Question

question
which fraction is equivalent to the repeating decimal 0.\overline{57}?
select the correct answer below:
\\(\frac{57}{100}
\\(\frac{575}{999}
\\(\frac{19}{33}
\\(\frac{19}{30}

Explanation:

Step1: Let $x = 0.\overline{57}$.

$x=0.575757\cdots$

Step2: Multiply $x$ by 100.

$100x = 57.575757\cdots$

Step3: Subtract $x$ from $100x$.

$100x - x=57.5757\cdots - 0.5757\cdots$
$99x = 57$

Step4: Solve for $x$.

$x=\frac{57}{99}=\frac{19}{33}$

Answer:

C. $\frac{19}{33}$