Given rational number is 29/243
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
243 = 35
29 and 243 have no common factors
Therefore, 29 and 243 are co-prime.
Now, we have to check that q is in the form of 2n5m
243 = 35
So, the denominator is not of the form 2n5m
Thus, 29/243 is a non- terminating repeating decimal.