string": "17,738.11201", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0094"}}, {"seed": 95, "data": {"pv_dec_string": "678,951.98415", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 4 small cubes", "__seed__": "0095"}}, {"seed": 96, "data": {"pv_dec_string": "545,144.93441", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 4 small cubes", "__seed__": "0096"}}, {"seed": 97, "data": {"pv_dec_string": "651.907127", "pv_ans_text": "6 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.61", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0097"}}, {"seed": 98, "data": {"pv_dec_string": "5,194.720551", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.463", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0098"}}, {"seed": 99, "data": {"pv_dec_string": "704,813.24581", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0099"}}, {"seed": 100, "data": {"pv_dec_string": "37,416.4489", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.06", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0100"}}, {"seed": 101, "data": {"pv_dec_string": "475,481.6849", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0101"}}, {"seed": 102, "data": {"pv_dec_string": "5,514,913.2553", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 3 small cubes", "__seed__": "0102"}}, {"seed": 103, "data": {"pv_dec_string": "354,128.4416", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.314", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 1 longs, and 4 small cubes", "__seed__": "0103"}}, {"seed": 104, "data": {"pv_dec_string": "9,369,564.9145", "pv_ans_text": "9 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.56", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0104"}}, {"seed": 105, "data": {"pv_dec_string": "146.611524", "pv_ans_text": "1 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.66", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0105"}}, {"seed": 106, "data": {"pv_dec_string": "8,168,300.1658", "pv_ans_text": "8 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.165", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 6 longs, and 5 small cubes", "__seed__": "0106"}}, {"seed": 107, "data": {"pv_dec_string": "825,480.7", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.604", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0107"}}, {"seed": 108, "data": {"pv_dec_string": "1,120,336.1523", "pv_ans_text": "1 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0108"}}, {"seed": 109, "data": {"pv_dec_string": "922,023.3657", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 4 small cubes", "__seed__": "0109"}}, {"seed": 110, "data": {"pv_dec_string": "6,553,961.9043", "pv_ans_text": "6 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0110"}}, {"seed": 111, "data": {"pv_dec_string": "63,430.1771", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 6 small cubes", "__seed__": "0111"}}, {"seed": 112, "data": {"pv_dec_string": "790.801038", "pv_ans_text": "7 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.566", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0112"}}, {"seed": 113, "data": {"pv_dec_string": "2,758,652.7832", "pv_ans_text": "2 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0113"}}, {"seed": 114, "data": {"pv_dec_string": "2,610.802021", "pv_ans_text": "2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.22", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0114"}}, {"seed": 115, "data": {"pv_dec_string": "2,173.03828", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.60", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0115"}}, {"seed": 116, "data": {"pv_dec_string": "1,143,995.8764", "pv_ans_text": "1 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.536", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0116"}}, {"seed": 117, "data": {"pv_dec_string": "86,295.873746", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0117"}}, {"seed": 118, "data": {"pv_dec_string": "1,074.74787", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 3 small cubes", "__seed__": "0118"}}, {"seed": 119, "data": {"pv_dec_string": "32,025.1136", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.364", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 4 small cubes", "__seed__": "0119"}}, {"seed": 120, "data": {"pv_dec_string": "60,558.5821", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.015", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 1 longs, and 5 small cubes", "__seed__": "0120"}}, {"seed": 121, "data": {"pv_dec_string": "9,055,350.9353", "pv_ans_text": "9 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0121"}}, {"seed": 122, "data": {"pv_dec_string": "17,264.53662", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 5 small cubes", "__seed__": "0122"}}, {"seed": 123, "data": {"pv_dec_string": "6,089.24182", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.66", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0123"}}, {"seed": 124, "data": {"pv_dec_string": "5,521.426033", "pv_ans_text": "5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.430", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0124"}}, {"seed": 125, "data": {"pv_dec_string": "1,506.46677", "pv_ans_text": "1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0125"}}, {"seed": 126, "data": {"pv_dec_string": "7,943.989748", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 1 small cubes", "__seed__": "0126"}}, {"seed": 127, "data": {"pv_dec_string": "348.861057", "pv_ans_text": "3 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.16", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0127"}}, {"seed": 128, "data": {"pv_dec_string": "508.721162", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0128"}}, {"seed": 129, "data": {"pv_dec_string": "81,520.795543", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.306", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 0 longs, and 6 small cubes", "__seed__": "0129"}}, {"seed": 130, "data": {"pv_dec_string": "2,424,866.5305", "pv_ans_text": "2 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.544", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0130"}}, {"seed": 131, "data": {"pv_dec_string": "3,738.07431", "pv_ans_text": "3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0131"}}, {"seed": 132, "data": {"pv_dec_string": "79,859.81686", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 5 small cubes", "__seed__": "0132"}}, {"seed": 133, "data": {"pv_dec_string": "135.78469", "pv_ans_text": "1 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.10", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0133"}}, {"seed": 134, "data": {"pv_dec_string": "921,114.91765", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0134"}}, {"seed": 135, "data": {"pv_dec_string": "217,096.71213", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0135"}}, {"seed": 136, "data": {"pv_dec_string": "742.233794", "pv_ans_text": "7 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.550", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0136"}}, {"seed": 137, "data": {"pv_dec_string": "377,543.2664", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 5 small cubes", "__seed__": "0137"}}, {"seed": 138, "data": {"pv_dec_string": "17,393.5119", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0138"}}, {"seed": 139, "data": {"pv_dec_string": "139,552.22393", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.62", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0139"}}, {"seed": 140, "data": {"pv_dec_string": "131,974.77339", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0140"}}, {"seed": 141, "data": {"pv_dec_string": "32,993.85506", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0141"}}, {"seed": 142, "data": {"pv_dec_string": "782,543.5039", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0142"}}, {"seed": 143, "data": {"pv_dec_string": "8,782.928117", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.00", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0143"}}, {"seed": 144, "data": {"pv_dec_string": "801.422686", "pv_ans_text": "8 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.544", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0144"}}, {"seed": 145, "data": {"pv_dec_string": "146,558.48407", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.542", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 4 longs, and 2 small cubes", "__seed__": "0145"}}, {"seed": 146, "data": {"pv_dec_string": "3,561.99045", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0146"}}, {"seed": 147, "data": {"pv_dec_string": "95,070.8742", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0147"}}, {"seed": 148, "data": {"pv_dec_string": "591.678943", "pv_ans_text": "5 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.10", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0148"}}, {"seed": 149, "data": {"pv_dec_string": "251.188032", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.616", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 6 small cubes", "__seed__": "0149"}}, {"seed": 150, "data": {"pv_dec_string": "755,019.1749", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0150"}}, {"seed": 151, "data": {"pv_dec_string": "2,307.36289", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 5 small cubes", "__seed__": "0151"}}, {"seed": 152, "data": {"pv_dec_string": "853,661.8932", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0152"}}, {"seed": 153, "data": {"pv_dec_string": "348.098958", "pv_ans_text": "3 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.34", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0153"}}, {"seed": 154, "data": {"pv_dec_string": "232,561.49625", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.03", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0154"}}, {"seed": 155, "data": {"pv_dec_string": "809,625.9976", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 1 small cubes", "__seed__": "0155"}}, {"seed": 156, "data": {"pv_dec_string": "1,886,731.1576", "pv_ans_text": "1 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 6 small cubes", "__seed__": "0156"}}, {"seed": 157, "data": {"pv_dec_string": "19,482.63463", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.415", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 5 small cubes", "__seed__": "0157"}}, {"seed": 158, "data": {"pv_dec_string": "797,252.81572", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.224", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0158"}}, {"seed": 159, "data": {"pv_dec_string": "208,795.207", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.34", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0159"}}, {"seed": 160, "data": {"pv_dec_string": "63,788.374884", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.63", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0160"}}, {"seed": 161, "data": {"pv_dec_string": "446,595.0882", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.534", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0161"}}, {"seed": 162, "data": {"pv_dec_string": "4,085,404.0564", "pv_ans_text": "4 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0162"}}, {"seed": 163, "data": {"pv_dec_string": "36,643.5208", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.034", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 3 longs, and 4 small cubes", "__seed__": "0163"}}, {"seed": 164, "data": {"pv_dec_string": "464,691.50463", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 3 small cubes", "__seed__": "0164"}}, {"seed": 165, "data": {"pv_dec_string": "46,309.4651", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.46", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0165"}}, {"seed": 166, "data": {"pv_dec_string": "3,292.65328", "pv_ans_text": "3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 4 small cubes", "__seed__": "0166"}}, {"seed": 167, "data": {"pv_dec_string": "6,444.2347", "pv_ans_text": "6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0167"}}, {"seed": 168, "data": {"pv_dec_string": "397,771.3654", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0168"}}, {"seed": 169, "data": {"pv_dec_string": "440,874.04981", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 4 small cubes", "__seed__": "0169"}}, {"seed": 170, "data": {"pv_dec_string": "702.275877", "pv_ans_text": "7 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 6 small cubes", "__seed__": "0170"}}, {"seed": 171, "data": {"pv_dec_string": "439,196.34765", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 1 small cubes", "__seed__": "0171"}}, {"seed": 172, "data": {"pv_dec_string": "172,827.98063", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.63", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0172"}}, {"seed": 173, "data": {"pv_dec_string": "59,430.690775", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.24", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0173"}}, {"seed": 174, "data": {"pv_dec_string": "9,206,151.9238", "pv_ans_text": "9 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 1 small cubes", "__seed__": "0174"}}, {"seed": 175, "data": {"pv_dec_string": "565,717.1749", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.53", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0175"}}, {"seed": 176, "data": {"pv_dec_string": "6,669.935279", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 1 small cubes", "__seed__": "0176"}}, {"seed": 177, "data": {"pv_dec_string": "653,422.3815", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0177"}}, {"seed": 178, "data": {"pv_dec_string": "63,720.404288", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 6 small cubes", "__seed__": "0178"}}, {"seed": 179, "data": {"pv_dec_string": "446,117.8821", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.025", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 2 longs, and 5 small cubes", "__seed__": "0179"}}, {"seed": 180, "data": {"pv_dec_string": "93,714.896177", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 6 small cubes", "__seed__": "0180"}}, {"seed": 181, "data": {"pv_dec_string": "4,034.214866", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0181"}}, {"seed": 182, "data": {"pv_dec_string": "939,595.2103", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 2 small cubes", "__seed__": "0182"}}, {"seed": 183, "data": {"pv_dec_string": "867.897767", "pv_ans_text": "8 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.30", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 0 longs, and 0 small cubes", "__seed__": "0183"}}, {"seed": 184, "data": {"pv_dec_string": "714,989.6004", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.16", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0184"}}, {"seed": 185, "data": {"pv_dec_string": "7,397.31053", "pv_ans_text": "7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0185"}}, {"seed": 186, "data": {"pv_dec_string": "855,049.70785", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.03", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0186"}}, {"seed": 187, "data": {"pv_dec_string": "27,074.4289", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 3 small cubes", "__seed__": "0187"}}, {"seed": 188, "data": {"pv_dec_string": "305,479.18946", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 1 small cubes", "__seed__": "0188"}}, {"seed": 189, "data": {"pv_dec_string": "61,086.6555", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.312", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0189"}}, {"seed": 190, "data": {"pv_dec_string": "18,785.46418", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 4 small cubes", "__seed__": "0190"}}, {"seed": 191, "data": {"pv_dec_string": "53,953.13492", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.300", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 0 longs, and 0 small cubes", "__seed__": "0191"}}, {"seed": 192, "data": {"pv_dec_string": "5,564.895669", "pv_ans_text": "5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.65", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0192"}}, {"seed": 193, "data": {"pv_dec_string": "20,370.729659", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 6 small cubes", "__seed__": "0193"}}, {"seed": 194, "data": {"pv_dec_string": "3,497,430.0103", "pv_ans_text": "3 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 5 small cubes", "__seed__": "0194"}}, {"seed": 195, "data": {"pv_dec_string": "31,204.889874", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.12", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0195"}}, {"seed": 196, "data": {"pv_dec_string": "916.502371", "pv_ans_text": "9 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.65", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0196"}}, {"seed": 197, "data": {"pv_dec_string": "361,005.9684", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 1 small cubes", "__seed__": "0197"}}, {"seed": 198, "data": {"pv_dec_string": "1,280.0394", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.43", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0198"}}, {"seed": 199, "data": {"pv_dec_string": "49,236.8765", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0199"}}, {"seed": 200, "data": {"pv_dec_string": "36,164.155811", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 3 small cubes", "__seed__": "0200"}}, {"seed": 201, "data": {"pv_dec_string": "141,633.03461", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 5 small cubes", "__seed__": "0201"}}, {"seed": 202, "data": {"pv_dec_string": "78,265.838708", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 1 small cubes", "__seed__": "0202"}}, {"seed": 203, "data": {"pv_dec_string": "7,097.591915", "pv_ans_text": "7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0203"}}, {"seed": 204, "data": {"pv_dec_string": "760,516.68857", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 1 small cubes", "__seed__": "0204"}}, {"seed": 205, "data": {"pv_dec_string": "1,339.348294", "pv_ans_text": "1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.26", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0205"}}, {"seed": 206, "data": {"pv_dec_string": "72,966.6456", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0206"}}, {"seed": 207, "data": {"pv_dec_string": "50,515.059225", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0207"}}, {"seed": 208, "data": {"pv_dec_string": "675,164.07828", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.143", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 4 longs, and 3 small cubes", "__seed__": "0208"}}, {"seed": 209, "data": {"pv_dec_string": "3,079.218936", "pv_ans_text": "3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 4 small cubes", "__seed__": "0209"}}, {"seed": 210, "data": {"pv_dec_string": "95,835.28609", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.665", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0210"}}, {"seed": 211, "data": {"pv_dec_string": "4,589.65289", "pv_ans_text": "4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.02", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 2 longs, and 0 small cubes", "__seed__": "0211"}}, {"seed": 212, "data": {"pv_dec_string": "9,844,117.7118", "pv_ans_text": "9 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.46", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0212"}}, {"seed": 213, "data": {"pv_dec_string": "57,837.0853", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 4 small cubes", "__seed__": "0213"}}, {"seed": 214, "data": {"pv_dec_string": "428,785.1069", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0214"}}, {"seed": 215, "data": {"pv_dec_string": "3,954.284377", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 2 small cubes", "__seed__": "0215"}}, {"seed": 216, "data": {"pv_dec_string": "690,787.15009", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.040", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0216"}}, {"seed": 217, "data": {"pv_dec_string": "280.062014", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.11", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0217"}}, {"seed": 218, "data": {"pv_dec_string": "507,104.7536", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.03", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0218"}}, {"seed": 219, "data": {"pv_dec_string": "1,033,045.991", "pv_ans_text": "1 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.31", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0219"}}, {"seed": 220, "data": {"pv_dec_string": "45,550.36887", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.13", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0220"}}, {"seed": 221, "data": {"pv_dec_string": "608,576.79856", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 2 small cubes", "__seed__": "0221"}}, {"seed": 222, "data": {"pv_dec_string": "1,234.74873", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 6 small cubes", "__seed__": "0222"}}, {"seed": 223, "data": {"pv_dec_string": "5,992.298601", "pv_ans_text": "5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.15", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0223"}}, {"seed": 