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Page 1 of 6, Mathematics, (Chapter-1) (Real Numbers), (Class X), Exercise 1.4, Question 1:, Without actually performing the long division, state whether the following, rational numbers will have a terminating decimal expansion or a non-, terminating repeating decimal expansion:, 13, 17, 64, 15, (i), 3125, (ii), 8, (iii), 455, (iv), 1600, 29, 23, 129, (v), 343, (vi), 2'5, (vii), 2 5 7, (viii), 15, 35, 77, (ix), 50, (x), 210, Answer 1:, 13, (i), 3125, 3125 = 5*, The denominator is of the form 5m., Hence, the decimal expansion of, 13, is terminating., 3125, 17, (ii), 8, 8 = 2', The denominator is of the form 2m., 17, Hence, the decimal expansion of, -is terminating., 8, 64, (ii), 455, 455 = 5 x 7 x 13, Since the denominator is not in the form 2m x 5", and it also contains 7, and 13 as its factors, its decimal expansion will be non-terminating, repeating., 1 | Page

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Page 2 of 6, 15, (iv), 1600, 1600 = 26 x 52, The denominator is of the form 2m x 5"., 15, Hence, the decimal expansion of, is terminating., 1600, 29, (v), 343, 343 = 7', Since the denominator is not in the form 2m x 5", and it has 7 as its, factor, the decimal expansion of, 29, is non-terminating repeating., 343, (vi), 23, The derfominator is of the form 2m x 5"., Hence, the decimal expansion of, 23, -is terminating., 2'x5, 129, (vii), Sincethe dehominator is not of the form 2m x 5", and it also has 7 as, its factor, the decimal expansion of, 129, -is non-terminating, 2' x5' x7, repeating., 6 2x3 2, (vii), 15 3x5 5, The denominator is of the form 5"., 6., -is terminating., 15, Hence, the decimal expansion of, 35, (ix), 7x5, 7, %3D, 50 10x5 10, 10 = 2x5, 2 | Page

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Page 3 of 6, The denominator is of the form 2m x 5"., Hence, the decimal expansion of, 35, is terminating., 50, 77, 11x7, 11, (x), 210 30x7, %3D, %3D, 30, 30 = 2x3x5, Since the denominator is not of the form 2m x 5", and it also has 3 as, 77, its factors, the decimal expansion of, is non-terminating repeating., 210, Question 2:, Write down the decimal expansions of those rational numbers in Question, 1 above which have terminating decimal expansions., Answer 2:, 13, =0.00416, 0.00416, 3125)13.00000, (i), 3125, 130, 1300, 13000, 12500, 5000, 3125, 18750, 18750, 3 | Page

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Page 4 of 6, 2.125, (i) "-2.125, 8) 17, 8, 16, 10, 8., 20, 16, 40, 40, 0.009375, 15, = 0.009375, 1600, (iv), 1600)15.000000, 150, 1500, 15000, 14400, 6000, 4800, 12000, 11200, 8000, 8000, 4 | Page

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Page 5 of 6, 0.115, (vi), 2'x5, 23, 23, 0.115, 200)23.000, 200, 230, 200, 300, 200, 1000, 1000, 0.4, 6 2x3 2, = 0.4, 15 3x5 5, (vii), 5)2.0, 20, 20, 0.7, 35, = 0.7, 50, 50)35.0, (ix), 350, 350, 5 | Page