Chapter 5 - Number Theory and the Real Number System - Chapter Summary, Review, and Test - Review Exercises - Page 335: 47

$0.\overline{113} = \dfrac{113}{999}$

RECALL: The repeating decimal $0.\overline{a}$ where $a$ is an integer and $100 \le a \le 999$ is equal to $\frac{a}{999}$. Thus, the given repeating decimal when expressed as a quotient of two integers in lowest terms is: $0.\overline{113} = \dfrac{113}{999}$