Question

question
find an equivalent fraction for the repeating decimal 0.\overline{25}.
select the correct answer below:
\\(\frac{1}{4}
\\(\frac{28}{111}
\\(\frac{25}{99}
\\(\frac{5}{18}

Explanation:

Step1: Let \(x = 0.\overline{25}\).

\(x=0.252525\cdots\)

Step2: Multiply \(x\) by 100.

Since there are 2 repeating digits, \(100x = 25.252525\cdots\)

Step3: Subtract \(x\) from \(100x\).

\(100x - x=25.2525\cdots - 0.2525\cdots\)
\(99x = 25\)

Step4: Solve for \(x\).

\(x=\frac{25}{99}\)

Answer:

C. \(\frac{25}{99}\)