Question

Without actually perforating the long division, find if 987 by 10500 will have terminating or non terminating repeating decimal expansion. Give reasons for your answer. ICSE board ka se answer uski hisab se aap SB dena ok ​

Answer 1

when we divide 987 by 10500 we get 0.094

that means it's not repeating decimal expansion.

Answer 2

If a fraction , in it's lowest terms , has no other

Prime factors except 2 and 5 it can be expressed

as a terminating decimal.

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i ) first write the fraction in it's lowest

terms for that

Write the numbers into product of prime

and find the HCF of them

987 = 3 × 7 × 47

10500 = 2 × 2 × 3 × 5 × 5 × 5 × 7

HCF of 987 and 10500 = 3 × 7 = 21

Therefore ,

Least form of the fraction = 987 / 10500

Divide numerator and denominator with HCF,

we get,

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

= 47 / 500

987 / 10500 = 47 / 500

Denominator = 500

= 2^2 × 5^2

We have only 2 and 5 as factors .

Therefore ,

987 / 10500 is terminating decimal.

hope it helps