Question

Without actually performing the long division state whether the following rational numbers will have terminating decimal expansion or non terminating repeating decimal expansion. (1) 459/500 (2) 219/750

Answer 1

1 is terminating decimal expantion

Answer 2

Answer:

Step-by-step explanation:

A number will have terminating decimal expansion only if its denominator has prime factorisation is of the form 2^m * 5^n.

(1) 459/500

Denominator is 500

500 = 2*2*5*5*5 = 2^2 * 5^3, which is of the form 2^m * 5^n, where m=2, n=3.

Therefore, 459/500 has a terminating decimal expansion

(2)219/750

Denominator is 750

750 = 2*3*5*5*5 = 2^1 * 3^1 * 5^3, which is not of the form 2^m * 5^n.

Therefore, 219/750 has a non-terminating and repeating decimal expansion.