Question

write 0.\overline{54} as a fraction.

Explanation:

Step1: Let \(x = 0.\overline{54}\)

\(x=0.545454\cdots\)

Step2: Multiply \(x\) by 100

Since there are 2 repeating digits, \(100x = 54.545454\cdots\)

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

\(100x - x=54.5454\cdots - 0.5454\cdots\)
\(99x = 54\)

Step4: Solve for \(x\)

\(x=\frac{54}{99}=\frac{6}{11}\)

Answer:

\(\frac{6}{11}\)