Chapter 11.2, Problem 3WE

a.

To determine

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

Answer to Problem 3WE

The decimal form of the rational number is $-0.\overline{4}$ .

Explanation of Solution

Given information:

The given fraction is,

  $-\frac{4}{9}$

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,

  $-\frac{4}{9}=-9\begin{array}{c}\hfill -0.44\\ \hfill \overline{)\begin{array}{l}40\\ \underset{\_}{-36}\\ 40\\ \underset{\_}{-36}\\ 04\end{array}}\end{array}$

Thus, the decimal form of the rational number is $-0.\overline{4}$ .

b.

To determine

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

Answer to Problem 3WE

The decimal form of the rational number is $-0.000\overline{4}$ .

Explanation of Solution

Given information:

The given fraction is,

  $-\frac{4}{9000}$

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,

  $-\frac{4}{9000}=-9000\begin{array}{c}\hfill -0.00044\\ \hfill \overline{)\begin{array}{l}40000\\ \underset{\_}{-36000}\\ 40000\\ \underset{\_}{-36000}\\ 4000\end{array}}\end{array}$

Thus, the decimal form of the rational number is $-0.000\overline{4}$ .