Chapter 0.2, Problem 20E

To determine

To write:.The given repeating decimal as a fraction.

Answer to Problem 20E

The given repeating decimal as a fraction is $\frac{4}{9}$ .

Explanation of Solution

Given information:

The numberis $0.\overline{4}$ .

Calculation:

Consider the number.

  $\begin{array}{c}N=\mathrm{0.444...}\\ 10N=10\left(\mathrm{0.444...}\right)\\ 10N-N=\mathrm{4.444...}-\mathrm{0.444...}\\ 9N=4\\ N=\frac{4}{9}\end{array}$