Question

The number of decimal place 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

We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is of the form, where m and n are non-negative integers.

Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.

This is given that the prime factorization of the denominator is of the form.

Hence, it has terminating decimal expansion which terminates after places of decimal.

Hence, the correct choice is (b).