224, "data": {"pv_dec_string": "86,567.120505", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.46", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0224"}}, {"seed": 225, "data": {"pv_dec_string": "9,029.670799", "pv_ans_text": "9 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0225"}}, {"seed": 226, "data": {"pv_dec_string": "6,035.75122", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0226"}}, {"seed": 227, "data": {"pv_dec_string": "91,518.29691", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.303", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0227"}}, {"seed": 228, "data": {"pv_dec_string": "74,232.118502", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.31", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0228"}}, {"seed": 229, "data": {"pv_dec_string": "23,134.9109", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0229"}}, {"seed": 230, "data": {"pv_dec_string": "588,589.15646", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 3 small cubes", "__seed__": "0230"}}, {"seed": 231, "data": {"pv_dec_string": "5,045.795989", "pv_ans_text": "5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.416", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 6 small cubes", "__seed__": "0231"}}, {"seed": 232, "data": {"pv_dec_string": "5,166,778.1676", "pv_ans_text": "5 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.150", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0232"}}, {"seed": 233, "data": {"pv_dec_string": "469.049134", "pv_ans_text": "4 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.500", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0233"}}, {"seed": 234, "data": {"pv_dec_string": "44,040.6109", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.060", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0234"}}, {"seed": 235, "data": {"pv_dec_string": "81,644.30839", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 3 small cubes", "__seed__": "0235"}}, {"seed": 236, "data": {"pv_dec_string": "8,091,026.1451", "pv_ans_text": "8 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 5 small cubes", "__seed__": "0236"}}, {"seed": 237, "data": {"pv_dec_string": "5,500,895.2311", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0237"}}, {"seed": 238, "data": {"pv_dec_string": "875.375074", "pv_ans_text": "8 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 2 small cubes", "__seed__": "0238"}}, {"seed": 239, "data": {"pv_dec_string": "1,118.07175", "pv_ans_text": "1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.36", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0239"}}, {"seed": 240, "data": {"pv_dec_string": "62,427.782455", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 1 small cubes", "__seed__": "0240"}}, {"seed": 241, "data": {"pv_dec_string": "63,714.75679", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.426", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 6 small cubes", "__seed__": "0241"}}, {"seed": 242, "data": {"pv_dec_string": "4,041.128001", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0242"}}, {"seed": 243, "data": {"pv_dec_string": "4,086.860773", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0243"}}, {"seed": 244, "data": {"pv_dec_string": "44,184.638841", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0244"}}, {"seed": 245, "data": {"pv_dec_string": "227,279.27204", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0245"}}, {"seed": 246, "data": {"pv_dec_string": "55,024.6715", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.46", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0246"}}, {"seed": 247, "data": {"pv_dec_string": "18,562.3414", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.30", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 0 longs, and 0 small cubes", "__seed__": "0247"}}, {"seed": 248, "data": {"pv_dec_string": "93,051.29915", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.31", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0248"}}, {"seed": 249, "data": {"pv_dec_string": "611.014001", "pv_ans_text": "6 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 2 small cubes", "__seed__": "0249"}}, {"seed": 250, "data": {"pv_dec_string": "937.658327", "pv_ans_text": "9 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0250"}}, {"seed": 251, "data": {"pv_dec_string": "672,424.78711", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.26", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0251"}}, {"seed": 252, "data": {"pv_dec_string": "9,966,258.7348", "pv_ans_text": "9 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0252"}}, {"seed": 253, "data": {"pv_dec_string": "8,607.227104", "pv_ans_text": "8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0253"}}, {"seed": 254, "data": {"pv_dec_string": "2,607.40858", "pv_ans_text": "2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.35", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0254"}}, {"seed": 255, "data": {"pv_dec_string": "384,057.9664", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.63", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0255"}}, {"seed": 256, "data": {"pv_dec_string": "433,858.1331", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0256"}}, {"seed": 257, "data": {"pv_dec_string": "16,271.8748", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.246", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 6 small cubes", "__seed__": "0257"}}, {"seed": 258, "data": {"pv_dec_string": "5,787.9224", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 4 small cubes", "__seed__": "0258"}}, {"seed": 259, "data": {"pv_dec_string": "287,913.45535", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.02", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 2 longs, and 0 small cubes", "__seed__": "0259"}}, {"seed": 260, "data": {"pv_dec_string": "50,837.83808", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0260"}}, {"seed": 261, "data": {"pv_dec_string": "79,188.1195", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0261"}}, {"seed": 262, "data": {"pv_dec_string": "1,366.665786", "pv_ans_text": "1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.24", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0262"}}, {"seed": 263, "data": {"pv_dec_string": "905.249154", "pv_ans_text": "9 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.544", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0263"}}, {"seed": 264, "data": {"pv_dec_string": "8,718.507184", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0264"}}, {"seed": 265, "data": {"pv_dec_string": "4,476.526749", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 4 small cubes", "__seed__": "0265"}}, {"seed": 266, "data": {"pv_dec_string": "65,383.55575", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0266"}}, {"seed": 267, "data": {"pv_dec_string": "2,556.63999", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 1 small cubes", "__seed__": "0267"}}, {"seed": 268, "data": {"pv_dec_string": "47,373.3252", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0268"}}, {"seed": 269, "data": {"pv_dec_string": "19,855.691517", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0269"}}, {"seed": 270, "data": {"pv_dec_string": "3,366,482.7229", "pv_ans_text": "3 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 2 small cubes", "__seed__": "0270"}}, {"seed": 271, "data": {"pv_dec_string": "722,234.7187", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 2 small cubes", "__seed__": "0271"}}, {"seed": 272, "data": {"pv_dec_string": "56,675.668026", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.654", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 5 longs, and 4 small cubes", "__seed__": "0272"}}, {"seed": 273, "data": {"pv_dec_string": "778,107.8675", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.212", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 1 longs, and 2 small cubes", "__seed__": "0273"}}, {"seed": 274, "data": {"pv_dec_string": "705,983.66439", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 3 small cubes", "__seed__": "0274"}}, {"seed": 275, "data": {"pv_dec_string": "287,382.01694", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.235", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 3 longs, and 5 small cubes", "__seed__": "0275"}}, {"seed": 276, "data": {"pv_dec_string": "56,869.5718", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0276"}}, {"seed": 277, "data": {"pv_dec_string": "97,247.5486", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 3 small cubes", "__seed__": "0277"}}, {"seed": 278, "data": {"pv_dec_string": "2,085,046.8288", "pv_ans_text": "2 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0278"}}, {"seed": 279, "data": {"pv_dec_string": "581,544.6178", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.223", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 2 longs, and 3 small cubes", "__seed__": "0279"}}, {"seed": 280, "data": {"pv_dec_string": "46,653.258151", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.626", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 2 longs, and 6 small cubes", "__seed__": "0280"}}, {"seed": 281, "data": {"pv_dec_string": "87,851.31558", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 3 small cubes", "__seed__": "0281"}}, {"seed": 282, "data": {"pv_dec_string": "8,994.02985", "pv_ans_text": "8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.242", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 4 longs, and 2 small cubes", "__seed__": "0282"}}, {"seed": 283, "data": {"pv_dec_string": "19,399.0384", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0283"}}, {"seed": 284, "data": {"pv_dec_string": "531,868.6372", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 3 small cubes", "__seed__": "0284"}}, {"seed": 285, "data": {"pv_dec_string": "635,402.62683", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 3 small cubes", "__seed__": "0285"}}, {"seed": 286, "data": {"pv_dec_string": "18,974.0647", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0286"}}, {"seed": 287, "data": {"pv_dec_string": "29,862.6932", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.616", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 6 small cubes", "__seed__": "0287"}}, {"seed": 288, "data": {"pv_dec_string": "73,016.26659", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.662", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 6 longs, and 2 small cubes", "__seed__": "0288"}}, {"seed": 289, "data": {"pv_dec_string": "415.116114", "pv_ans_text": "4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 4 small cubes", "__seed__": "0289"}}, {"seed": 290, "data": {"pv_dec_string": "908.899032", "pv_ans_text": "9 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.11", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0290"}}, {"seed": 291, "data": {"pv_dec_string": "737,529.7304", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 1 small cubes", "__seed__": "0291"}}, {"seed": 292, "data": {"pv_dec_string": "80,017.7436", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0292"}}, {"seed": 293, "data": {"pv_dec_string": "194,929.5574", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.62", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0293"}}, {"seed": 294, "data": {"pv_dec_string": "57,526.18268", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.415", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 1 longs, and 5 small cubes", "__seed__": "0294"}}, {"seed": 295, "data": {"pv_dec_string": "251.40917", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.34", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0295"}}, {"seed": 296, "data": {"pv_dec_string": "158,840.1525", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 2 small cubes", "__seed__": "0296"}}, {"seed": 297, "data": {"pv_dec_string": "4,406,239.9244", "pv_ans_text": "4 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 1 small cubes", "__seed__": "0297"}}, {"seed": 298, "data": {"pv_dec_string": "6,919.47509", "pv_ans_text": "6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.465", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 5 small cubes", "__seed__": "0298"}}, {"seed": 299, "data": {"pv_dec_string": "1,996,463.4122", "pv_ans_text": "1 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0299"}}, {"seed": 300, "data": {"pv_dec_string": "3,306,529.6039", "pv_ans_text": "3 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0300"}}, {"seed": 301, "data": {"pv_dec_string": "9,934,637.3831", "pv_ans_text": "9 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.102", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0301"}}, {"seed": 302, "data": {"pv_dec_string": "34,154.622085", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0302"}}, {"seed": 303, "data": {"pv_dec_string": "91,391.01174", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 1 small cubes", "__seed__": "0303"}}, {"seed": 304, "data": {"pv_dec_string": "837,864.28645", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 6 small cubes", "__seed__": "0304"}}, {"seed": 305, "data": {"pv_dec_string": "8,314,981.8719", "pv_ans_text": "8 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0305"}}, {"seed": 306, "data": {"pv_dec_string": "43,152.36903", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.10", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0306"}}, {"seed": 307, "data": {"pv_dec_string": "7,847,046.2057", "pv_ans_text": "7 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 1 small cubes", "__seed__": "0307"}}, {"seed": 308, "data": {"pv_dec_string": "49,919.289", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.31", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0308"}}, {"seed": 309, "data": {"pv_dec_string": "307.592742", "pv_ans_text": "3 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.40", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0309"}}, {"seed": 310, "data": {"pv_dec_string": "3,528.18038", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 1 small cubes", "__seed__": "0310"}}, {"seed": 311, "data": {"pv_dec_string": "8,020.60862", "pv_ans_text": "8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0311"}}, {"seed": 312, "data": {"pv_dec_string": "9,456.09771", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.46", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0312"}}, {"seed": 313, "data": {"pv_dec_string": "985,838.6301", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0313"}}, {"seed": 314, "data": {"pv_dec_string": "337.797338", "pv_ans_text": "3 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 3 small cubes", "__seed__": "0314"}}, {"seed": 315, "data": {"pv_dec_string": "4,166.59545", "pv_ans_text": "4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.26", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0315"}}, {"seed": 316, "data": {"pv_dec_string": "12,577.54092", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0316"}}, {"seed": 317, "data": {"pv_dec_string": "13,220.5415", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 6 small cubes", "__seed__": "0317"}}, {"seed": 318, "data": {"pv_dec_string": "58,338.88669", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 3 small cubes", "__seed__": "0318"}}, {"seed": 319, "data": {"pv_dec_string": "85,766.84954", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.64", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0319"}}, {"seed": 320, "data": {"pv_dec_string": "7,806,121.5261", "pv_ans_text": "7 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.613", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 1 longs, and 3 small cubes", "__seed__": "0320"}}, {"seed": 321, "data": {"pv_dec_string": "769,698.6412", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.43", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0321"}}, {"seed": 322, "data": {"pv_dec_string": "3,129,439.7098", "pv_ans_text": "3 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0322"}}, {"seed": 323, "data": {"pv_dec_string": "495,622.67101", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0323"}}, {"seed": 324, "data": {"pv_dec_string": "342.756916", "pv_ans_text": "3 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.160", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0324"}}, {"seed": 325, "data": {"pv_dec_string": "62,897.08", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.123", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0325"}}, {"seed": 326, "data": {"pv_dec_string": "7,821.226341", "pv_ans_text": "7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 1 small cubes", "__seed__": "0326"}}, {"seed": 327, "data": {"pv_dec_string": "958,837.98104", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 4 small cubes", "__seed__": "0327"}}, {"seed": 328, "data": {"pv_dec_string": "831.123956", "pv_ans_text": "8 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 6 small cubes", "__seed__": "0328"}}, {"seed": 329, "data": {"pv_dec_string": "70,758.2605", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 3 small cubes", "__seed__": "0329"}}, {"seed": 330, "data": {"pv_dec_string": "73,660.7028", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0330"}}, {"seed": 331, "data": {"pv_dec_string": "82,040.70796", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.140", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0331"}}, {"seed": 332, "data": {"pv_dec_string": "136,738.7053", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.33", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0332"}}, {"seed": 333, "data": {"pv_dec_string": "394,186.16", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.60", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0333"}}, {"seed": 334, "data": {"pv_dec_string": "1,854.53683", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.425", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0334"}}, {"seed": 335, "data": {"pv_dec_string": "5,323.574836", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.12", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0335"}}, {"seed": 336, "data": {"pv_dec_string": "1,617.33557", "pv_ans_text": "1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.433", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 3 longs, and 3 small cubes", "__seed__": "0336"}}, {"seed": 337, "data": {"pv_dec_string": "29,346.217977", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0337"}}, {"seed": 338, "data": {"pv_dec_string": "3,681.92628", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 5 small cubes", "__seed__": "0338"}}, {"seed": 339, "data": {"pv_dec_string": "159.832643", "pv_ans_text": "1 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.311", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0339"}}, {"seed": 340, "data": {"pv_dec_string": "191,155.804", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.05", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0340"}}, {"seed": 341, "data": {"pv_dec_string": "506.376899", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 2 small cubes", "__seed__": "0341"}}, {"seed": 342, "data": {"pv_dec_string": "7,244,854.2629", "pv_ans_text": "7 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.244", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0342"}}, {"seed": 343, "data": {"pv_dec_string": "5,355.39343", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 2 small cubes", "__seed__": "0343"}}, {"seed": 344, "data": {"pv_dec_string": "43,089.6943", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.46", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0344"}}, {"seed": 345, "data": {"pv_dec_string": "939,701.9682", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 2 small cubes", "__seed__": "0345"}}, {"seed": 346, "data": {"pv_dec_string": "6,402.627215", "pv_ans_text": "6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.463", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0346"}}, {"seed": 347, "data": {"pv_dec_string": "648,592.0118", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.004", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 0 longs, and 4 small cubes", "__seed__": "0347"}}, {"seed": 348, "data": {"pv_dec_string": "5,702.79479", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.62", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0348"}}, {"seed": 349, "data": {"pv_dec_string": "30,566.7741", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.06", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0349"}}, {"seed": 350, "data": {"pv_dec_string": "90,954.943983", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.566", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0350"}}, {"seed": 351, "data": {"pv_dec_string": "3,268.53408", "pv_ans_text": "3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.06", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0351"}}, {"seed": 