# How do you convert -0.13 (3 being repeated) to a fraction?

Mar 21, 2016

$- \frac{2}{15}$

#### Explanation:

We first let -0.13 (3 being repeated) be $x$.

Since $x$ is recurring in 1 decimal places, we multiply it by ${10}^{1}$.

$10 x = - 1.33$

Next, we subtract them.

$10 x - x = - 1.33 - \left(- 0.13\right)$

$9 x = - 1.2$

Lastly, we divide both sides by 9 to get $x$ as a fraction.

$x = - \frac{1.2}{9}$

$= - \frac{12}{90}$

$= - \frac{2}{15}$

Mar 22, 2016

$- 0.13$
$x = - 0.133$
$10 x = - 1.33$
$100 x = - 13.33$
$100 x - 10 x = - 13.33 - 1.33$
$90 x = - 14.66$
$x = - \frac{1466}{9000}$
now cancel it by yourself