Question

what is a special character of denominator which makes the fraction as terminating or non terminating recurring decimals

Answer 1

If the denominator is in the form of 2^n5^m then its terminating, if not, it is nonterminating recurring, where n and m are non-negative integers.

Answer 2

If the denominator is of the form 2^m * 5^n  where m,n∈N∪{0}, then the decimal form is terminating. If it is not in the form, i.e. if there is any other prime number in its factorization, then the decimal form is non-terminating recurring.  

However, before checking if the denominator is in the form 2^m 5^n, we should first remove any common factors from the numerator and denominator.