352, "data": {"pv_dec_string": "1,833.50005", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.242", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 4 longs, and 2 small cubes", "__seed__": "0352"}}, {"seed": 353, "data": {"pv_dec_string": "963.52528", "pv_ans_text": "9 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0353"}}, {"seed": 354, "data": {"pv_dec_string": "584,839.5518", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.623", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0354"}}, {"seed": 355, "data": {"pv_dec_string": "31,549.846364", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.614", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 4 small cubes", "__seed__": "0355"}}, {"seed": 356, "data": {"pv_dec_string": "58,962.343596", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 5 small cubes", "__seed__": "0356"}}, {"seed": 357, "data": {"pv_dec_string": "314.075106", "pv_ans_text": "3 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0357"}}, {"seed": 358, "data": {"pv_dec_string": "168,277.72178", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.54", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0358"}}, {"seed": 359, "data": {"pv_dec_string": "11,488.9556", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0359"}}, {"seed": 360, "data": {"pv_dec_string": "6,601.72982", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 2 small cubes", "__seed__": "0360"}}, {"seed": 361, "data": {"pv_dec_string": "770,133.4157", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.20", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0361"}}, {"seed": 362, "data": {"pv_dec_string": "8,557,726.063", "pv_ans_text": "8 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.01", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0362"}}, {"seed": 363, "data": {"pv_dec_string": "436,203.12842", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0363"}}, {"seed": 364, "data": {"pv_dec_string": "7,979.32948", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.464", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 6 longs, and 4 small cubes", "__seed__": "0364"}}, {"seed": 365, "data": {"pv_dec_string": "703,984.5767", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.31", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0365"}}, {"seed": 366, "data": {"pv_dec_string": "91,406.1316", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0366"}}, {"seed": 367, "data": {"pv_dec_string": "91,352.01559", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.214", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 1 longs, and 4 small cubes", "__seed__": "0367"}}, {"seed": 368, "data": {"pv_dec_string": "39,688.5301", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 1 small cubes", "__seed__": "0368"}}, {"seed": 369, "data": {"pv_dec_string": "1,395,461.5225", "pv_ans_text": "1 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0369"}}, {"seed": 370, "data": {"pv_dec_string": "3,659.022855", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0370"}}, {"seed": 371, "data": {"pv_dec_string": "301,466.9024", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.463", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0371"}}, {"seed": 372, "data": {"pv_dec_string": "436,148.10088", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.46", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0372"}}, {"seed": 373, "data": {"pv_dec_string": "73,495.03998", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0373"}}, {"seed": 374, "data": {"pv_dec_string": "3,084,855.4168", "pv_ans_text": "3 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.46", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0374"}}, {"seed": 375, "data": {"pv_dec_string": "376,366.3907", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0375"}}, {"seed": 376, "data": {"pv_dec_string": "3,478,795.791", "pv_ans_text": "3 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0376"}}, {"seed": 377, "data": {"pv_dec_string": "770.07757", "pv_ans_text": "7 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0377"}}, {"seed": 378, "data": {"pv_dec_string": "13,749.270741", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0378"}}, {"seed": 379, "data": {"pv_dec_string": "789,641.52047", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.214", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 1 longs, and 4 small cubes", "__seed__": "0379"}}, {"seed": 380, "data": {"pv_dec_string": "98,768.04972", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 3 small cubes", "__seed__": "0380"}}, {"seed": 381, "data": {"pv_dec_string": "6,872,541.3881", "pv_ans_text": "6 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 2 small cubes", "__seed__": "0381"}}, {"seed": 382, "data": {"pv_dec_string": "442,077.3833", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 2 small cubes", "__seed__": "0382"}}, {"seed": 383, "data": {"pv_dec_string": "28,256.936626", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.616", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 1 longs, and 6 small cubes", "__seed__": "0383"}}, {"seed": 384, "data": {"pv_dec_string": "3,545.174991", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.44", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0384"}}, {"seed": 385, "data": {"pv_dec_string": "93,810.9747", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 1 small cubes", "__seed__": "0385"}}, {"seed": 386, "data": {"pv_dec_string": "7,956,511.4464", "pv_ans_text": "7 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.13", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0386"}}, {"seed": 387, "data": {"pv_dec_string": "71,934.26453", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0387"}}, {"seed": 388, "data": {"pv_dec_string": "893,196.9694", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.26", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0388"}}, {"seed": 389, "data": {"pv_dec_string": "96,232.60442", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 3 small cubes", "__seed__": "0389"}}, {"seed": 390, "data": {"pv_dec_string": "8,665,055.9222", "pv_ans_text": "8 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.045", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 4 longs, and 5 small cubes", "__seed__": "0390"}}, {"seed": 391, "data": {"pv_dec_string": "94,648.754846", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.53", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0391"}}, {"seed": 392, "data": {"pv_dec_string": "3,458.11545", "pv_ans_text": "3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.156", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 5 longs, and 6 small cubes", "__seed__": "0392"}}, {"seed": 393, "data": {"pv_dec_string": "328,367.468", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.631", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 3 longs, and 1 small cubes", "__seed__": "0393"}}, {"seed": 394, "data": {"pv_dec_string": "246,120.6419", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.366", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 6 small cubes", "__seed__": "0394"}}, {"seed": 395, "data": {"pv_dec_string": "7,971,138.1513", "pv_ans_text": "7 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0395"}}, {"seed": 396, "data": {"pv_dec_string": "1,833.543391", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.046", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 6 small cubes", "__seed__": "0396"}}, {"seed": 397, "data": {"pv_dec_string": "4,813,145.9021", "pv_ans_text": "4 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.461", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 1 small cubes", "__seed__": "0397"}}, {"seed": 398, "data": {"pv_dec_string": "821,154.1434", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.62", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0398"}}, {"seed": 399, "data": {"pv_dec_string": "50,358.599067", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 2 small cubes", "__seed__": "0399"}}, {"seed": 400, "data": {"pv_dec_string": "90,877.12913", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.565", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0400"}}, {"seed": 401, "data": {"pv_dec_string": "179,604.8447", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.23", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0401"}}, {"seed": 402, "data": {"pv_dec_string": "294,353.222", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0402"}}, {"seed": 403, "data": {"pv_dec_string": "432,721.7921", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 2 small cubes", "__seed__": "0403"}}, {"seed": 404, "data": {"pv_dec_string": "633,415.0506", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.120", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0404"}}, {"seed": 405, "data": {"pv_dec_string": "460,524.61694", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.355", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0405"}}, {"seed": 406, "data": {"pv_dec_string": "46,597.550517", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.626", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 6 small cubes", "__seed__": "0406"}}, {"seed": 407, "data": {"pv_dec_string": "135,161.71229", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0407"}}, {"seed": 408, "data": {"pv_dec_string": "13,025.18901", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.35", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 5 small cubes", "__seed__": "0408"}}, {"seed": 409, "data": {"pv_dec_string": "7,398.082216", "pv_ans_text": "7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.24", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0409"}}, {"seed": 410, "data": {"pv_dec_string": "40,525.6441", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0410"}}, {"seed": 411, "data": {"pv_dec_string": "40,917.009", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.22", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0411"}}, {"seed": 412, "data": {"pv_dec_string": "8,093.205831", "pv_ans_text": "8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.40", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0412"}}, {"seed": 413, "data": {"pv_dec_string": "7,254.251038", "pv_ans_text": "7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 1 small cubes", "__seed__": "0413"}}, {"seed": 414, "data": {"pv_dec_string": "11,905.302735", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.52", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0414"}}, {"seed": 415, "data": {"pv_dec_string": "31,597.630808", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.51", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0415"}}, {"seed": 416, "data": {"pv_dec_string": "9,110.917", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 6 small cubes", "__seed__": "0416"}}, {"seed": 417, "data": {"pv_dec_string": "952,433.58204", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0417"}}, {"seed": 418, "data": {"pv_dec_string": "4,370.691508", "pv_ans_text": "4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0418"}}, {"seed": 419, "data": {"pv_dec_string": "12,416.06862", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.501", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 0 longs, and 1 small cubes", "__seed__": "0419"}}, {"seed": 420, "data": {"pv_dec_string": "23,471.8035", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0420"}}, {"seed": 421, "data": {"pv_dec_string": "135,009.55012", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.430", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0421"}}, {"seed": 422, "data": {"pv_dec_string": "18,298.469302", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.113", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0422"}}, {"seed": 423, "data": {"pv_dec_string": "91,289.3948", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 5 small cubes", "__seed__": "0423"}}, {"seed": 424, "data": {"pv_dec_string": "1,649.70177", "pv_ans_text": "1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 3 small cubes", "__seed__": "0424"}}, {"seed": 425, "data": {"pv_dec_string": "9,888.035495", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.322", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 2 longs, and 2 small cubes", "__seed__": "0425"}}, {"seed": 426, "data": {"pv_dec_string": "207,047.42745", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 5 small cubes", "__seed__": "0426"}}, {"seed": 427, "data": {"pv_dec_string": "3,959.3713", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.545", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0427"}}, {"seed": 428, "data": {"pv_dec_string": "4,852,182.8028", "pv_ans_text": "4 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.050", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0428"}}, {"seed": 429, "data": {"pv_dec_string": "9,459.922324", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.42", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0429"}}, {"seed": 430, "data": {"pv_dec_string": "113,181.5834", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.10", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0430"}}, {"seed": 431, "data": {"pv_dec_string": "10,636.2138", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0431"}}, {"seed": 432, "data": {"pv_dec_string": "223.05312", "pv_ans_text": "2 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 4 small cubes", "__seed__": "0432"}}, {"seed": 433, "data": {"pv_dec_string": "593,607.83728", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.612", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 2 small cubes", "__seed__": "0433"}}, {"seed": 434, "data": {"pv_dec_string": "4,374,813.7708", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.341", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 4 longs, and 1 small cubes", "__seed__": "0434"}}, {"seed": 435, "data": {"pv_dec_string": "485,285.59605", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.44", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0435"}}, {"seed": 436, "data": {"pv_dec_string": "5,789.63937", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0436"}}, {"seed": 437, "data": {"pv_dec_string": "30,900.010713", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0437"}}, {"seed": 438, "data": {"pv_dec_string": "9,756.93983", "pv_ans_text": "9 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0438"}}, {"seed": 439, "data": {"pv_dec_string": "93,122.21482", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.46", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0439"}}, {"seed": 440, "data": {"pv_dec_string": "12,604.574773", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.405", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 0 longs, and 5 small cubes", "__seed__": "0440"}}, {"seed": 441, "data": {"pv_dec_string": "6,213.081556", "pv_ans_text": "6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0441"}}, {"seed": 442, "data": {"pv_dec_string": "1,383,900.638", "pv_ans_text": "1 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.455", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 5 longs, and 5 small cubes", "__seed__": "0442"}}, {"seed": 443, "data": {"pv_dec_string": "763,050.56284", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0443"}}, {"seed": 444, "data": {"pv_dec_string": "9,562.394475", "pv_ans_text": "9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0444"}}, {"seed": 445, "data": {"pv_dec_string": "3,934.5228", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 1 small cubes", "__seed__": "0445"}}, {"seed": 446, "data": {"pv_dec_string": "4,455.915745", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.10", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0446"}}, {"seed": 447, "data": {"pv_dec_string": "62,768.37707", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0447"}}, {"seed": 448, "data": {"pv_dec_string": "8,377.901792", "pv_ans_text": "8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0448"}}, {"seed": 449, "data": {"pv_dec_string": "11,770.642", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.233", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 3 longs, and 3 small cubes", "__seed__": "0449"}}, {"seed": 450, "data": {"pv_dec_string": "4,945.964246", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0450"}}, {"seed": 451, "data": {"pv_dec_string": "363.170173", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.560", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0451"}}, {"seed": 452, "data": {"pv_dec_string": "930,025.03687", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.336", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 3 longs, and 6 small cubes", "__seed__": "0452"}}, {"seed": 453, "data": {"pv_dec_string": "54,954.69099", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 3 small cubes", "__seed__": "0453"}}, {"seed": 454, "data": {"pv_dec_string": "353,087.4736", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 4 small cubes", "__seed__": "0454"}}, {"seed": 455, "data": {"pv_dec_string": "78,544.7066", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 4 small cubes", "__seed__": "0455"}}, {"seed": 456, "data": {"pv_dec_string": "17,631.470196", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0456"}}, {"seed": 457, "data": {"pv_dec_string": "6,611.799484", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.610", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0457"}}, {"seed": 458, "data": {"pv_dec_string": "301.573909", "pv_ans_text": "3 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.252", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0458"}}, {"seed": 459, "data": {"pv_dec_string": "4,907.371894", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0459"}}, {"seed": 460, "data": {"pv_dec_string": "4,818.668177", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0460"}}, {"seed": 461, "data": {"pv_dec_string": "731,224.4664", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 5 small cubes", "__seed__": "0461"}}, {"seed": 462, "data": {"pv_dec_string": "794,727.3181", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.133", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 3 small cubes", "__seed__": "0462"}}, {"seed": 463, "data": {"pv_dec_string": "98,397.1219", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 3 small cubes", "__seed__": "0463"}}, {"seed": 464, "data": {"pv_dec_string": "5,287.24558", "pv_ans_text": "5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.03", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0464"}}, {"seed": 465, "data": {"pv_dec_string": "3,447.611666", "pv_ans_text": "3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.516", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 1 longs, and 6 small cubes", "__seed__": "0465"}}, {"seed": 466, "data": {"pv_dec_string": "314,961.2457", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.520", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0466"}}, {"seed": 467, "data": {"pv_dec_string": "61,670.805018", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0467"}}, {"seed": 468, "data": {"pv_dec_string": "528,303.49747", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0468"}}, {"seed": 469, "data": {"pv_dec_string": "40,010.0853", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0469"}}, {"seed": 470, "data": {"pv_dec_string": "561,665.55232", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0470"}}, {"seed": 471, "data": {"pv_dec_string": "283,659.0039", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.23", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0471"}}, {"seed": 472, "data": {"pv_dec_string": "57,784.936701", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0472"}}, {"seed": 473, "data": {"pv_dec_string": "9,191.311321", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.60", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0473"}}, {"seed": 474, "data": {"pv_dec_string": "104,620.7243", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.566", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0474"}}, {"seed": 475, "data": {"pv_dec_string": "336,057.78824", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 6 small cubes", "__seed__": "0475"}}, {"seed": 476, "data": {"pv_dec_string": "207.314866", "pv_ans_text": "2 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0476"}}, {"seed": 477, "data": {"pv_dec_string": "176,336.0296", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 2 small cubes", "__seed__": "0477"}}, {"seed": 478, "data": {"pv_dec_string": "517.045891", "pv_ans_text": "5 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0478"}}, {"seed": 479, "data": {"pv_dec_string": "9,657,469.3516", "pv_ans_text": "9 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.11", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0479"}}, {"seed": 480, "data": {"pv_dec_string": "5,908,653.7197", "pv_ans_text": "5 