Question

convert this repeating decimal into a fraction. simplify completely. 0.overline{2}=\frac{?}{}

Explanation:

Step1: Let x = 0.222...

$x = 0.\overline{2}$

Step2: Multiply x by 10

$10x=2.222...$

Step3: Subtract x from 10x

$10x - x=2.222... - 0.222...$
$9x = 2$

Step4: Solve for x

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

Answer:

$\frac{2}{9}$