Answer
The repeating decimal as a fraction in lowest term we sum the obtained infinite geometric series. = $\frac{47}{99}$
Work Step by Step
Given repeating decimal can be written as an infinite geometric series.
= $\frac{47}{100}$ + $\frac{47}{10000}$ + $\frac{47}{1000000}$ + .....................................
First term $a_{1}$ = $\frac{47}{100}$
Common ratio = $\frac{1}{100}$
To express the repeating decimal as a fraction in lowest term we sum the obtained infinite geometric series.
= $\frac{a_{1}}{1 - r}$ = $\frac{\frac{47}{100}}{1 - \frac{1}{100}}$ = $\frac{\frac{47}{100}}{\frac{99}{100}}$ = $\frac{47}{99}$
