Question

What will be the minimum value of  a, in the number  16×a/10800 for which the given number will have a terminating decimal expansion?​

Answer 1

Answer:

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.