Which of the following has/have terminating decimal expansion(s)?

(a) 

(b) 

(c) 

(d) 

Formula used:

A fraction has a terminating decimal expansion if its denominator can be expressed in the form 2^m × 5ⁿ, where m and n are non-negative integers.

Calculation:

(a)  = 

⇒ 1250 = 2 × 625 = 2 × 5⁴

Since the denominator has a factor can be expressed in the form 2m × 5n, the decimal expansion is terminating.

(b)  = 

⇒ 3125 = 3 × 5⁵

Since the denominator has a factor can be expressed in the form 2m × 5n, the decimal expansion is terminating.

(c) is in its simplest form.

455 = 5 × 7 × 13

The denominator is not in the form 2^m × 5ⁿ, so the decimal expansion is non-terminating.

(d)

192 = 2⁶ × 3

The denominator is not in the form 2^m × 5ⁿ, so the decimal expansion is non-terminating.

∴ (a) and (b) have terminating decimal expansions.