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

Let x = p/q be a rational number, such that the prime factorization of q is of the form 2ⁿ 5^m, where n, m are non-negative integers. Then x has a decimal expansion which terminates.

So 1/3 should be multiplied by 3/10 so that it is in the form of 2ⁿ5^m.