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 3 small cubes", "__seed__": "0480"}}, {"seed": 481, "data": {"pv_dec_string": "1,751,872.1532", "pv_ans_text": "1 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 4 small cubes", "__seed__": "0481"}}, {"seed": 482, "data": {"pv_dec_string": "1,841,473.9819", "pv_ans_text": "1 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.645", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0482"}}, {"seed": 483, "data": {"pv_dec_string": "32,808.691136", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0483"}}, {"seed": 484, "data": {"pv_dec_string": "9,301,538.9075", "pv_ans_text": "9 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0484"}}, {"seed": 485, "data": {"pv_dec_string": "6,081.42154", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 5 small cubes", "__seed__": "0485"}}, {"seed": 486, "data": {"pv_dec_string": "5,174.075541", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 3 small cubes", "__seed__": "0486"}}, {"seed": 487, "data": {"pv_dec_string": "2,295.94507", "pv_ans_text": "2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 1 small cubes", "__seed__": "0487"}}, {"seed": 488, "data": {"pv_dec_string": "131,405.2641", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.42", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0488"}}, {"seed": 489, "data": {"pv_dec_string": "2,259.10405", "pv_ans_text": "2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.514", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 1 longs, and 4 small cubes", "__seed__": "0489"}}, {"seed": 490, "data": {"pv_dec_string": "9,809.24314", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.56", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0490"}}, {"seed": 491, "data": {"pv_dec_string": "31,271.770901", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 4 small cubes", "__seed__": "0491"}}, {"seed": 492, "data": {"pv_dec_string": "6,808.545966", "pv_ans_text": "6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 2 small cubes", "__seed__": "0492"}}, {"seed": 493, "data": {"pv_dec_string": "73,587.9248", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.10", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0493"}}, {"seed": 494, "data": {"pv_dec_string": "673.074952", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.152", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 5 longs, and 2 small cubes", "__seed__": "0494"}}, {"seed": 495, "data": {"pv_dec_string": "68,942.351007", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0495"}}, {"seed": 496, "data": {"pv_dec_string": "981.201931", "pv_ans_text": "9 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.063", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 3 small cubes", "__seed__": "0496"}}, {"seed": 497, "data": {"pv_dec_string": "180,046.83061", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.45", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0497"}}, {"seed": 498, "data": {"pv_dec_string": "957,185.2138", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 6 small cubes", "__seed__": "0498"}}, {"seed": 499, "data": {"pv_dec_string": "55,822.217152", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0499"}}, {"seed": 500, "data": {"pv_dec_string": "393.249557", "pv_ans_text": "3 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.10", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0500"}}, {"seed": 501, "data": {"pv_dec_string": "525.260441", "pv_ans_text": "5 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 3 small cubes", "__seed__": "0501"}}, {"seed": 502, "data": {"pv_dec_string": "9,284.719835", "pv_ans_text": "9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.26", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0502"}}, {"seed": 503, "data": {"pv_dec_string": "52,968.280489", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0503"}}, {"seed": 504, "data": {"pv_dec_string": "46,624.47799", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0504"}}, {"seed": 505, "data": {"pv_dec_string": "8,668,903.0735", "pv_ans_text": "8 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.625", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 2 longs, and 5 small cubes", "__seed__": "0505"}}, {"seed": 506, "data": {"pv_dec_string": "6,355,809.0884", "pv_ans_text": "6 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0506"}}, {"seed": 507, "data": {"pv_dec_string": "605,626.49952", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.355", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0507"}}, {"seed": 508, "data": {"pv_dec_string": "31,072.5843", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.051", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 5 longs, and 1 small cubes", "__seed__": "0508"}}, {"seed": 509, "data": {"pv_dec_string": "106.507507", "pv_ans_text": "1 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.263", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 6 longs, and 3 small cubes", "__seed__": "0509"}}, {"seed": 510, "data": {"pv_dec_string": "3,825.133573", "pv_ans_text": "3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 3 small cubes", "__seed__": "0510"}}, {"seed": 511, "data": {"pv_dec_string": "69,882.688314", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.03", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0511"}}, {"seed": 512, "data": {"pv_dec_string": "320.778245", "pv_ans_text": "3 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0512"}}, {"seed": 513, "data": {"pv_dec_string": "37,337.873065", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0513"}}, {"seed": 514, "data": {"pv_dec_string": "48,751.8653", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.40", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0514"}}, {"seed": 515, "data": {"pv_dec_string": "329,347.1443", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.442", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 4 longs, and 2 small cubes", "__seed__": "0515"}}, {"seed": 516, "data": {"pv_dec_string": "36,502.78607", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 6 small cubes", "__seed__": "0516"}}, {"seed": 517, "data": {"pv_dec_string": "86,988.9298", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0517"}}, {"seed": 518, "data": {"pv_dec_string": "5,807,616.0845", "pv_ans_text": "5 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.520", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0518"}}, {"seed": 519, "data": {"pv_dec_string": "790,364.3465", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.123", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0519"}}, {"seed": 520, "data": {"pv_dec_string": "94,879.422345", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.13", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0520"}}, {"seed": 521, "data": {"pv_dec_string": "657,517.0504", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0521"}}, {"seed": 522, "data": {"pv_dec_string": "113,605.09929", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.35", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0522"}}, {"seed": 523, "data": {"pv_dec_string": "5,625,138.9498", "pv_ans_text": "5 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.51", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0523"}}, {"seed": 524, "data": {"pv_dec_string": "726,972.14966", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.65", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0524"}}, {"seed": 525, "data": {"pv_dec_string": "864,528.62658", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0525"}}, {"seed": 526, "data": {"pv_dec_string": "7,792.397334", "pv_ans_text": "7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.32", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0526"}}, {"seed": 527, "data": {"pv_dec_string": "843.896157", "pv_ans_text": "8 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.022", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 2 longs, and 2 small cubes", "__seed__": "0527"}}, {"seed": 528, "data": {"pv_dec_string": "3,764,071.916", "pv_ans_text": "3 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.11", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0528"}}, {"seed": 529, "data": {"pv_dec_string": "33,591.39239", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.51", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0529"}}, {"seed": 530, "data": {"pv_dec_string": "7,683,109.0547", "pv_ans_text": "7 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.43", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 3 longs, and 0 small cubes", "__seed__": "0530"}}, {"seed": 531, "data": {"pv_dec_string": "33,433.133213", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.102", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0531"}}, {"seed": 532, "data": {"pv_dec_string": "625,911.367", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0532"}}, {"seed": 533, "data": {"pv_dec_string": "6,049.40335", "pv_ans_text": "6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.05", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0533"}}, {"seed": 534, "data": {"pv_dec_string": "958,708.639", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.62", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0534"}}, {"seed": 535, "data": {"pv_dec_string": "4,844,827.4699", "pv_ans_text": "4 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 3 small cubes", "__seed__": "0535"}}, {"seed": 536, "data": {"pv_dec_string": "355,759.2494", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0536"}}, {"seed": 537, "data": {"pv_dec_string": "987.543269", "pv_ans_text": "9 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 4 small cubes", "__seed__": "0537"}}, {"seed": 538, "data": {"pv_dec_string": "6,018,104.3596", "pv_ans_text": "6 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0538"}}, {"seed": 539, "data": {"pv_dec_string": "1,897.308675", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.13", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0539"}}, {"seed": 540, "data": {"pv_dec_string": "17,423.841522", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0540"}}, {"seed": 541, "data": {"pv_dec_string": "533,317.1246", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 5 small cubes", "__seed__": "0541"}}, {"seed": 542, "data": {"pv_dec_string": "8,435,143.8569", "pv_ans_text": "8 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0542"}}, {"seed": 543, "data": {"pv_dec_string": "62,901.236794", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0543"}}, {"seed": 544, "data": {"pv_dec_string": "8,005.231529", "pv_ans_text": "8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 2 small cubes", "__seed__": "0544"}}, {"seed": 545, "data": {"pv_dec_string": "45,417.567107", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.54", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0545"}}, {"seed": 546, "data": {"pv_dec_string": "20,512.0156", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0546"}}, {"seed": 547, "data": {"pv_dec_string": "6,240.96098", "pv_ans_text": "6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.52", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0547"}}, {"seed": 548, "data": {"pv_dec_string": "427.029693", "pv_ans_text": "4 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.16", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0548"}}, {"seed": 549, "data": {"pv_dec_string": "297,341.89315", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.624", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 2 longs, and 4 small cubes", "__seed__": "0549"}}, {"seed": 550, "data": {"pv_dec_string": "2,304.64261", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.04", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0550"}}, {"seed": 551, "data": {"pv_dec_string": "14,031.625588", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0551"}}, {"seed": 552, "data": {"pv_dec_string": "113,924.67689", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 4 small cubes", "__seed__": "0552"}}, {"seed": 553, "data": {"pv_dec_string": "9,818.14194", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 6 small cubes", "__seed__": "0553"}}, {"seed": 554, "data": {"pv_dec_string": "9,823.833953", "pv_ans_text": "9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.144", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0554"}}, {"seed": 555, "data": {"pv_dec_string": "4,847.914525", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.500", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0555"}}, {"seed": 556, "data": {"pv_dec_string": "60,323.880154", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0556"}}, {"seed": 557, "data": {"pv_dec_string": "1,852.55833", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.01", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0557"}}, {"seed": 558, "data": {"pv_dec_string": "553.886056", "pv_ans_text": "5 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.311", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0558"}}, {"seed": 559, "data": {"pv_dec_string": "889,320.5304", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.666", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 6 longs, and 6 small cubes", "__seed__": "0559"}}, {"seed": 560, "data": {"pv_dec_string": "4,497.5498", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.13", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0560"}}, {"seed": 561, "data": {"pv_dec_string": "110.416916", "pv_ans_text": "1 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.035", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 3 longs, and 5 small cubes", "__seed__": "0561"}}, {"seed": 562, "data": {"pv_dec_string": "9,518.34736", "pv_ans_text": "9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0562"}}, {"seed": 563, "data": {"pv_dec_string": "248,955.8881", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.65", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0563"}}, {"seed": 564, "data": {"pv_dec_string": "64,739.83175", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 2 small cubes", "__seed__": "0564"}}, {"seed": 565, "data": {"pv_dec_string": "616.862766", "pv_ans_text": "6 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.55", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0565"}}, {"seed": 566, "data": {"pv_dec_string": "347,704.69734", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.50", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0566"}}, {"seed": 567, "data": {"pv_dec_string": "958,282.40911", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0567"}}, {"seed": 568, "data": {"pv_dec_string": "4,914.300005", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0568"}}, {"seed": 569, "data": {"pv_dec_string": "58,437.11806", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.66", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0569"}}, {"seed": 570, "data": {"pv_dec_string": "88,213.6905", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 5 small cubes", "__seed__": "0570"}}, {"seed": 571, "data": {"pv_dec_string": "465.309376", "pv_ans_text": "4 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0571"}}, {"seed": 572, "data": {"pv_dec_string": "5,431,969.0855", "pv_ans_text": "5 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.54", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0572"}}, {"seed": 573, "data": {"pv_dec_string": "8,190.542288", "pv_ans_text": "8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0573"}}, {"seed": 574, "data": {"pv_dec_string": "90,550.3591", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 6 small cubes", "__seed__": "0574"}}, {"seed": 575, "data": {"pv_dec_string": "508,794.4673", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.03", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0575"}}, {"seed": 576, "data": {"pv_dec_string": "56,983.34399", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0576"}}, {"seed": 577, "data": {"pv_dec_string": "73,072.4084", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.36", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0577"}}, {"seed": 578, "data": {"pv_dec_string": "23,006.8314", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0578"}}, {"seed": 579, "data": {"pv_dec_string": "97,744.2217", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0579"}}, {"seed": 580, "data": {"pv_dec_string": "4,684.517749", "pv_ans_text": "4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.06", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0580"}}, {"seed": 581, "data": {"pv_dec_string": "984.456857", "pv_ans_text": "9 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.432", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 3 longs, and 2 small cubes", "__seed__": "0581"}}, {"seed": 582, "data": {"pv_dec_string": "742.553837", "pv_ans_text": "7 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.03", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 3 small cubes", "__seed__": "0582"}}, {"seed": 583, "data": {"pv_dec_string": "89,802.755738", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 5 small cubes", "__seed__": "0583"}}, {"seed": 584, "data": {"pv_dec_string": "713,427.6201", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 4 small cubes", "__seed__": "0584"}}, {"seed": 585, "data": {"pv_dec_string": "453,247.82696", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.36", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0585"}}, {"seed": 586, "data": {"pv_dec_string": "957,699.25476", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0586"}}, {"seed": 587, "data": {"pv_dec_string": "262,666.1511", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 5 small cubes", "__seed__": "0587"}}, {"seed": 588, "data": {"pv_dec_string": "6,867.32262", "pv_ans_text": "6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0588"}}, {"seed": 589, "data": {"pv_dec_string": "9,159.55203", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0589"}}, {"seed": 590, "data": {"pv_dec_string": "4,263.48154", "pv_ans_text": "4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0590"}}, {"seed": 591, "data": {"pv_dec_string": "729.99314", "pv_ans_text": "7 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 4 small cubes", "__seed__": "0591"}}, {"seed": 592, "data": {"pv_dec_string": "68,144.45219", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.42", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0592"}}, {"seed": 593, "data": {"pv_dec_string": "71,466.1901", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.62", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 2 small cubes", "__seed__": "0593"}}, {"seed": 594, "data": {"pv_dec_string": "4,437,488.3262", "pv_ans_text": "4 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0594"}}, {"seed": 595, "data": {"pv_dec_string": "685,495.54545", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.426", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 2 longs, and 6 small cubes", "__seed__": "0595"}}, {"seed": 596, "data": {"pv_dec_string": "7,996.970757", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.25", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0596"}}, {"seed": 597, "data": {"pv_dec_string": "363,619.7338", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.061", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 6 longs, and 1 small cubes", "__seed__": "0597"}}, {"seed": 598, "data": {"pv_dec_string": "1,303,850.6301", "pv_ans_text": "1 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.303", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0598"}}, {"seed": 599, "data": {"pv_dec_string": "42,526.15964", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 2 small cubes", "__seed__": "0599"}}, {"seed": 600, "data": {"pv_dec_string": "700,939.32591", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.161", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0600"}}, {"seed": 601, "data": {"pv_dec_string": "409.821554", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 4 small cubes", "__seed__": "0601"}}, {"seed": 602, "data": {"pv_dec_string": "656,251.17377", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.162", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 2 small cubes", "__seed__": "0602"}}, {"seed": 603, "data": {"pv_dec_string": "86,119.6943", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0603"}}, {"seed": 604, "data": {"pv_dec_string": "5,731.57209", "pv_ans_text": "5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.56", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 6 small cubes", "__seed__": "0604"}}, {"seed": 605, "data": {"pv_dec_string": "792.48029", "pv_ans_text": "7 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 2 small cubes", "__seed__": "0605"}}, {"seed": 606, "data": {"pv_dec_string": "76,574.331288", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 1 small cubes", "__seed__": "0606"}}, {"seed": 