Chapter 12, Problem 26SGA

To determine

To find: the fraction.

Answer to Problem 26SGA

  $\frac{1760}{333}$

Explanation of Solution

Given information:

  $5.\overline{123}$

Calculation:

Convert $5.\overline{123}$ into fractions as follows:

  $\begin{array}{c}x=5.\overline{123}\\ x=\mathrm{5.123....}\mathrm{...}\left(1\right)\\ 1000x=\mathrm{5123.123...}\left[\text{Multiply both sides by 1000}\right]\mathrm{...}\left(2\right)\\ 1000x-x=\mathrm{5123.123...}-\mathrm{5.123....}\left[\text{Subtract equation}\left(2\right)\text{ from }\left(1\right)\right]\\ 999x=5118\\ x=\frac{5118}{999}\\ =\frac{1706}{999}\end{array}$

Thus the fraction is $\frac{1706}{999}$ .