Chapter 8.8, Problem 76CCR

To determine

The decimal form of the fraction $-\frac{5}{11}$ Use a bar to show a repeating decimal.

Answer to Problem 76CCR

  $-0.\overline{45}$

Explanation of Solution

Given:

The fraction: $-\frac{5}{11}$

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: $-\frac{5}{11}$

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

  $\begin{array}{l}11\begin{array}{c}\hfill 0.4545\\ \hfill \overline{)\begin{array}{l}5.000\\ \underset{\_}{0}\\ 50\\ \underset{\_}{44}\\ 60\\ \underset{\_}{55}\\ 50\\ \underset{\_}{44}\\ 60\end{array}}\end{array}\\ \underset{\_}{55}\\ 5\end{array}$

Observe that the division is repeating the initial numerator after every 2 numbers in quotient. So, the decimal equivalent is repeating.

Thus, the equivalent decimal for the given fraction is $-0.\overline{45}$ .