607, "data": {"pv_dec_string": "258.098688", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.012", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 1 longs, and 2 small cubes", "__seed__": "0607"}}, {"seed": 608, "data": {"pv_dec_string": "98,943.88918", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0608"}}, {"seed": 609, "data": {"pv_dec_string": "13,562.57251", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 3 small cubes", "__seed__": "0609"}}, {"seed": 610, "data": {"pv_dec_string": "9,419.915559", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 4 small cubes", "__seed__": "0610"}}, {"seed": 611, "data": {"pv_dec_string": "2,252.84739", "pv_ans_text": "2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0611"}}, {"seed": 612, "data": {"pv_dec_string": "8,071,847.4454", "pv_ans_text": "8 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 2 small cubes", "__seed__": "0612"}}, {"seed": 613, "data": {"pv_dec_string": "3,913.813677", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.264", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 6 longs, and 4 small cubes", "__seed__": "0613"}}, {"seed": 614, "data": {"pv_dec_string": "83,545.6844", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0614"}}, {"seed": 615, "data": {"pv_dec_string": "2,553.13492", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0615"}}, {"seed": 616, "data": {"pv_dec_string": "5,919.19634", "pv_ans_text": "5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 2 small cubes", "__seed__": "0616"}}, {"seed": 617, "data": {"pv_dec_string": "3,514.99978", "pv_ans_text": "3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.565", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 5 small cubes", "__seed__": "0617"}}, {"seed": 618, "data": {"pv_dec_string": "504.608568", "pv_ans_text": "5 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 4 small cubes", "__seed__": "0618"}}, {"seed": 619, "data": {"pv_dec_string": "1,274,595.1134", "pv_ans_text": "1 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 5 small cubes", "__seed__": "0619"}}, {"seed": 620, "data": {"pv_dec_string": "96,703.2989", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.640", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0620"}}, {"seed": 621, "data": {"pv_dec_string": "7,332.97415", "pv_ans_text": "7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 1 small cubes", "__seed__": "0621"}}, {"seed": 622, "data": {"pv_dec_string": "3,986,949.2907", "pv_ans_text": "3 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 6 small cubes", "__seed__": "0622"}}, {"seed": 623, "data": {"pv_dec_string": "72,052.82582", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 6 small cubes", "__seed__": "0623"}}, {"seed": 624, "data": {"pv_dec_string": "467.595195", "pv_ans_text": "4 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.51", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0624"}}, {"seed": 625, "data": {"pv_dec_string": "51,057.31084", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 5 small cubes", "__seed__": "0625"}}, {"seed": 626, "data": {"pv_dec_string": "8,191,172.611", "pv_ans_text": "8 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 1 small cubes", "__seed__": "0626"}}, {"seed": 627, "data": {"pv_dec_string": "463,448.128", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.241", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 4 longs, and 1 small cubes", "__seed__": "0627"}}, {"seed": 628, "data": {"pv_dec_string": "888.627853", "pv_ans_text": "8 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.015", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 1 longs, and 5 small cubes", "__seed__": "0628"}}, {"seed": 629, "data": {"pv_dec_string": "33,502.49337", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 6 small cubes", "__seed__": "0629"}}, {"seed": 630, "data": {"pv_dec_string": "14,189.02908", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.42", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0630"}}, {"seed": 631, "data": {"pv_dec_string": "8,734,999.7937", "pv_ans_text": "8 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 4 small cubes", "__seed__": "0631"}}, {"seed": 632, "data": {"pv_dec_string": "25,799.73402", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0632"}}, {"seed": 633, "data": {"pv_dec_string": "8,156.58495", "pv_ans_text": "8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.00", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0633"}}, {"seed": 634, "data": {"pv_dec_string": "594.359025", "pv_ans_text": "5 is in the hundreds (100) place. 9 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0634"}}, {"seed": 635, "data": {"pv_dec_string": "858,733.43134", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.334", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0635"}}, {"seed": 636, "data": {"pv_dec_string": "91,443.83802", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.56", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0636"}}, {"seed": 637, "data": {"pv_dec_string": "71,228.18386", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0637"}}, {"seed": 638, "data": {"pv_dec_string": "688,681.6818", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 6 small cubes", "__seed__": "0638"}}, {"seed": 639, "data": {"pv_dec_string": "3,242,565.9735", "pv_ans_text": "3 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 6 small cubes", "__seed__": "0639"}}, {"seed": 640, "data": {"pv_dec_string": "9,131,171.3091", "pv_ans_text": "9 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0640"}}, {"seed": 641, "data": {"pv_dec_string": "728,516.74", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.413", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 3 small cubes", "__seed__": "0641"}}, {"seed": 642, "data": {"pv_dec_string": "4,923.91238", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0642"}}, {"seed": 643, "data": {"pv_dec_string": "22,586.001197", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 4 small cubes", "__seed__": "0643"}}, {"seed": 644, "data": {"pv_dec_string": "9,620.98892", "pv_ans_text": "9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.212", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 1 longs, and 2 small cubes", "__seed__": "0644"}}, {"seed": 645, "data": {"pv_dec_string": "118,829.1737", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0645"}}, {"seed": 646, "data": {"pv_dec_string": "93,448.6691", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.11", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0646"}}, {"seed": 647, "data": {"pv_dec_string": "33,012.516218", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.00", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0647"}}, {"seed": 648, "data": {"pv_dec_string": "47,878.0181", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.22", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0648"}}, {"seed": 649, "data": {"pv_dec_string": "7,766,701.9477", "pv_ans_text": "7 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 3 small cubes", "__seed__": "0649"}}, {"seed": 650, "data": {"pv_dec_string": "737.875089", "pv_ans_text": "7 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0650"}}, {"seed": 651, "data": {"pv_dec_string": "3,709.83337", "pv_ans_text": "3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 1 small cubes", "__seed__": "0651"}}, {"seed": 652, "data": {"pv_dec_string": "93,861.780946", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 4 small cubes", "__seed__": "0652"}}, {"seed": 653, "data": {"pv_dec_string": "512,110.16362", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.050", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0653"}}, {"seed": 654, "data": {"pv_dec_string": "2,756.279067", "pv_ans_text": "2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.354", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 4 small cubes", "__seed__": "0654"}}, {"seed": 655, "data": {"pv_dec_string": "66,891.9288", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.23", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0655"}}, {"seed": 656, "data": {"pv_dec_string": "5,257.32345", "pv_ans_text": "5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.40", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0656"}}, {"seed": 657, "data": {"pv_dec_string": "35,692.2933", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.006", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 0 longs, and 6 small cubes", "__seed__": "0657"}}, {"seed": 658, "data": {"pv_dec_string": "93,172.6873", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.653", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 5 longs, and 3 small cubes", "__seed__": "0658"}}, {"seed": 659, "data": {"pv_dec_string": "7,903.962854", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.62", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0659"}}, {"seed": 660, "data": {"pv_dec_string": "79,608.09259", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.332", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0660"}}, {"seed": 661, "data": {"pv_dec_string": "66,999.168999", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 5 small cubes", "__seed__": "0661"}}, {"seed": 662, "data": {"pv_dec_string": "7,991,951.8695", "pv_ans_text": "7 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0662"}}, {"seed": 663, "data": {"pv_dec_string": "4,069.711105", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.443", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0663"}}, {"seed": 664, "data": {"pv_dec_string": "62,282.0494", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.41", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0664"}}, {"seed": 665, "data": {"pv_dec_string": "6,520.935115", "pv_ans_text": "6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 6 small cubes", "__seed__": "0665"}}, {"seed": 666, "data": {"pv_dec_string": "33,068.92002", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.22", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0666"}}, {"seed": 667, "data": {"pv_dec_string": "18,992.541067", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.13", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0667"}}, {"seed": 668, "data": {"pv_dec_string": "933.422755", "pv_ans_text": "9 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.040", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0668"}}, {"seed": 669, "data": {"pv_dec_string": "317.980264", "pv_ans_text": "3 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0669"}}, {"seed": 670, "data": {"pv_dec_string": "41,190.313576", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 5 small cubes", "__seed__": "0670"}}, {"seed": 671, "data": {"pv_dec_string": "2,391,823.7938", "pv_ans_text": "2 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.35", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0671"}}, {"seed": 672, "data": {"pv_dec_string": "4,508.754409", "pv_ans_text": "4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.53", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0672"}}, {"seed": 673, "data": {"pv_dec_string": "22,578.3995", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0673"}}, {"seed": 674, "data": {"pv_dec_string": "830,563.22637", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.21", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 1 longs, and 0 small cubes", "__seed__": "0674"}}, {"seed": 675, "data": {"pv_dec_string": "30,209.35821", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0675"}}, {"seed": 676, "data": {"pv_dec_string": "319,452.8791", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.20", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0676"}}, {"seed": 677, "data": {"pv_dec_string": "761,730.6138", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 3 small cubes", "__seed__": "0677"}}, {"seed": 678, "data": {"pv_dec_string": "82,901.52169", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 6 small cubes", "__seed__": "0678"}}, {"seed": 679, "data": {"pv_dec_string": "5,850.166181", "pv_ans_text": "5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 1 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.126", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 2 longs, and 6 small cubes", "__seed__": "0679"}}, {"seed": 680, "data": {"pv_dec_string": "939,275.63641", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 4 small cubes", "__seed__": "0680"}}, {"seed": 681, "data": {"pv_dec_string": "85,260.410559", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.65", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0681"}}, {"seed": 682, "data": {"pv_dec_string": "16,814.268625", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0682"}}, {"seed": 683, "data": {"pv_dec_string": "6,707.681542", "pv_ans_text": "6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.115", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 5 small cubes", "__seed__": "0683"}}, {"seed": 684, "data": {"pv_dec_string": "6,581.720731", "pv_ans_text": "6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.651", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 5 longs, and 1 small cubes", "__seed__": "0684"}}, {"seed": 685, "data": {"pv_dec_string": "90,792.8862", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0685"}}, {"seed": 686, "data": {"pv_dec_string": "487,557.1018", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.05", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0686"}}, {"seed": 687, "data": {"pv_dec_string": "339,860.9632", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.623", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0687"}}, {"seed": 688, "data": {"pv_dec_string": "732,552.8782", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 4 small cubes", "__seed__": "0688"}}, {"seed": 689, "data": {"pv_dec_string": "85,916.179", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.120", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0689"}}, {"seed": 690, "data": {"pv_dec_string": "9,524,548.7494", "pv_ans_text": "9 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.210", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 1 longs, and 0 small cubes", "__seed__": "0690"}}, {"seed": 691, "data": {"pv_dec_string": "9,245,805.5629", "pv_ans_text": "9 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0691"}}, {"seed": 692, "data": {"pv_dec_string": "899,553.64537", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0692"}}, {"seed": 693, "data": {"pv_dec_string": "247,043.0552", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 6 small cubes", "__seed__": "0693"}}, {"seed": 694, "data": {"pv_dec_string": "50,081.98468", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 1 small cubes", "__seed__": "0694"}}, {"seed": 695, "data": {"pv_dec_string": "967,723.9863", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.04", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0695"}}, {"seed": 696, "data": {"pv_dec_string": "87,001.290583", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.611", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 1 longs, and 1 small cubes", "__seed__": "0696"}}, {"seed": 697, "data": {"pv_dec_string": "564.947175", "pv_ans_text": "5 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.20", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0697"}}, {"seed": 698, "data": {"pv_dec_string": "84,951.504433", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.621", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 2 longs, and 1 small cubes", "__seed__": "0698"}}, {"seed": 699, "data": {"pv_dec_string": "706,267.52101", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 2 small cubes", "__seed__": "0699"}}, {"seed": 700, "data": {"pv_dec_string": "494,606.301", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 2 small cubes", "__seed__": "0700"}}, {"seed": 701, "data": {"pv_dec_string": "6,457,746.8211", "pv_ans_text": "6 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.125", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 2 longs, and 5 small cubes", "__seed__": "0701"}}, {"seed": 702, "data": {"pv_dec_string": "3,993.996908", "pv_ans_text": "3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.431", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 3 longs, and 1 small cubes", "__seed__": "0702"}}, {"seed": 703, "data": {"pv_dec_string": "17,171.7979", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.661", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 6 longs, and 1 small cubes", "__seed__": "0703"}}, {"seed": 704, "data": {"pv_dec_string": "8,793.481122", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.23", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0704"}}, {"seed": 705, "data": {"pv_dec_string": "97,068.199189", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 4 small cubes", "__seed__": "0705"}}, {"seed": 706, "data": {"pv_dec_string": "761,500.6857", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.26", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0706"}}, {"seed": 707, "data": {"pv_dec_string": "81,558.63792", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.141", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 1 small cubes", "__seed__": "0707"}}, {"seed": 708, "data": {"pv_dec_string": "3,152.22462", "pv_ans_text": "3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.313", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 1 longs, and 3 small cubes", "__seed__": "0708"}}, {"seed": 709, "data": {"pv_dec_string": "39,177.75574", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0709"}}, {"seed": 710, "data": {"pv_dec_string": "7,657.31811", "pv_ans_text": "7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 2 small cubes", "__seed__": "0710"}}, {"seed": 711, "data": {"pv_dec_string": "54,993.29184", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0711"}}, {"seed": 712, "data": {"pv_dec_string": "53,603.8012", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.043", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 4 longs, and 3 small cubes", "__seed__": "0712"}}, {"seed": 713, "data": {"pv_dec_string": "78,853.3397", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 4 longs, and 5 small cubes", "__seed__": "0713"}}, {"seed": 714, "data": {"pv_dec_string": "7,483,592.1798", "pv_ans_text": "7 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.12", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0714"}}, {"seed": 715, "data": {"pv_dec_string": "812,331.5141", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.35", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0715"}}, {"seed": 716, "data": {"pv_dec_string": "842,937.45048", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.434", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0716"}}, {"seed": 717, "data": {"pv_dec_string": "952,580.8636", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.20", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0717"}}, {"seed": 718, "data": {"pv_dec_string": "56,154.143008", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.360", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0718"}}, {"seed": 719, "data": {"pv_dec_string": "4,069.29044", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 6 small cubes", "__seed__": "0719"}}, {"seed": 720, "data": {"pv_dec_string": "43,802.5939", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.54", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0720"}}, {"seed": 721, "data": {"pv_dec_string": "36,201.78521", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.32", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0721"}}, {"seed": 722, "data": {"pv_dec_string": "4,929.640995", "pv_ans_text": "4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.31", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0722"}}, {"seed": 723, "data": {"pv_dec_string": "74,581.800161", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 0 small cubes", "__seed__": "0723"}}, {"seed": 724, "data": {"pv_dec_string": "379.792877", "pv_ans_text": "3 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.424", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0724"}}, {"seed": 725, "data": {"pv_dec_string": "431,519.67153", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0725"}}, {"seed": 726, "data": {"pv_dec_string": "242.350666", "pv_ans_text": "2 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 6 small cubes", "__seed__": "0726"}}, {"seed": 727, "data": {"pv_dec_string": "5,012,323.9415", "pv_ans_text": "5 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 4 small cubes", "__seed__": "0727"}}, {"seed": 728, "data": {"pv_dec_string": "169.286858", "pv_ans_text": "1 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 2 small cubes", "__seed__": "0728"}}, {"seed": 729, "data": {"pv_dec_string": "874,740.9987", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0729"}}, {"seed": 