# The smallest rational number by which

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).