Question

1. which of the following fractions would convert to a repeating decimal with a value greater than one? a. $\frac{14}{9}$ b. $\frac{13}{2}$ c. $\frac{5}{8}$ d. $\frac{2}{3}$

Explanation:

Step1: Convert each fraction to decimal

• For $\frac{14}{9}$, $14\div9 = 1.\overline{5}$
• For $\frac{13}{2}$, $13\div2=6.5$
• For $\frac{5}{8}$, $5\div8 = 0.625$
• For $\frac{2}{3}$, $2\div3=0.\overline{6}$

Step2: Check conditions

We want a repeating - decimal greater than 1. $\frac{5}{8}=0.625$ is not a repeating decimal and is less than 1. $\frac{13}{2} = 6.5$ is not a repeating decimal. $\frac{2}{3}=0.\overline{6}$ is a repeating decimal but less than 1. $\frac{14}{9}=1.\overline{5}$ is a repeating decimal and greater than 1.

Answer:

A. $\frac{14}{9}$