Question

Without actual division, show that each of the following rational
numbers is a nonterminating repeating decimal.
129 (2²×5³×7²)​

Answer 1

129/22 x 57 x 75 We know 2, 5 or 7 is not a factor of 129, so it is in its simplest form.  Moreover, (2^2× 5^3× 7^2) ≠ (2^m × 5^n)  Hence, the given rational is non-terminating repeating decimal.