730, "data": {"pv_dec_string": "8,617.17652", "pv_ans_text": "8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.640", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0730"}}, {"seed": 731, "data": {"pv_dec_string": "401.984989", "pv_ans_text": "4 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.414", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 1 longs, and 4 small cubes", "__seed__": "0731"}}, {"seed": 732, "data": {"pv_dec_string": "37,724.2441", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.110", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0732"}}, {"seed": 733, "data": {"pv_dec_string": "66,725.0104", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 6 small cubes", "__seed__": "0733"}}, {"seed": 734, "data": {"pv_dec_string": "2,808.836224", "pv_ans_text": "2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 0 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.62", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 2 longs, and 0 small cubes", "__seed__": "0734"}}, {"seed": 735, "data": {"pv_dec_string": "340,234.6135", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.52", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0735"}}, {"seed": 736, "data": {"pv_dec_string": "665,992.2856", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.544", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 4 longs, and 4 small cubes", "__seed__": "0736"}}, {"seed": 737, "data": {"pv_dec_string": "195,322.36664", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.00", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0737"}}, {"seed": 738, "data": {"pv_dec_string": "4,358,542.4759", "pv_ans_text": "4 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.152", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 5 longs, and 2 small cubes", "__seed__": "0738"}}, {"seed": 739, "data": {"pv_dec_string": "5,683,739.0065", "pv_ans_text": "5 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0739"}}, {"seed": 740, "data": {"pv_dec_string": "1,761.956818", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.14", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0740"}}, {"seed": 741, "data": {"pv_dec_string": "206.837884", "pv_ans_text": "2 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.60", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0741"}}, {"seed": 742, "data": {"pv_dec_string": "4,771.093363", "pv_ans_text": "4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0742"}}, {"seed": 743, "data": {"pv_dec_string": "7,240.413262", "pv_ans_text": "7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0743"}}, {"seed": 744, "data": {"pv_dec_string": "8,386,835.872", "pv_ans_text": "8 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.00", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 0 longs, and 0 small cubes", "__seed__": "0744"}}, {"seed": 745, "data": {"pv_dec_string": "74,756.686781", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.35", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 5 small cubes", "__seed__": "0745"}}, {"seed": 746, "data": {"pv_dec_string": "537.914867", "pv_ans_text": "5 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0746"}}, {"seed": 747, "data": {"pv_dec_string": "1,036.36743", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.51", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0747"}}, {"seed": 748, "data": {"pv_dec_string": "6,950,461.4897", "pv_ans_text": "6 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0748"}}, {"seed": 749, "data": {"pv_dec_string": "5,817.526451", "pv_ans_text": "5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.56", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0749"}}, {"seed": 750, "data": {"pv_dec_string": "69,459.90945", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0750"}}, {"seed": 751, "data": {"pv_dec_string": "847.787409", "pv_ans_text": "8 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.46", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0751"}}, {"seed": 752, "data": {"pv_dec_string": "59,361.921332", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0752"}}, {"seed": 753, "data": {"pv_dec_string": "86,389.51687", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0753"}}, {"seed": 754, "data": {"pv_dec_string": "7,902.323125", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.124", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 2 longs, and 4 small cubes", "__seed__": "0754"}}, {"seed": 755, "data": {"pv_dec_string": "5,987,048.7444", "pv_ans_text": "5 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.343", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 4 longs, and 3 small cubes", "__seed__": "0755"}}, {"seed": 756, "data": {"pv_dec_string": "75,674.733", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.44", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0756"}}, {"seed": 757, "data": {"pv_dec_string": "98,087.0557", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 3 small cubes", "__seed__": "0757"}}, {"seed": 758, "data": {"pv_dec_string": "7,884.50219", "pv_ans_text": "7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.42", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0758"}}, {"seed": 759, "data": {"pv_dec_string": "49,542.51327", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.240", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0759"}}, {"seed": 760, "data": {"pv_dec_string": "19,184.8258", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 4 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.15", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0760"}}, {"seed": 761, "data": {"pv_dec_string": "51,080.080568", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.10", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 0 small cubes", "__seed__": "0761"}}, {"seed": 762, "data": {"pv_dec_string": "5,764,032.1888", "pv_ans_text": "5 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 6 small cubes", "__seed__": "0762"}}, {"seed": 763, "data": {"pv_dec_string": "533,443.29396", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 5 small cubes", "__seed__": "0763"}}, {"seed": 764, "data": {"pv_dec_string": "81,599.901247", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.05", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 0 longs, and 5 small cubes", "__seed__": "0764"}}, {"seed": 765, "data": {"pv_dec_string": "6,628.527655", "pv_ans_text": "6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.53", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0765"}}, {"seed": 766, "data": {"pv_dec_string": "20,928.773068", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0766"}}, {"seed": 767, "data": {"pv_dec_string": "24,955.55033", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.151", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 5 longs, and 1 small cubes", "__seed__": "0767"}}, {"seed": 768, "data": {"pv_dec_string": "26,755.261478", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 4 small cubes", "__seed__": "0768"}}, {"seed": 769, "data": {"pv_dec_string": "6,826,814.1725", "pv_ans_text": "6 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.655", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 5 longs, and 5 small cubes", "__seed__": "0769"}}, {"seed": 770, "data": {"pv_dec_string": "82,909.6545", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 3 small cubes", "__seed__": "0770"}}, {"seed": 771, "data": {"pv_dec_string": "5,085.12886", "pv_ans_text": "5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.254", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 5 longs, and 4 small cubes", "__seed__": "0771"}}, {"seed": 772, "data": {"pv_dec_string": "4,450.976869", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 5 small cubes", "__seed__": "0772"}}, {"seed": 773, "data": {"pv_dec_string": "93,224.9635", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0773"}}, {"seed": 774, "data": {"pv_dec_string": "5,490.949572", "pv_ans_text": "5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.132", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 3 longs, and 2 small cubes", "__seed__": "0774"}}, {"seed": 775, "data": {"pv_dec_string": "249,418.07046", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0775"}}, {"seed": 776, "data": {"pv_dec_string": "76,928.682578", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0776"}}, {"seed": 777, "data": {"pv_dec_string": "79,521.4746", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.411", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 4 flats, 1 longs, and 1 small cubes", "__seed__": "0777"}}, {"seed": 778, "data": {"pv_dec_string": "7,217,279.2913", "pv_ans_text": "7 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.63", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 3 small cubes", "__seed__": "0778"}}, {"seed": 779, "data": {"pv_dec_string": "37,351.74724", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 5 small cubes", "__seed__": "0779"}}, {"seed": 780, "data": {"pv_dec_string": "60,355.563083", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.61", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0780"}}, {"seed": 781, "data": {"pv_dec_string": "72,510.77394", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 4 longs, and 4 small cubes", "__seed__": "0781"}}, {"seed": 782, "data": {"pv_dec_string": "1,215.64469", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.356", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 5 longs, and 6 small cubes", "__seed__": "0782"}}, {"seed": 783, "data": {"pv_dec_string": "31,032.31364", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.10", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0783"}}, {"seed": 784, "data": {"pv_dec_string": "361,980.33679", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.542", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 4 longs, and 2 small cubes", "__seed__": "0784"}}, {"seed": 785, "data": {"pv_dec_string": "74,974.237335", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 1 small cubes", "__seed__": "0785"}}, {"seed": 786, "data": {"pv_dec_string": "5,176.2117", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.03", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0786"}}, {"seed": 787, "data": {"pv_dec_string": "1,189,449.2318", "pv_ans_text": "1 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.54", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0787"}}, {"seed": 788, "data": {"pv_dec_string": "11,213.06566", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.336", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 3 flats, 3 longs, and 6 small cubes", "__seed__": "0788"}}, {"seed": 789, "data": {"pv_dec_string": "762,862.1783", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 1 small cubes", "__seed__": "0789"}}, {"seed": 790, "data": {"pv_dec_string": "4,450,723.3507", "pv_ans_text": "4 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.161", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0790"}}, {"seed": 791, "data": {"pv_dec_string": "364.9546", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 3 small cubes", "__seed__": "0791"}}, {"seed": 792, "data": {"pv_dec_string": "217.069415", "pv_ans_text": "2 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0792"}}, {"seed": 793, "data": {"pv_dec_string": "50,945.8187", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 5 small cubes", "__seed__": "0793"}}, {"seed": 794, "data": {"pv_dec_string": "141,901.89934", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0794"}}, {"seed": 795, "data": {"pv_dec_string": "43,186.660148", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 1 small cubes", "__seed__": "0795"}}, {"seed": 796, "data": {"pv_dec_string": "137,851.7021", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 3 small cubes", "__seed__": "0796"}}, {"seed": 797, "data": {"pv_dec_string": "5,536.22213", "pv_ans_text": "5 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 1 longs, and 5 small cubes", "__seed__": "0797"}}, {"seed": 798, "data": {"pv_dec_string": "3,106.82246", "pv_ans_text": "3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.55", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0798"}}, {"seed": 799, "data": {"pv_dec_string": "3,521,844.4536", "pv_ans_text": "3 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.315", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 5 small cubes", "__seed__": "0799"}}, {"seed": 800, "data": {"pv_dec_string": "5,679.23631", "pv_ans_text": "5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 7 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.64", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 4 small cubes", "__seed__": "0800"}}, {"seed": 801, "data": {"pv_dec_string": "12,060.309532", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.53", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0801"}}, {"seed": 802, "data": {"pv_dec_string": "25,412.9946", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.64", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0802"}}, {"seed": 803, "data": {"pv_dec_string": "63,119.30709", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.12", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0803"}}, {"seed": 804, "data": {"pv_dec_string": "2,319.32316", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.216", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 1 longs, and 6 small cubes", "__seed__": "0804"}}, {"seed": 805, "data": {"pv_dec_string": "528.611971", "pv_ans_text": "5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.65", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0805"}}, {"seed": 806, "data": {"pv_dec_string": "4,222.44803", "pv_ans_text": "4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0806"}}, {"seed": 807, "data": {"pv_dec_string": "9,149.21273", "pv_ans_text": "9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.22", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 2 flats, 2 longs, and 0 small cubes", "__seed__": "0807"}}, {"seed": 808, "data": {"pv_dec_string": "4,040.807341", "pv_ans_text": "4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0808"}}, {"seed": 809, "data": {"pv_dec_string": "6,905,625.8948", "pv_ans_text": "6 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 2 small cubes", "__seed__": "0809"}}, {"seed": 810, "data": {"pv_dec_string": "3,495,953.8336", "pv_ans_text": "3 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.36", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0810"}}, {"seed": 811, "data": {"pv_dec_string": "47,839.835786", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0811"}}, {"seed": 812, "data": {"pv_dec_string": "9,154,959.8552", "pv_ans_text": "9 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0812"}}, {"seed": 813, "data": {"pv_dec_string": "314,495.91847", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.13", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 3 small cubes", "__seed__": "0813"}}, {"seed": 814, "data": {"pv_dec_string": "289.930605", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.63", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0814"}}, {"seed": 815, "data": {"pv_dec_string": "825,963.4766", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.16", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0815"}}, {"seed": 816, "data": {"pv_dec_string": "237.941262", "pv_ans_text": "2 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0816"}}, {"seed": 817, "data": {"pv_dec_string": "9,340.88687", "pv_ans_text": "9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.46", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 6 longs, and 0 small cubes", "__seed__": "0817"}}, {"seed": 818, "data": {"pv_dec_string": "94,426.0761", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.06", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0818"}}, {"seed": 819, "data": {"pv_dec_string": "360.260845", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.303", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 0 longs, and 3 small cubes", "__seed__": "0819"}}, {"seed": 820, "data": {"pv_dec_string": "286.688937", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.20", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0820"}}, {"seed": 821, "data": {"pv_dec_string": "2,158.943999", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.420", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 2 longs, and 0 small cubes", "__seed__": "0821"}}, {"seed": 822, "data": {"pv_dec_string": "57,481.5844", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 1 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 5 small cubes", "__seed__": "0822"}}, {"seed": 823, "data": {"pv_dec_string": "5,537,224.0507", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 6 small cubes", "__seed__": "0823"}}, {"seed": 824, "data": {"pv_dec_string": "24,528.3852", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 3 longs, and 6 small cubes", "__seed__": "0824"}}, {"seed": 825, "data": {"pv_dec_string": "68,574.5651", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.61", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0825"}}, {"seed": 826, "data": {"pv_dec_string": "227,068.9355", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.114", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 1 longs, and 4 small cubes", "__seed__": "0826"}}, {"seed": 827, "data": {"pv_dec_string": "8,730.023861", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0827"}}, {"seed": 828, "data": {"pv_dec_string": "79,031.768639", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0828"}}, {"seed": 829, "data": {"pv_dec_string": "239,935.63914", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.50", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0829"}}, {"seed": 830, "data": {"pv_dec_string": "2,934,528.6203", "pv_ans_text": "2 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 8 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 5 small cubes", "__seed__": "0830"}}, {"seed": 831, "data": {"pv_dec_string": "896,738.241", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.304", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 0 longs, and 4 small cubes", "__seed__": "0831"}}, {"seed": 832, "data": {"pv_dec_string": "72,358.849275", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.01", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0832"}}, {"seed": 833, "data": {"pv_dec_string": "701.719424", "pv_ans_text": "7 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.101", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 0 longs, and 1 small cubes", "__seed__": "0833"}}, {"seed": 834, "data": {"pv_dec_string": "39,180.06854", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0834"}}, {"seed": 835, "data": {"pv_dec_string": "88,060.3143", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.330", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0835"}}, {"seed": 836, "data": {"pv_dec_string": "25,780.892389", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.35", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0836"}}, {"seed": 837, "data": {"pv_dec_string": "96,401.159261", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 3 small cubes", "__seed__": "0837"}}, {"seed": 838, "data": {"pv_dec_string": "470.628804", "pv_ans_text": "4 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 4 small cubes", "__seed__": "0838"}}, {"seed": 839, "data": {"pv_dec_string": "97,627.968335", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 2 small cubes", "__seed__": "0839"}}, {"seed": 840, "data": {"pv_dec_string": "3,141,451.0023", "pv_ans_text": "3 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.154", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 5 longs, and 4 small cubes", "__seed__": "0840"}}, {"seed": 841, "data": {"pv_dec_string": "93,040.007926", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 4 small cubes", "__seed__": "0841"}}, {"seed": 842, "data": {"pv_dec_string": "81,095.770751", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.041", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 1 small cubes", "__seed__": "0842"}}, {"seed": 843, "data": {"pv_dec_string": "645,005.069", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 6 small cubes", "__seed__": "0843"}}, {"seed": 844, "data": {"pv_dec_string": "19,341.179", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.560", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 5 flats, 6 longs, and 0 small cubes", "__seed__": "0844"}}, {"seed": 845, "data": {"pv_dec_string": "764.960367", "pv_ans_text": "7 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.06", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0845"}}, {"seed": 846, "data": {"pv_dec_string": "7,623,486.4051", "pv_ans_text": "7 is in the millions (1,000,000) place. 