## College Algebra (6th Edition)

The repeating decimal as a fraction in lowest term = $\frac{529}{999}$
Given repeating decimal can be written as an infinite geometric series. = $\frac{529}{1000}$ + $\frac{529}{1000000}$ + $\frac{529}{1000000000}$ + ..................................... First term $a_{1}$ = $\frac{529}{1000}$ Common ratio = $\frac{1}{1000}$ To express the repeating decimal as a fraction in lowest term we sum the obtained infinite geometric series. = $\frac{a_{1}}{1 - r}$ = $\frac{\frac{529}{1000}}{1 - \frac{1}{1000}}$ = $\frac{\frac{529}{1000}}{\frac{999}{1000}}$ = $\frac{529}{999}$