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) $\frac{3}{10}$
(b) $\frac{1}{10}$
(c) 3
(d) $\frac{3}{100}$
Solution:
For terminating the decimal expansion after one place of decimal, the highest power of $m$ and $n$ in $2^{m} \times 5^{n}$ should be 1 .
Let $m=n=1$
We will get:
$\frac{1}{3} \times \frac{3}{10}=\frac{1}{10}$
$=0.1$
Thus, it is evident that we multiplied it by $\frac{3}{10}$
Hence, the correct choice is (a).
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