Question

question
find an equivalent fraction for the repeating decimal 0.\overline{16}. (be sure to enter the fraction in reduced form.)
provide your answer below:

Explanation:

Step1: Let x = 0.1616...

$x = 0.1616\cdots$

Step2: Multiply x by 100

$100x=16.1616\cdots$

Step3: Subtract x from 100x

$100x - x=16.1616\cdots - 0.1616\cdots$
$99x = 16$

Step4: Solve for x

$x=\frac{16}{99}$

Answer:

$\frac{16}{99}$