# Question #0426c

Jan 5, 2017

$0.8 \overline{7} = \frac{79}{90}$

#### Explanation:

Let $x = 0.8 \overline{7}$

$\implies 10 x = 8. \overline{7}$

$\implies 10 x - x = 8. \overline{7} - 0.8 \overline{7}$

$\implies 9 x = 8.7 - 0.8$

$\implies 9 x = 7.9$

$\implies 9 x = \frac{79}{10}$

$\implies x = \frac{79}{10} \cdot \frac{1}{9}$

$\therefore x = \frac{79}{90}$

This technique of multiplying by $10$ (or a power of $10$) and subtracting can be used to find the fractional representation of any number with infinitely repeating decimal digits. This answer contains a detailed explanation.