Question

write whether the rational number 51 divided by 1500 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Answer 1

51/1500 will be written as below in exponential form (denominator)

51/2^2×3×5^3

it will have a non terminating but repeating decimal expansion since the denominator is not exactly of the form 2^n×5^m.