Question
The number \(0.3\overline{2}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is:
(a) \( \frac{8}{25} \)
(b) \( \frac{29}{90} \)
(c) \( \frac{32}{99} \)
(d) \( \frac{32}{199} \)
Solution
Let \( x = 0.3\overline{2} = 0.32222\ldots \)
Multiply by 10:
\[ 10x = 3.2222\ldots \]
Multiply by 100:
\[ 100x = 32.2222\ldots \]
Subtract:
\[ 100x – 10x = 32.2222\ldots – 3.2222\ldots \]
\[ 90x = 29 \]
\[ x = \frac{29}{90} \]
Final Answer
✔ Correct option: (b) \( \frac{29}{90} \)