Question

question
convert the following repeating decimal to a fraction in simplest form.
.63

Explanation:

Step1: Let x = 0.6363...

$x = 0.6363\cdots$

Step2: Multiply x by 100

$100x=63.6363\cdots$

Step3: Subtract x from 100x

$100x - x=63.6363\cdots - 0.6363\cdots$
$99x = 63$

Step4: Solve for x

$x=\frac{63}{99}$

Step5: Simplify the fraction

$x=\frac{63\div9}{99\div9}=\frac{7}{11}$

Answer:

$\frac{7}{11}$