I think math shortcuts and tricks are groovy. Here’s an arithmetic trick to find the fractional form of a repeating decimal.
Generally speaking, if the repeating decimal has a as the repetend, then the fraction that is represented by that repeating decimal is just a/Z where Z is a number with the same number of digits as a, but all the digits are 9’s.
For example, the let’s find the fractional form of 0.567567…
a = 567 => 0.567567… = 567/999 (= 21/37 after reduction)