Chapter 11.2, Problem 1WE

a.

To determine

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

Answer to Problem 1WE

The decimal form of the rational number is $0.\overline{6}$ .

Explanation of Solution

Given information:

The given fraction is,

  $\frac{2}{3}$

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,

  $\frac{2}{3}=3\begin{array}{c}\hfill 0.66\\ \hfill \overline{)\begin{array}{l}20\\ \underset{\_}{-18}\\ 20\\ \underset{\_}{-18}\\ 02\end{array}}\end{array}$

Thus, the decimal form of the rational number is $0.\overline{6}$ .

b.

To determine

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

Answer to Problem 1WE

The decimal form of the rational number is $0.0\overline{6}$ .

Explanation of Solution

Given information:

The given fraction is,

  $\frac{2}{30}$

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,

  $\frac{2}{30}=30\begin{array}{c}\hfill 0.066\\ \hfill \overline{)\begin{array}{l}200\\ \underset{\_}{-180}\\ 200\\ \underset{\_}{-180}\\ 020\end{array}}\end{array}$

Thus, the decimal form of the rational number is $0.0\overline{6}$ .