What is the value of \(0.\overline{7}+0.\overline{25}-0.\overline{2}\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{80}{99}\)
A pure recurring decimal equals the repeating block over as many 9s as it has digits: \(0.\overline{7}=\frac{7}{9}\), \(0.\overline{25}=\frac{25}{99}\).
\(\displaystyle0.\overline{7}-0.\overline{2}=\frac{7}{9}-\frac{2}{9}=\frac{5}{9}=\frac{55}{99}\)
\(\displaystyle0.\overline{25}=\frac{25}{99}\)
\(\displaystyle\frac{55}{99}+\frac{25}{99}=\frac{80}{99}\)