Question

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after

(a) one decimal place
(b) two decimal place
(c) three decimal place
(d) four decimal place

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 (d).