# How do you convert 0.6 (6 being repeated) to a fraction?

Mar 4, 2016

$0. \overline{6} = \frac{2}{3}$

#### Explanation:

Multiply by $10$ to shift one place to the left and subtract the starting number to cancel out the repeating decimal.

To do this multiply by $\left(10 - 1\right)$:

$\left(10 - 1\right) \cdot 0. \overline{6} = 6. \overline{6} - 0. \overline{6} = 6$

Then divide both sides by $\left(10 - 1\right)$ to find:

$0. \overline{6} = \frac{6}{10 - 1} = \frac{6}{9} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \cdot 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \cdot 3} = \frac{2}{3}$