Given rational number is

is terminating if

a) p and q are co-prime &

b) q is of the form of 2ⁿ 5^m where n and m are non-negative integers.

Firstly, we check co-prime

129 = 3 × 43

Denominator = 2² ×5⁷ ×7⁵

129 and 2² ×5⁷ ×7⁵ have no common factors

Therefore, 129 and 2² ×5⁷ ×7⁵ are co-prime.

Now, we have to check that q is in the form of 2ⁿ5^m

Denominator = 2² ×5⁷ ×7⁵

So, denominator is not of the form 2ⁿ5^m

Thus, is a non-terminating repeating decimal.