Question

Without actually performing the long division, find if 987/10500 will have terminating or non - terminating repeating decimal expansion. Give reasons for your answer.​

Answer 1

Given number 98710500

Let us find the HCF of the 987 and 10500.

987 = 3 × 7 × 47

10500 = 2 × 2 × 3 × 5 × 5 × 5 × 7

HCF of (987, 10500) = 3 × 7

HCF of (987, 10500) = 21

Divide numerator and denominator with HCF, then we get

= (987 / 21) / (10500 / 21)

= 47 / 500

987 / 10500 = 47 / 500

Denominator 500 can be written as

500 = 22 × 52

We have only 2 and 5 as factors.

∴ 987 / 10500 is terminating decimal.

if a fraction has no other prime factors other than 2 and 5, it can be represented in its lowest terms as the terminating decimal expansion.

Hope it will help you