Chapter 11.2, Problem 16WE

To determine

To find: The rational number as the terminating or repeating decimal.

Answer to Problem 16WE

The decimal form of the rational number is $0.\overline{594}$ .

Explanation of Solution

Given information:

The given fraction is,

  $\frac{22}{37}$

Concept used:

If the remainder of the division is zero, the decimal form of the fraction is called a terminating.

The given fraction can be written as,

  $\frac{22}{37}=37\begin{array}{c}\hfill 0.594594\\ \hfill \overline{)\begin{array}{l}220\\ \underset{\_}{-185}\\ 0350\\ \underset{\_}{-333}\\ 0170\\ \underset{\_}{-148}\\ 220\\ \underset{\_}{-185}\\ 0350\\ \underset{\_}{-333}\\ 0170\\ \underset{\_}{-148}\\ 22\end{array}}\end{array}$

Thus, the decimal form of the rational number is $0.\overline{594}$ .