Without actually performing the long division, find if 987/10500 will have terminating or non - terminating repeating decimal expansion. Give reasons for your answer.
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Given number 98710500
Let us find the HCF of the 987 and 10500.
987 = 3 × 7 × 47
10500 = 2 × 2 × 3 × 5 × 5 × 5 × 7
HCF of (987, 10500) = 3 × 7
HCF of (987, 10500) = 21
Divide numerator and denominator with HCF, then we get
= (987 / 21) / (10500 / 21)
= 47 / 500
987 / 10500 = 47 / 500
Denominator 500 can be written as
500 = 22 × 52
We have only 2 and 5 as factors.
∴ 987 / 10500 is terminating decimal.
if a fraction has no other prime factors other than 2 and 5, it can be represented in its lowest terms as the terminating decimal expansion.
Hope it will help you
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