Chapter 12.3, Problem 8CFU

To determine

To calculate:

The given repeating decimal as a fraction.

Answer to Problem 8CFU

The repeating decimal as a fraction of $0.\overline{7}$ is $\frac{7}{9}$ .

Explanation of Solution

Given information:

Repeating decimal $=0.\overline{7}$

Calculation:

  $0.\overline{7}=\frac{7}{10}+\frac{7}{100}+\frac{7}{1000}+\mathrm{...}$

In this series, $a_1=\frac{7}{10}$ and $r=\frac{1}{10}$

  $\begin{array}{l}S=\frac{a_1}{1-r}\\ =\frac{\frac{7}{10}}{1-\frac{1}{10}}\\ =\frac{7}{9}\\ =\frac{7}{9}\end{array}$

Hence, the repeating decimal as a fraction is $\frac{7}{9}$ .