Question

question
convert the following repeating decimal to a fraction in simplest form.
.\overline{71}

Explanation:

Step1: Let x = 0.7171...

$x = 0.\overline{71}$

Step2: Multiply by 100

Since there are 2 repeating digits, multiply x by 100. So $100x=71.7171...$

Step3: Subtract x from 100x

$100x - x=(71.7171...) - (0.7171...)$
$99x = 71$

Step4: Solve for x

$x=\frac{71}{99}$
Since 71 and 99 have no common factors other than 1, the fraction is in simplest form.

Answer:

$\frac{71}{99}$