Answer :

Given rational number is

is terminating if

a) p and q are co-prime &

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

__Firstly, we check co-prime__

129 = 3 × 43

Denominator = 2^{2} ×5^{7} ×7^{5}

129 and 2^{2} ×5^{7} ×7^{5} have no common factors

Therefore, 129 and 2^{2} ×5^{7} ×7^{5} are co-prime.

Now, we have to check that q is in the form of 2^{n}5^{m}

Denominator = 2^{2} ×5^{7} ×7^{5}

So, denominator is not of the form 2^{n}5^{m}

Thus, is a **non-terminating repeating** decimal.

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