Without actually performing long division, find if 987/10500 will have terminating or non-terminating decimal expansion. Give reasons for your answer
Answers
Answer:
Hey!
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.
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peace!
Answer:
it is terminating decimal expansion
as 987 divided by 10500 it will give 0.094
so this is terminating.