What is the value of \(0.\overline{36}+0.\overline{5}-0.\overline{18}\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{73}{99}\)
A pure recurring decimal equals the repeating block over as many 9s as it has digits: \(0.\overline{36}=\frac{36}{99}\), \(0.\overline{5}=\frac{5}{9}\), \(0.\overline{18}=\frac{18}{99}\).
\(\displaystyle0.\overline{5}=\frac{5}{9}=\frac{55}{99}\)
\(\displaystyle\frac{36}{99}+\frac{55}{99}-\frac{18}{99}=\frac{36+55-18}{99}\)
\(\displaystyle=\frac{73}{99}\)