Chapter 3.1, Problem 25PPS

To determine

The decimal form of the fraction $\frac{33}{45}$ . Use a bar to show a repeating decimal.

Answer to Problem 25PPS

  $0.7\overline{3}$

Explanation of Solution

Given:

The fraction, $\frac{33}{45}$ .

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, $\frac{33}{45}$ .

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

  $45\begin{array}{c}\hfill 0.733\\ \hfill \overline{)\begin{array}{l}33.000\\ \underset{\_}{00}\\ 330\\ \underset{\_}{315}\\ 150\\ \underset{\_}{135}\\ 150\\ \underset{\_}{135}\\ 15\end{array}}\end{array}$

Observe that after second step the dividend is repeating. So the second decimal of the quotient is repeating.

Thus, the equivalent decimal for the given fraction is $0.7\overline{3}$ .