Question
The smallest rational number by which \( \frac{1}{3} \) should be multiplied so that its decimal expansion terminates after one place of decimal is:
(a) \( \frac{1}{10} \)
(b) \( \frac{3}{10} \)
(c) 3
(d) 30
Solution
We want: \[ \frac{1}{3} \times x = \text{terminating decimal with one decimal place} \]
A terminating decimal has denominator of the form \(2^m \times 5^n\).
To get one decimal place, denominator should be \(10 = 2 \times 5\).
Multiply \( \frac{1}{3} \) by 3 to eliminate 3 in denominator: \[ \frac{1}{3} \times 3 = 1 \]
Now to get one decimal place: \[ 1 \times \frac{1}{10} = \frac{1}{10} \]
So total multiplier: \[ 3 \times \frac{1}{10} = \frac{3}{10} \]
Final Answer
✔ Correct option: (b) \( \frac{3}{10} \)