Question
The number \(0.\overline{3}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is:
(a) \( \frac{33}{100} \)
(b) \( \frac{3}{10} \)
(c) \( \frac{1}{3} \)
(d) \( \frac{3}{100} \)
Solution
Let \( x = 0.\overline{3} \)
\[ x = 0.3333\ldots \]
Multiply both sides by 10:
\[ 10x = 3.3333\ldots \]
Subtract the original equation:
\[ 10x – x = 3.3333\ldots – 0.3333\ldots \]
\[ 9x = 3 \]
\[ x = \frac{3}{9} = \frac{1}{3} \]
Final Answer
✔ Correct option: (c) \( \frac{1}{3} \)