Question

convert this repeating decimal into a fraction. simplify completely. 0.\overline{4}=\frac{4}{?}

Explanation:

Step1: Let x = 0.444...

$x = 0.\overline{4}$

Step2: Multiply both sides by 10

$10x=4.444...$

Step3: Subtract the original equation from the multiplied - one

$10x - x=(4.444...) - (0.444...)$
$9x = 4$

Step4: Solve for x

$x=\frac{4}{9}$

Answer:

$\frac{4}{9}$