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Question
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
Yes, after simplification denominator has factor 53 – 22 and which is of the type 2m. 5n.
So, this is terminating decimal.
∵ `987/10500 = 47/500`
= `47/(5^3 . 2^2) xx 2/2`
= `94/(5^3 xx 2^3)`
= `94/(10)^3`
= `94/1000`
= 0.094
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