Answer
The rational number of $0.54\overline{54}$ is $\frac{54}{99}$.
Work Step by Step
$0.54\overline{54}$ = $\frac{54}{100}$ + $\frac{54}{10000}$ + $\frac{54}{1000000}$ + ...
The sum is the total sum of all the terms of the infinite geometric series with $a_{1} = \frac{54}{100}$ and $r = \frac{1}{100}$ whose general term $a_{n} = \frac{54}{100}(\frac{1}{100})^{n - 1}$ with n = number of terms in the series.
For $0.54\overline{54}$, it is equal to $\frac{\frac{54}{100}}{1 - \frac{1}{100}}$
= $\frac{54}{99}$
The rational number of $0.54\overline{54}$ is $\frac{54}{99}$.
