Question

Without actually performing long division ,state why 129/6^2×5^3 is a non terminating repeating decimal expansion.

Answer 1

cos the denomenator contains 6 and 3

Answer 2

Fractions or rational numbers have terminating decimal expansion if and only if their denominator can be expressed as 5^a × 2^b.

But the given number's denominator has a factor of 6^2, that is, 2^2 × 3^2.
Hence it has a non terminating decimal expansion