Micro-challenge: Special Event
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12-27-2022, 10:42 PM
Post: #20
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RE: Micro-challenge: Special Event
(12-27-2022 08:28 PM)John Keith Wrote: 4945/2016, hence the repeating decimals ,,,, Assuming fraction fully reduced., here is the math to convert to repeating decimals. Denominator 2016 = (25 * 50) * 63 non-repeating digits (after decimal point) = max(5, 0) = 5 We wanted smallest exponent k, such that 10^k ≡ 1 (mod 63) 1 (mod 63) is equivalent to 1 (mod 9) and 1 (mod 7), but 10^k ≡ 1^k ≡ 1 (mod 9) 1/7 = 0.(142857) --> repeating digits = k = order of 10 (mod 7) = 6 lua> 4945 / 2016 2.452876984126984 --> 4945/2016 = 2. 45287 (698412) |
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