Question
The value of \(0.\overline{23} + 0.\overline{22}\) is:
(a) 0.45
(b) 0.43
(c) 0.54
(d) 0.45
Solution
Convert recurring decimals into fractions:
\[ 0.\overline{23} = \frac{23}{99} \]
\[ 0.\overline{22} = \frac{22}{99} \]
Add them:
\[ \frac{23}{99} + \frac{22}{99} = \frac{45}{99} \]
Simplify:
\[ \frac{45}{99} = \frac{5}{11} \]
Convert back to decimal:
\[ \frac{5}{11} = 0.\overline{45} \]
Final Answer
✔ Correct option: (a) 0.45 (repeating)