Question

without actually performing the long division,find if 987/10500 will have terminating or non-terminating decimal expansion. give reason for your answer

Answer 1

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 
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 these helps you.
:)