# How do you find the repeating decimal 0.7 with 7 repeated as a fraction?

Jan 14, 2017

$\frac{7}{9}$

#### Explanation:

$x = 0.777777777777 \ldots . .$

since only one digit recurs multiply by $10$

$10 x = 7.77777777777777 \ldots .$

now subtract the two eqns. to eliminate the recurring digits

$10 x = 7.77777777777777 \ldots .$

## _

$\text{ } x = 0.777777777777 \ldots . .$

## ____

$9 x = 7$

$x = \frac{7}{9}$