Question

convert this repeating decimal into a fraction. simplify completely. 0.\overline{23}=\frac{?}{}

Explanation:

Step1: Let x = 0.2323...

$x = 0.\overline{23}$

Step2: Multiply x by 100

$100x=23.2323...$

Step3: Subtract x from 100x

$100x - x=23.2323... - 0.2323...$
$99x = 23$

Step4: Solve for x

$x=\frac{23}{99}$

Answer:

$\frac{23}{99}$