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1. Euclids Algorithm and Real Numbers
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Q2 of 128 Page 20

Following real numbers are expressed in decimal form. Find whether they are rational or not. If rational. express them in form p/q. Comment on factors of q:

Let × = 0. 142857142857142…. …eq(1)


As there are 6 repeating digits. So we multiply by 106


106 × = 142857. 14285714…. …..eq(2)


Subtracting (1) from (2):


99999 × = 142857




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Questions · 128
1. Euclids Algorithm and Real Numbers
1 2 3 4 5 6 1 1 1 2 3 4 1 1 1 1 2 2 2 2 3 3 3 4 4 4 4 4 5 6 7 8 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43
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