How do you convert 0.7777 as a fraction?

Nov 7, 2015

Derivation of Raja's given answer may prove useful!
Method can be applied to repeating groups of decimal values

Explanation:

$x = 0.7777 \overline{7}$ ...................(1)

$10 x = 7.777 \overline{7}$....................(2)

(2) - (1)

$x \left(10 - 1\right) = 7$
$x = \frac{7}{9}$