Without actually performing the long division, find if 987/10500 will have terminating or non-terminating repeating decimal expansion. Give reasons for your answer.
Solution:
Given:
The fraction 987/10500
Let us divide numerator and denominator by 21, we get
987/10500 = (987 ÷ 21) / (10500 ÷ 21)
= 47/500
So,
The prime factors for denominator 500 = 2 × 2 × 5 × 5 × 5
Since it is of the form: 2n, 5n
Hence it is a terminating decimal.
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