Answer
the repeating decimal as a fraction in lowest term = $\frac{257}{999}$
Work Step by Step
Given repeating decimal can be written as an infinite geometric series.
= $\frac{257}{1000}$ + $\frac{257}{1000000}$ + $\frac{257}{1000000000}$ + .....................................
First term $a_{1}$ = $\frac{257}{1000}$
Common ratio = $\frac{1}{1000}$
To express the repeating decimal as a fraction in lowest term we sum the obtained infinite geometric series.
= $\frac{a_{1}}{1 - r}$ = $\frac{\frac{257}{1000}}{1 - \frac{1}{1000}}$ = $\frac{\frac{257}{1000}}{\frac{999}{1000}}$ = $\frac{257}{999}$