Answer
The rational number of $0.88\bar{8}$ is $\frac{8}{9}$.
Work Step by Step
$0.88\bar{8}$ = $\frac{8}{10}$ + $\frac{8}{100}$ + $\frac{8}{1000}$ + ...
The sum is the total sum of all the terms of the infinite geometric series with $a_{1} = \frac{8}{10}$ and $r = \frac{1}{10}$ whose general term $a_{n} = \frac{8}{10}(\frac{1}{10})^{n - 1}$ with n = number of terms in the series.
For $0.88\bar{8}$, it is equal to $\frac{\frac{8}{10}}{1 - \frac{1}{10}}$
= $\frac{8}{9}$
The rational number of $0.88\bar{8}$ is $\frac{8}{9}$.
