Question

determine the fraction that is equivalent to the repeating decimal 0.98̅. (be sure to enter the fraction in reduced form.) provide your answer below:

Explanation:

Step1: Let \(x = 0.\overline{98}\)

\(x=0.989898\cdots\)

Step2: Multiply \(x\) by 100

Since there are 2 repeating digits, \(100x = 98.9898\cdots\)

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

\(100x - x=98.9898\cdots - 0.9898\cdots\)
\(99x = 98\)

Step4: Solve for \(x\)

\(x=\frac{98}{99}\)

Answer:

\(\frac{98}{99}\)