The number of decimal places after which the decimal expansion of the rational number 23/(2^2 x 5) will terminate, is A. 1 B. 2

Question

The number of decimal places after which the decimal expansion of the rational number \(\frac{23}{2^2\times 5}\) will terminate, is

A. 1

B. 2

C. 3

D. 4

Answer 1

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.

The maximum power of 2 or 5 in the given rational number is 2.

So, it will terminate after 2 places of decimals.