Chapter 3.2, Problem 68SR

To determine

To find: the fraction $\frac{4}{7}$ as decimals.

Answer to Problem 68SR

The fraction $\frac{4}{7}$ in decimal form is $0.\overline{571428}$ .

Explanation of Solution

Given:

The fraction is $\frac{4}{7}$ .

Calculation:

The decimal of the fraction is calculated as follows:

  $\begin{array}{c}\frac{4}{7}=\left(7\begin{array}{c}\hfill 0.571428\\ \hfill \overline{)\begin{array}{l}\underset{\_}{\begin{array}{l}40\\ 35\end{array}}\\ \underset{\_}{\begin{array}{l}050\\ 049\end{array}}\\ \underset{\_}{\begin{array}{l}0010\\ 0007\end{array}}\\ \underset{\_}{\begin{array}{l}00030\\ 00028\end{array}}\\ \underset{\_}{\begin{array}{l}000020\\ 000014\end{array}}\\ \underset{\_}{\begin{array}{l}0000060\\ 0000056\end{array}}\\ 0000004\end{array}}\end{array}\right)\\ =0.\overline{571428}\end{array}$

Thus, the fraction $\frac{4}{7}$ in decimal form is $0.\overline{571428}$ .