We know, 29/343 = 29/73
Given rational number is 29/343
p/q is terminating if
a) p and q are co-prime &
b) q is of the form of 2n 5m where n and m are non-negative integers.
Firstly we check co-prime
29 = 29 × 1
343 = 7 × 7 × 7
29 and 343 have no common factors
Therefore, 29 and 343 are co-prime.
Now, we have to check that q is in the form of 2n5m
343 = 73
So, the denominator is not of the form 2n5m
Thus, 29/343 is a non-terminating repeating decimal.