Question
The value of \(0.\overline{2} \times 0.\overline{5}\) is:
(a) 1
(b) \( \frac{10}{9} \)
(c) \( \frac{10}{81} \)
(d) \( \frac{10}{99} \)
Solution
Convert recurring decimals into fractions:
\[ 0.\overline{2} = \frac{2}{9} \]
\[ 0.\overline{5} = \frac{5}{9} \]
Multiply them:
\[ \frac{2}{9} \times \frac{5}{9} = \frac{10}{81} \]
Final Answer
✔ Correct option: (c) \( \frac{10}{81} \)