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.

Answer 1

Yes, after simplification denominator has factor 5³ – 2² and which is of the type 2^m. 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