Move the decimal point to the right the number of places equal to the number of repeating digits. Subtract the original number. (Digits after the first instance of the pattern will be canceled.) Divide the result by a number of 9s equal to the number of repeating digits. Simplify the result.
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Example: 5.3181818_18
There are 2 repeating digits, so we subtract ...
... 531.8_18 -5.3_18 = 526.5
and divide by 99 . . . . . . two 9s, one for each of the two repeating digits
... = 526.5/99 = 5625/990 = 117/22 = 5 17/22
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More formally, if S is the value of the original number, and it has n repeating digits, you compute
.. (S·10^n - S)/(10^n -1) = S(10^n -1)/(10^n -1) = S
