Question

convert this repeating decimal into a fraction. simplify completely. 0.\overline{1}=\frac{?}{?}

Explanation:

Step1: Let x = 0.111...

$x = 0.\overline{1}$

Step2: Multiply both sides by 10

$10x=1.\overline{1}$

Step3: Subtract the original equation from the multiplied - one

$10x - x=(1.\overline{1})-(0.\overline{1})$
$9x = 1$

Step4: Solve for x

$x=\frac{1}{9}$

Answer:

$\frac{1}{9}$