# How do you add repeating decimals?

Apr 17, 2015

You have to transform them in fraction using this way that is the most easier and faster way, and the add the fractions.

The fraction has at the numerator the difference between all the number without the dot and that part of the number that is not repeating without the dot, and at the denominator a number whose digits are a number of $9$ for how many digit are repeating, and a number of $0$ for how much digits are between the dot and the repeating digits.

Maybe it's better to see it in some examples:

E.G.: $12.3 \overline{45} = \frac{12345 - 123}{990} = \ldots$

$0.2 \overline{56} = \frac{256 - 2}{990} = \ldots$

$0. \overline{3} = \frac{3 - 0}{9}$

$12.15 \overline{6} = \frac{12156 - 1215}{900} = \ldots$.