Chapter 3.1, Problem 27PPS

To determine

The decimal form of the fraction $-\frac{2}{9}$ . Use a bar to show a repeating decimal.

Answer to Problem 27PPS

  $-0.\overline{2}$

Explanation of Solution

Given:

The fraction, $-\frac{2}{9}$ .

Concept Used:

To convert a fraction into an equivalent decimal, use long division method and divide the numerator by the denominator.

Calculation:

Consider the fraction, $-\frac{2}{9}$ .

In order to write the fraction as a decimal, use long division method and divide the numerator by the denominator as shown below,

  $9\begin{array}{c}\hfill 0.222\\ \hfill \overline{)\begin{array}{l}2.000\\ \underset{\_}{0}\\ 20\\ \underset{\_}{18}\\ 20\\ \underset{\_}{18}\\ 20\\ \underset{\_}{18}\\ 2\end{array}}\end{array}$

Observe that the dividend is repeating as initial numerator in every successive division. So, the quotient will be repeating as well.

Thus, the equivalent decimal for the given fraction is $-0.\overline{2}$ .