Question

convert this repeating decimal into a fraction. simplify completely. 0.overline{19}=\frac{19}{?}

Explanation:

Step1: Let \(x = 0.\overline{19}\)

\(x=0.191919\cdots\)

Step2: Multiply \(x\) by 100

Since there are 2 repeating digits, \(100x = 19.191919\cdots\)

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

\(100x - x=19.1919\cdots - 0.1919\cdots\), which gives \(99x = 19\)

Step4: Solve for \(x\)

\(x=\frac{19}{99}\)

Answer:

\(\frac{19}{99}\)