6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.231", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 2 flats, 3 longs, and 1 small cubes", "__seed__": "0846"}}, {"seed": 847, "data": {"pv_dec_string": "2,929.397663", "pv_ans_text": "2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 3 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.415", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 5 small cubes", "__seed__": "0847"}}, {"seed": 848, "data": {"pv_dec_string": "8,838.84131", "pv_ans_text": "8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0848"}}, {"seed": 849, "data": {"pv_dec_string": "2,143.019342", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 1 small cubes", "__seed__": "0849"}}, {"seed": 850, "data": {"pv_dec_string": "43,485.55361", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 8 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0850"}}, {"seed": 851, "data": {"pv_dec_string": "3,141,471.7747", "pv_ans_text": "3 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0851"}}, {"seed": 852, "data": {"pv_dec_string": "366.081626", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.14", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0852"}}, {"seed": 853, "data": {"pv_dec_string": "76,660.90167", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.106", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 0 longs, and 6 small cubes", "__seed__": "0853"}}, {"seed": 854, "data": {"pv_dec_string": "8,738,863.2886", "pv_ans_text": "8 is in the millions (1,000,000) place. 7 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.134", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0854"}}, {"seed": 855, "data": {"pv_dec_string": "6,860.917275", "pv_ans_text": "6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.16", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0855"}}, {"seed": 856, "data": {"pv_dec_string": "7,058,415.8888", "pv_ans_text": "7 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.346", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 4 longs, and 6 small cubes", "__seed__": "0856"}}, {"seed": 857, "data": {"pv_dec_string": "1,056.246383", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 6 longs, and 6 small cubes", "__seed__": "0857"}}, {"seed": 858, "data": {"pv_dec_string": "49,217.5895", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 1 is in the tens (10) place. 7 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0858"}}, {"seed": 859, "data": {"pv_dec_string": "63,775.77899", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.54", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 4 longs, and 0 small cubes", "__seed__": "0859"}}, {"seed": 860, "data": {"pv_dec_string": "4,292.332829", "pv_ans_text": "4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.35", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 5 small cubes", "__seed__": "0860"}}, {"seed": 861, "data": {"pv_dec_string": "2,860,849.7696", "pv_ans_text": "2 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.435", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 3 longs, and 5 small cubes", "__seed__": "0861"}}, {"seed": 862, "data": {"pv_dec_string": "59,158.9345", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 0 small cubes", "__seed__": "0862"}}, {"seed": 863, "data": {"pv_dec_string": "2,437.833286", "pv_ans_text": "2 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.041", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 4 longs, and 1 small cubes", "__seed__": "0863"}}, {"seed": 864, "data": {"pv_dec_string": "7,907.06143", "pv_ans_text": "7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.14", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0864"}}, {"seed": 865, "data": {"pv_dec_string": "5,806,329.2269", "pv_ans_text": "5 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 5 small cubes", "__seed__": "0865"}}, {"seed": 866, "data": {"pv_dec_string": "76,300.30147", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 0 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0866"}}, {"seed": 867, "data": {"pv_dec_string": "564,909.6677", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 9 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.11", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 1 longs, and 1 small cubes", "__seed__": "0867"}}, {"seed": 868, "data": {"pv_dec_string": "246,635.7395", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 7 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.52", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 5 flats, 2 longs, and 0 small cubes", "__seed__": "0868"}}, {"seed": 869, "data": {"pv_dec_string": "98,118.42689", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 5 small cubes", "__seed__": "0869"}}, {"seed": 870, "data": {"pv_dec_string": "2,199.05934", "pv_ans_text": "2 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.46", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 6 small cubes", "__seed__": "0870"}}, {"seed": 871, "data": {"pv_dec_string": "71,556.0343", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.24", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0871"}}, {"seed": 872, "data": {"pv_dec_string": "13,823.78826", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 3 is in the units (1) place. 7 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.61", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 6 flats, 1 longs, and 0 small cubes", "__seed__": "0872"}}, {"seed": 873, "data": {"pv_dec_string": "812,949.4641", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.01", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0873"}}, {"seed": 874, "data": {"pv_dec_string": "423,821.4807", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.640", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0874"}}, {"seed": 875, "data": {"pv_dec_string": "84,047.65976", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 0 longs, and 2 small cubes", "__seed__": "0875"}}, {"seed": 876, "data": {"pv_dec_string": "1,004.49533", "pv_ans_text": "1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 4 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0876"}}, {"seed": 877, "data": {"pv_dec_string": "53,683.2606", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 4 small cubes", "__seed__": "0877"}}, {"seed": 878, "data": {"pv_dec_string": "629,607.87665", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 5 small cubes", "__seed__": "0878"}}, {"seed": 879, "data": {"pv_dec_string": "58,290.90895", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 9 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.462", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 2 small cubes", "__seed__": "0879"}}, {"seed": 880, "data": {"pv_dec_string": "286.457961", "pv_ans_text": "2 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.36", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 6 longs, and 0 small cubes", "__seed__": "0880"}}, {"seed": 881, "data": {"pv_dec_string": "4,827.75142", "pv_ans_text": "4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 3 small cubes", "__seed__": "0881"}}, {"seed": 882, "data": {"pv_dec_string": "523,490.0661", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 0 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 2 small cubes", "__seed__": "0882"}}, {"seed": 883, "data": {"pv_dec_string": "2,389.112245", "pv_ans_text": "2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.45", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0883"}}, {"seed": 884, "data": {"pv_dec_string": "88,645.20293", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 6 small cubes", "__seed__": "0884"}}, {"seed": 885, "data": {"pv_dec_string": "366,546.6353", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 6 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 4 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0885"}}, {"seed": 886, "data": {"pv_dec_string": "670.618051", "pv_ans_text": "6 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.20", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 0 small cubes", "__seed__": "0886"}}, {"seed": 887, "data": {"pv_dec_string": "8,455.05376", "pv_ans_text": "8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0887"}}, {"seed": 888, "data": {"pv_dec_string": "843,156.4569", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.65", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 6 longs, and 5 small cubes", "__seed__": "0888"}}, {"seed": 889, "data": {"pv_dec_string": "53,556.6062", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.26", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 2 flats, 6 longs, and 0 small cubes", "__seed__": "0889"}}, {"seed": 890, "data": {"pv_dec_string": "936,941.4462", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 1 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0890"}}, {"seed": 891, "data": {"pv_dec_string": "825,355.96755", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.24", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 4 longs, and 0 small cubes", "__seed__": "0891"}}, {"seed": 892, "data": {"pv_dec_string": "777,035.8932", "pv_ans_text": "7 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.60", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0892"}}, {"seed": 893, "data": {"pv_dec_string": "78,197.30602", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 0 longs, and 2 small cubes", "__seed__": "0893"}}, {"seed": 894, "data": {"pv_dec_string": "212.661875", "pv_ans_text": "2 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.042", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 4 longs, and 2 small cubes", "__seed__": "0894"}}, {"seed": 895, "data": {"pv_dec_string": "774.592938", "pv_ans_text": "7 is in the hundreds (100) place. 7 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.563", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 6 longs, and 3 small cubes", "__seed__": "0895"}}, {"seed": 896, "data": {"pv_dec_string": "399.02823", "pv_ans_text": "3 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 0 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.452", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 5 longs, and 2 small cubes", "__seed__": "0896"}}, {"seed": 897, "data": {"pv_dec_string": "9,404.114128", "pv_ans_text": "9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 0 small cubes", "__seed__": "0897"}}, {"seed": 898, "data": {"pv_dec_string": "8,762.405902", "pv_ans_text": "8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 2 is in the units (1) place. 4 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.65", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 5 longs, and 0 small cubes", "__seed__": "0898"}}, {"seed": 899, "data": {"pv_dec_string": "53,858.22873", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0899"}}, {"seed": 900, "data": {"pv_dec_string": "5,855.016295", "pv_ans_text": "5 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.03", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0900"}}, {"seed": 901, "data": {"pv_dec_string": "5,342.745307", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 0 small cubes", "__seed__": "0901"}}, {"seed": 902, "data": {"pv_dec_string": "16,906.543097", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0902"}}, {"seed": 903, "data": {"pv_dec_string": "38,842.3546", "pv_ans_text": "3 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.26", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 6 small cubes", "__seed__": "0903"}}, {"seed": 904, "data": {"pv_dec_string": "1,791.97631", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.00", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0904"}}, {"seed": 905, "data": {"pv_dec_string": "25,049.17248", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.31", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 3 flats, 1 longs, and 0 small cubes", "__seed__": "0905"}}, {"seed": 906, "data": {"pv_dec_string": "488.553994", "pv_ans_text": "4 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0906"}}, {"seed": 907, "data": {"pv_dec_string": "49,435.9773", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.541", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 4 longs, and 1 small cubes", "__seed__": "0907"}}, {"seed": 908, "data": {"pv_dec_string": "1,793.640606", "pv_ans_text": "1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.315", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 3 flats, 1 longs, and 5 small cubes", "__seed__": "0908"}}, {"seed": 909, "data": {"pv_dec_string": "3,603.68699", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 0 is in the tens (10) place. 3 is in the units (1) place. 6 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.53", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 3 longs, and 0 small cubes", "__seed__": "0909"}}, {"seed": 910, "data": {"pv_dec_string": "369.719855", "pv_ans_text": "3 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 1 small cubes", "__seed__": "0910"}}, {"seed": 911, "data": {"pv_dec_string": "20,664.93707", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 4 small cubes", "__seed__": "0911"}}, {"seed": 912, "data": {"pv_dec_string": "1,949.42253", "pv_ans_text": "1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 9 is in the units (1) place. 4 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.64", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 6 flats, 4 longs, and 0 small cubes", "__seed__": "0912"}}, {"seed": 913, "data": {"pv_dec_string": "2,506.185793", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 0 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.14", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 4 small cubes", "__seed__": "0913"}}, {"seed": 914, "data": {"pv_dec_string": "8,569.87741", "pv_ans_text": "8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0914"}}, {"seed": 915, "data": {"pv_dec_string": "92,356.81497", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 6 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.006", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 0 longs, and 6 small cubes", "__seed__": "0915"}}, {"seed": 916, "data": {"pv_dec_string": "613,460.6016", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 6 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.01", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 1 longs, and 0 small cubes", "__seed__": "0916"}}, {"seed": 917, "data": {"pv_dec_string": "6,952.544401", "pv_ans_text": "6 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 5 is in the tens (10) place. 2 is in the units (1) place. 5 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.45", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0917"}}, {"seed": 918, "data": {"pv_dec_string": "1,896.79976", "pv_ans_text": "1 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 9 is in the tens (10) place. 6 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.20", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0918"}}, {"seed": 919, "data": {"pv_dec_string": "58,720.458901", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 0 is in the units (1) place. 4 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 5 longs, and 2 small cubes", "__seed__": "0919"}}, {"seed": 920, "data": {"pv_dec_string": "94,455.4786", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 4 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.45", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 5 small cubes", "__seed__": "0920"}}, {"seed": 921, "data": {"pv_dec_string": "401,914.6125", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 1 is in the tens (10) place. 4 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.35", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0921"}}, {"seed": 922, "data": {"pv_dec_string": "235,612.61329", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 3 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.465", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 4 flats, 6 longs, and 5 small cubes", "__seed__": "0922"}}, {"seed": 923, "data": {"pv_dec_string": "61,713.3033", "pv_ans_text": "6 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.14", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 4 longs, and 0 small cubes", "__seed__": "0923"}}, {"seed": 924, "data": {"pv_dec_string": "456,025.26972", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 2 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0924"}}, {"seed": 925, "data": {"pv_dec_string": "1,959,889.8676", "pv_ans_text": "1 is in the millions (1,000,000) place. 9 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 8 is in the tens (10) place. 9 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.20", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 2 flats, 0 longs, and 0 small cubes", "__seed__": "0925"}}, {"seed": 926, "data": {"pv_dec_string": "5,085,415.9562", "pv_ans_text": "5 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.61", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 6 longs, and 1 small cubes", "__seed__": "0926"}}, {"seed": 927, "data": {"pv_dec_string": "586.677972", "pv_ans_text": "5 is in the hundreds (100) place. 8 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.40", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 0 longs, and 0 small cubes", "__seed__": "0927"}}, {"seed": 928, "data": {"pv_dec_string": "76,740.269862", "pv_ans_text": "7 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 0 is in the units (1) place. 2 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.02", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 2 small cubes", "__seed__": "0928"}}, {"seed": 929, "data": {"pv_dec_string": "25,188.4471", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 4 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "2.15", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0929"}}, {"seed": 930, "data": {"pv_dec_string": "9,273.148411", "pv_ans_text": "9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 5 small cubes", "__seed__": "0930"}}, {"seed": 931, "data": {"pv_dec_string": "83,935.9738", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.15", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0931"}}, {"seed": 932, "data": {"pv_dec_string": "3,647.14824", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 4 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.12", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 1 longs, and 2 small cubes", "__seed__": "0932"}}, {"seed": 933, "data": {"pv_dec_string": "440,838.21874", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 8 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.06", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0933"}}, {"seed": 934, "data": {"pv_dec_string": "288,575.91133", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "2.24", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 2 longs, and 4 small cubes", "__seed__": "0934"}}, {"seed": 935, "data": {"pv_dec_string": "332.125964", "pv_ans_text": "3 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 1 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.60", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 0 longs, and 0 small cubes", "__seed__": "0935"}}, {"seed": 936, "data": {"pv_dec_string": "196,526.143", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 1 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.406", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 0 longs, and 6 small cubes", "__seed__": "0936"}}, {"seed": 937, "data": {"pv_dec_string": "598,335.03118", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.41", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0937"}}, {"seed": 938, "data": {"pv_dec_string": "301,195.6591", "pv_ans_text": "3 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 6 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.062", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 6 longs, and 2 small cubes", "__seed__": "0938"}}, {"seed": 939, "data": {"pv_dec_string": "107,943.1317", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.04", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 4 longs, and 0 small cubes", "__seed__": "0939"}}, {"seed": 940, "data": {"pv_dec_string": "80,682.696192", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 6 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.53", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 3 small cubes", "__seed__": "0940"}}, {"seed": 941, "data": {"pv_dec_string": "649,055.55455", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 5 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.11", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 1 flats, 1 longs, and 0 small cubes", "__seed__": "0941"}}, {"seed": 942, "data": {"pv_dec_string": "2,204,324.5056", "pv_ans_text": "2 is in the millions (1,000,000) place. 2 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 2 is in the tens (10) place. 4 is in the units (1) place. 5 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 2 longs, and 5 small cubes", "__seed__": "0942"}}, {"seed": 943, "data": {"pv_dec_string": "148,050.6121", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 4 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 0 is in the units (1) place. 