Question

Without actually performing the long division, find if 987\10500 will have terminating or nonterminating repeating decimal expansion. Give reason for your answer.

Answer 1

Hi,

________________________________

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.

I hope thos helps you.

:)

Answer 2

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