#### Answer

$0.888888 = \frac{8}{9}$

#### Work Step by Step

$0.88888$
$=\frac{8}{10} +\frac{8}{10^{2}}+\frac{8}{10^{3}}+...$
$=\Sigma^{\infty}_{n=1} \frac{8}{10} (\frac{1}{10})^{n-r}$
$a=\frac{8}{10}$ and $r=\frac{1}{10}$
Therefore
$0.8888 = \frac{a}{1-r}$
$=\frac{\frac{8}{10}}{1-\frac{1}{10}}$
$=\frac{8}{9}$