Question

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

Explanation:

Step1: Let x equal the decimal.

Let $x = 0.\overline{63}$.

Step2: Multiply x by a power of 10.

Since two digits repeat, multiply by 100: $100x=63.\overline{63}$.

Step3: Subtract x from 100x.

$100x - x=63.\overline{63}-0.\overline{63}$.
$99x = 63$.

Step4: Solve for x.

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

Step5: Simplify the fraction.

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

Answer:

$\frac{7}{11}$