Answer
The repeating decimal as a fraction in lowest term = $\frac{5}{9}$
Work Step by Step
Given repeating decimal can be written as an infinite geometric series.
= $\frac{5}{10}$ + $\frac{5}{100}$ + $\frac{5}{1000}$ + $\frac{5}{10000}$ + .....................................
First term $a_{1}$ = $\frac{5}{10}$
Common ratio = $\frac{1}{10}$
To express the repeating decimal as a fraction in lowest term we sum the obtained infinite geometric series.
= $\frac{a_{1}}{1 - r}$ = $\frac{\frac{5}{10}}{1 - \frac{1}{10}}$ = $\frac{\frac{5}{10}}{\frac{9}{10}}$ = $\frac{5}{9}$