Question

The smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates after one place of decimal , is

Answer 1

3/5 is the smallest rational number.

Answer 2

The smallest number is $\bold{\frac{1}{10}}$.

Solution:

To get a terminating decimal digit we use $2m \times 5n$ in the denominator.

The number of decimal digit is proportional to “m” and “n” the decimal digit is m if m > n and n if decimal digit is n.

Hence if the denominator is 2, 5 or 10 we find the decimal digits termination after one place

So the smallest number that can be multiplies by $\frac{1}{3}$ is $\frac{1}{10}$, as $\frac{1}{10}$ has 0.1.

It is the smallest decimal expansion that can be nothing is smaller than 1 except zero but that won’t be decimal.