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Topic: Periodic decimals coincidence? (Read 373 times) |
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JocK
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Periodic decimals coincidence?
« on: May 26th, 2006, 4:19pm » |
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1/11 = 0. 0 9 0 9 0 9 ... ------> 0+9 = 9 2/11 = 0. 1 8 1 8 1 8 ... ------> 1+8 = 9 1/7 = 0. 142 857 142 857 142 857 ... ------> 142 + 857 = 999 2/7 = 0. 285 714 285 714 285 714 ... ------> 285+714 = 999 1/13 = 0. 076 923 076 923 076 923 ... ------> 076+923 = 999 2/13 = 0. 153 846 153 846 153 846 ... ------> 153+846 = 999 3/13 = 0. 230769 230769 230769 ... ------> 230+769 = 999 1/91 = 0. 010 989 010 989 010 989 ... ------> 010+989=999 1/73 = 0. 0136 9863 0136 9863 ... ------> 0136+9863 = 9999 1/17 = 0. 05882352 94117647 05882352 94117647... ------> 05882352+94117647 = 99999999 Coincidence..?
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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Barukh
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Re: Periodic decimals coincidence?
« Reply #1 on: May 27th, 2006, 4:29am » |
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No.
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Eigenray
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Re: Periodic decimals coincidence?
« Reply #2 on: May 27th, 2006, 3:50pm » |
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A fraction a/n, with (10a, n)=1, has this property iff for some r>0, the order of 10 mod p has even part 2r for all primes p|n.
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