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. $\frac{2}{3}$ 5. express $0.overline{2}$ as a fraction in simplest form.

Explanation:

Step1: Convert each fraction to decimal

A. $\frac{14}{9}=14\div9 = 1.\overline{5}$
B. $\frac{13}{2}=13\div2 = 6.5$ (non - repeating)
C. $\frac{5}{8}=5\div8 = 0.625$ (non - repeating)
D. $\frac{2}{3}=2\div3 = 0.\overline{6}$

Step2: Check the conditions

We want a repeating decimal greater than 1. Option A ($1.\overline{5}$) and Option D ($0.\overline{6}$) are repeating decimals. But only Option A is greater than 1.

for second part:

Step1: Let $x = 0.\overline{2}$

Then $10x=2.\overline{2}$

Step2: Subtract $x$ from $10x$

$10x - x=(2.\overline{2})-(0.\overline{2})$
$9x = 2$

Step3: Solve for $x$

$x=\frac{2}{9}$

Answer:

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