# Find the Fractional Form of a Repeating Decimal

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)

Written on April 9, 2013