Chapter 11.2, Problem 16OE

To determine

To find: Whether the decimal form terminates or repeats.

Answer to Problem 16OE

The decimal form repeats.

Explanation of Solution

Given information:

The given fraction is,

  $\frac{8}{13}$

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,

  $-\frac{8}{13}=-13\begin{array}{c}\hfill -0.6153846\\ \hfill \overline{)\begin{array}{l}080\\ \underset{\_}{-78}\\ 020\\ \underset{\_}{-013}\\ 070\\ \underset{\_}{-65}\\ 050\\ \underset{\_}{-039}\\ 0110\\ \underset{\_}{-104}\\ 0060\\ \underset{\_}{-052}\\ 080\\ \underset{\_}{-078}\\ 020\end{array}}\end{array}$

The remainder of the division is not zero, so the decimal form is repeating.

Thus, the decimal form repeats.