Question

convert the following repeating decimal to a fraction in simplest form. .4

Explanation:

Step1: Let x = 0.444...

$x = 0.\overline{4}$

Step2: Multiply both sides by 10

$10x=4.\overline{4}$

Step3: Subtract x from 10x

$10x - x=4.\overline{4}-0.\overline{4}$
$9x = 4$

Step4: Solve for x

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

Answer:

$\frac{4}{9}$