6 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.66", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 6 longs, and 6 small cubes", "__seed__": "0943"}}, {"seed": 944, "data": {"pv_dec_string": "6,382.324914", "pv_ans_text": "6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 8 is in the tens (10) place. 2 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 4 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.32", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 2 small cubes", "__seed__": "0944"}}, {"seed": 945, "data": {"pv_dec_string": "7,854,818.115", "pv_ans_text": "7 is in the millions (1,000,000) place. 8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.25", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 5 small cubes", "__seed__": "0945"}}, {"seed": 946, "data": {"pv_dec_string": "478,402.0453", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 0 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.43", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 3 small cubes", "__seed__": "0946"}}, {"seed": 947, "data": {"pv_dec_string": "692,095.86144", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 8 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.21", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 2 longs, and 1 small cubes", "__seed__": "0947"}}, {"seed": 948, "data": {"pv_dec_string": "56,532.04067", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 3 is in the tens (10) place. 2 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.34", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 4 small cubes", "__seed__": "0948"}}, {"seed": 949, "data": {"pv_dec_string": "5,198.972383", "pv_ans_text": "5 is in the thousands (1,000) place. 1 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.665", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 6 flats, 6 longs, and 5 small cubes", "__seed__": "0949"}}, {"seed": 950, "data": {"pv_dec_string": "49,236.38851", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 3 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.160", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0950"}}, {"seed": 951, "data": {"pv_dec_string": "9,325,367.1311", "pv_ans_text": "9 is in the millions (1,000,000) place. 3 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 2 longs, and 2 small cubes", "__seed__": "0951"}}, {"seed": 952, "data": {"pv_dec_string": "2,597.35258", "pv_ans_text": "2 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.55", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 5 longs, and 5 small cubes", "__seed__": "0952"}}, {"seed": 953, "data": {"pv_dec_string": "2,521,395.027", "pv_ans_text": "2 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.63", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 6 flats, 3 longs, and 0 small cubes", "__seed__": "0953"}}, {"seed": 954, "data": {"pv_dec_string": "5,344.965075", "pv_ans_text": "5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.44", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 2 flats, 4 longs, and 4 small cubes", "__seed__": "0954"}}, {"seed": 955, "data": {"pv_dec_string": "43,743.352731", "pv_ans_text": "4 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 3 is in the units (1) place. 3 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.23", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 2 longs, and 3 small cubes", "__seed__": "0955"}}, {"seed": 956, "data": {"pv_dec_string": "16,233.134131", "pv_ans_text": "1 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 3 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.334", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 3 flats, 3 longs, and 4 small cubes", "__seed__": "0956"}}, {"seed": 957, "data": {"pv_dec_string": "403,988.8993", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.043", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 0 flats, 4 longs, and 3 small cubes", "__seed__": "0957"}}, {"seed": 958, "data": {"pv_dec_string": "5,178,719.7962", "pv_ans_text": "5 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.50", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 5 flats, 0 longs, and 0 small cubes", "__seed__": "0958"}}, {"seed": 959, "data": {"pv_dec_string": "94,499.24734", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 9 is in the tens (10) place. 9 is in the units (1) place. 2 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.06", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 6 small cubes", "__seed__": "0959"}}, {"seed": 960, "data": {"pv_dec_string": "430.555043", "pv_ans_text": "4 is in the hundreds (100) place. 3 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 3 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.03", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 0 flats, 3 longs, and 0 small cubes", "__seed__": "0960"}}, {"seed": 961, "data": {"pv_dec_string": "3,797.707445", "pv_ans_text": "3 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.40", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 4 longs, and 0 small cubes", "__seed__": "0961"}}, {"seed": 962, "data": {"pv_dec_string": "2,742.71599", "pv_ans_text": "2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 4 is in the tens (10) place. 2 is in the units (1) place. 7 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.23", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0962"}}, {"seed": 963, "data": {"pv_dec_string": "50,269.987299", "pv_ans_text": "5 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 6 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 1 longs, and 5 small cubes", "__seed__": "0963"}}, {"seed": 964, "data": {"pv_dec_string": "7,654.194937", "pv_ans_text": "7 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 5 is in the tens (10) place. 4 is in the units (1) place. 1 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 4 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.434", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 3 longs, and 4 small cubes", "__seed__": "0964"}}, {"seed": 965, "data": {"pv_dec_string": "602,231.97942", "pv_ans_text": "6 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 3 is in the tens (10) place. 1 is in the units (1) place. 9 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.232", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 2 flats, 3 longs, and 2 small cubes", "__seed__": "0965"}}, {"seed": 966, "data": {"pv_dec_string": "867.855769", "pv_ans_text": "8 is in the hundreds (100) place. 6 is in the tens (10) place. 7 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.23", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 2 flats, 3 longs, and 0 small cubes", "__seed__": "0966"}}, {"seed": 967, "data": {"pv_dec_string": "829,619.94884", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 1 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "3.503", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 5 flats, 0 longs, and 3 small cubes", "__seed__": "0967"}}, {"seed": 968, "data": {"pv_dec_string": "4,410.74516", "pv_ans_text": "4 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 1 is in the tens (10) place. 0 is in the units (1) place. 7 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "5.54", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 4 small cubes", "__seed__": "0968"}}, {"seed": 969, "data": {"pv_dec_string": "913,051.0574", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 5 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.44", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 4 flats, 4 longs, and 0 small cubes", "__seed__": "0969"}}, {"seed": 970, "data": {"pv_dec_string": "7,001,439.9936", "pv_ans_text": "7 is in the millions (1,000,000) place. 0 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 3 is in the tens (10) place. 9 is in the units (1) place. 9 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.51", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 1 small cubes", "__seed__": "0970"}}, {"seed": 971, "data": {"pv_dec_string": "3,629.072512", "pv_ans_text": "3 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 2 is in the tens (10) place. 9 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 2 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.405", "units_block_choice": "large cubes", "blocks_ans_text": "4 large cubes, 4 flats, 0 longs, and 5 small cubes", "__seed__": "0971"}}, {"seed": 972, "data": {"pv_dec_string": "6,456,871.1775", "pv_ans_text": "6 is in the millions (1,000,000) place. 4 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.16", "units_block_choice": "large cubes", "blocks_ans_text": "5 large cubes, 1 flats, 6 longs, and 0 small cubes", "__seed__": "0972"}}, {"seed": 973, "data": {"pv_dec_string": "707.183939", "pv_ans_text": "7 is in the hundreds (100) place. 0 is in the tens (10) place. 7 is in the units (1) place. 1 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 9 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.324", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 2 longs, and 4 small cubes", "__seed__": "0973"}}, {"seed": 974, "data": {"pv_dec_string": "919,470.8577", "pv_ans_text": "9 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 4 is in the hundreds (100) place. 7 is in the tens (10) place. 0 is in the units (1) place. 8 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.42", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 4 longs, and 2 small cubes", "__seed__": "0974"}}, {"seed": 975, "data": {"pv_dec_string": "83,995.2365", "pv_ans_text": "8 is in the ten-thousands (10,000) place. 3 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 5 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.30", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 3 flats, 3 longs, and 0 small cubes", "__seed__": "0975"}}, {"seed": 976, "data": {"pv_dec_string": "883.808518", "pv_ans_text": "8 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 8 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 1 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "1.002", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 0 flats, 0 longs, and 2 small cubes", "__seed__": "0976"}}, {"seed": 977, "data": {"pv_dec_string": "326.666437", "pv_ans_text": "3 is in the hundreds (100) place. 2 is in the tens (10) place. 6 is in the units (1) place. 6 is in the tenths (1/10) place. 6 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 3 is in the hundred-thousandths (1/100,000) place. 7 is in the millionths (1/1,000,00) place. ", "blocks_dec": "3.41", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 4 flats, 1 longs, and 0 small cubes", "__seed__": "0977"}}, {"seed": 978, "data": {"pv_dec_string": "854,271.11268", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 4 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 7 is in the tens (10) place. 1 is in the units (1) place. 1 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 2 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.51", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 1 longs, and 0 small cubes", "__seed__": "0978"}}, {"seed": 979, "data": {"pv_dec_string": "375.041558", "pv_ans_text": "3 is in the hundreds (100) place. 7 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.35", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 3 flats, 5 longs, and 0 small cubes", "__seed__": "0979"}}, {"seed": 980, "data": {"pv_dec_string": "597,573.9572", "pv_ans_text": "5 is in the hundred-thousands (100,000) place. 9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 7 is in the tens (10) place. 3 is in the units (1) place. 9 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 5 longs, and 0 small cubes", "__seed__": "0980"}}, {"seed": 981, "data": {"pv_dec_string": "852,764.91544", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 2 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 9 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 4 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.36", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 6 small cubes", "__seed__": "0981"}}, {"seed": 982, "data": {"pv_dec_string": "28,736.0489", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 3 is in the tens (10) place. 6 is in the units (1) place. 0 is in the tenths (1/10) place. 4 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 9 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 0 longs, and 4 small cubes", "__seed__": "0982"}}, {"seed": 983, "data": {"pv_dec_string": "2,105,390.5284", "pv_ans_text": "2 is in the millions (1,000,000) place. 1 is in the hundred-thousands (100,000) place. 0 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 9 is in the tens (10) place. 0 is in the units (1) place. 5 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 8 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.352", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 5 longs, and 2 small cubes", "__seed__": "0983"}}, {"seed": 984, "data": {"pv_dec_string": "426,353.5172", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 2 is in the ten-thousands (10,000) place. 6 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 5 is in the tens (10) place. 3 is in the units (1) place. 5 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.60", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 6 longs, and 0 small cubes", "__seed__": "0984"}}, {"seed": 985, "data": {"pv_dec_string": "281,064.72956", "pv_ans_text": "2 is in the hundred-thousands (100,000) place. 8 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 0 is in the hundreds (100) place. 6 is in the tens (10) place. 4 is in the units (1) place. 7 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 5 is in the ten-thousandths (1/10,000) place. 6 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "4.50", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 5 longs, and 0 small cubes", "__seed__": "0985"}}, {"seed": 986, "data": {"pv_dec_string": "483.070621", "pv_ans_text": "4 is in the hundreds (100) place. 8 is in the tens (10) place. 3 is in the units (1) place. 0 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.04", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 0 longs, and 4 small cubes", "__seed__": "0986"}}, {"seed": 987, "data": {"pv_dec_string": "471,376.2368", "pv_ans_text": "4 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 7 is in the tens (10) place. 6 is in the units (1) place. 2 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "1.31", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 1 flats, 3 longs, and 1 small cubes", "__seed__": "0987"}}, {"seed": 988, "data": {"pv_dec_string": "5,579,835.0037", "pv_ans_text": "5 is in the millions (1,000,000) place. 5 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 9 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 3 is in the tens (10) place. 5 is in the units (1) place. 0 is in the tenths (1/10) place. 0 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 7 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "4.41", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 4 longs, and 1 small cubes", "__seed__": "0988"}}, {"seed": 989, "data": {"pv_dec_string": "1,288.581401", "pv_ans_text": "1 is in the thousands (1,000) place. 2 is in the hundreds (100) place. 8 is in the tens (10) place. 8 is in the units (1) place. 5 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "2.05", "units_block_choice": "large cubes", "blocks_ans_text": "2 large cubes, 0 flats, 5 longs, and 0 small cubes", "__seed__": "0989"}}, {"seed": 990, "data": {"pv_dec_string": "20,301.059", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 0 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 0 is in the tens (10) place. 1 is in the units (1) place. 0 is in the tenths (1/10) place. 5 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 0 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.22", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 2 longs, and 2 small cubes", "__seed__": "0990"}}, {"seed": 991, "data": {"pv_dec_string": "177,844.32588", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 7 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 8 is in the hundreds (100) place. 4 is in the tens (10) place. 4 is in the units (1) place. 3 is in the tenths (1/10) place. 2 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 8 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "6.06", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 6 longs, and 0 small cubes", "__seed__": "0991"}}, {"seed": 992, "data": {"pv_dec_string": "851,998.8156", "pv_ans_text": "8 is in the hundred-thousands (100,000) place. 5 is in the ten-thousands (10,000) place. 1 is in the thousands (1,000) place. 9 is in the hundreds (100) place. 9 is in the tens (10) place. 8 is in the units (1) place. 8 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 5 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "5.01", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 0 longs, and 1 small cubes", "__seed__": "0992"}}, {"seed": 993, "data": {"pv_dec_string": "25,312.27085", "pv_ans_text": "2 is in the ten-thousands (10,000) place. 5 is in the thousands (1,000) place. 3 is in the hundreds (100) place. 1 is in the tens (10) place. 2 is in the units (1) place. 2 is in the tenths (1/10) place. 7 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 8 is in the ten-thousandths (1/10,000) place. 5 is in the hundred-thousandths (1/100,000) place. ", "blocks_dec": "1.516", "units_block_choice": "large cubes", "blocks_ans_text": "1 large cubes, 5 flats, 1 longs, and 6 small cubes", "__seed__": "0993"}}, {"seed": 994, "data": {"pv_dec_string": "118,665.1313", "pv_ans_text": "1 is in the hundred-thousands (100,000) place. 1 is in the ten-thousands (10,000) place. 8 is in the thousands (1,000) place. 6 is in the hundreds (100) place. 6 is in the tens (10) place. 5 is in the units (1) place. 1 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 1 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "6.054", "units_block_choice": "large cubes", "blocks_ans_text": "6 large cubes, 0 flats, 5 longs, and 4 small cubes", "__seed__": "0994"}}, {"seed": 995, "data": {"pv_dec_string": "257.933121", "pv_ans_text": "2 is in the hundreds (100) place. 5 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 3 is in the thousandths (1/1000) place. 1 is in the ten-thousandths (1/10,000) place. 2 is in the hundred-thousandths (1/100,000) place. 1 is in the millionths (1/1,000,00) place. ", "blocks_dec": "4.16", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 4 flats, 1 longs, and 6 small cubes", "__seed__": "0995"}}, {"seed": 996, "data": {"pv_dec_string": "880.219698", "pv_ans_text": "8 is in the hundreds (100) place. 8 is in the tens (10) place. 0 is in the units (1) place. 2 is in the tenths (1/10) place. 1 is in the hundredths (1/100) place. 9 is in the thousandths (1/1000) place. 6 is in the ten-thousandths (1/10,000) place. 9 is in the hundred-thousandths (1/100,000) place. 8 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.33", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 3 longs, and 3 small cubes", "__seed__": "0996"}}, {"seed": 997, "data": {"pv_dec_string": "218.936305", "pv_ans_text": "2 is in the hundreds (100) place. 1 is in the tens (10) place. 8 is in the units (1) place. 9 is in the tenths (1/10) place. 3 is in the hundredths (1/100) place. 6 is in the thousandths (1/1000) place. 3 is in the ten-thousandths (1/10,000) place. 0 is in the hundred-thousandths (1/100,000) place. 5 is in the millionths (1/1,000,00) place. ", "blocks_dec": "6.15", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 6 flats, 1 longs, and 5 small cubes", "__seed__": "0997"}}, {"seed": 998, "data": {"pv_dec_string": "8,597.980476", "pv_ans_text": "8 is in the thousands (1,000) place. 5 is in the hundreds (100) place. 9 is in the tens (10) place. 7 is in the units (1) place. 9 is in the tenths (1/10) place. 8 is in the hundredths (1/100) place. 0 is in the thousandths (1/1000) place. 4 is in the ten-thousandths (1/10,000) place. 7 is in the hundred-thousandths (1/100,000) place. 6 is in the millionths (1/1,000,00) place. ", "blocks_dec": "5.52", "units_block_choice": "flats", "blocks_ans_text": "0 large cubes, 5 flats, 5 longs, and 2 small cubes", "__seed__": "0998"}}, {"seed": 999, "data": {"pv_dec_string": "97,727.7972", "pv_ans_text": "9 is in the ten-thousands (10,000) place. 7 is in the thousands (1,000) place. 7 is in the hundreds (100) place. 2 is in the tens (10) place. 7 is in the units (1) place. 7 is in the tenths (1/10) place. 9 is in the hundredths (1/100) place. 7 is in the thousandths (1/1000) place. 2 is in the ten-thousandths (1/10,000) place. ", "blocks_dec": "3.356", "units_block_choice": "large cubes", "blocks_ans_text": "3 large cubes, 3 flats, 5 longs, and 6 small cubes", "__seed__": "0999"}}]}]} \ No newline at end of file