Question

Without actually performing the long divison, 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 `5^(3).2^(2)` and which is of the type `2^(m).5(m)`. So, this is terminating decimal
`therefore (987)/(10500)=(47)/(500)=(47)/(5^(3).2^(2))xx(2)/(2)`
`(94)/(5^(3).2^(3))=(94)/((10)^(3))=0.094`