Micro-challenge: Special Event

[Albert Chan]

(12-27-2022 08:28 PM)John Keith Wrote:  4945/2016, hence the repeating decimals ,,,,
Result: a string, "2.45287_698412_", where the underscores surround the repeating digits.

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)