Question

without actually performing long division , find if 987/10500 will have terminating decimal expansion. give reasons for your answer.

Answer 1

Solution:-

given by:-

10500) 98700 (0.094



94500
-
___________

42000

- 42000
_________________


your answer is 0.094 ans

Answer 2

Hello dear!!! ✌️✌️


Here is your answer goes like this :
_______________________________________


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......

i ) first write the fraction in it's lowest

terms for that

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 THIS WILL HELP YOU ✌️✌️


HAVE A GREAT DAY DEAR........


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