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

3/10
1/3 * 3/10 = 1/10 = 0.1

Answer 2

Answer and explanation:

To find : The smallest rational number by which $\frac{1}{3}$ should be multiplied so that its decimal expansion terminates after one place of decimal is?

Solution :

To get a terminating decimal digit we use $2m\times 3n$ 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.

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.