Question
The value of \(0.\overline{4}\) in the form \( \frac{p}{q} \), where \(q \neq 0\), is:
(a) \( \frac{4}{9} \)
(b) \( \frac{2}{5} \)
(c) \( \frac{1}{5} \)
(d) \( \frac{4}{5} \)
Solution
Let \( x = 0.\overline{4} \)
Then,
\[ x = 0.4444\ldots \]
Multiply both sides by 10:
\[ 10x = 4.4444\ldots \]
Subtract the first equation from the second:
\[ 10x – x = 4.4444\ldots – 0.4444\ldots \]
\[ 9x = 4 \]
\[ x = \frac{4}{9} \]
Final Answer
✔ Correct option: (a) \( \frac{4}{9} \)