Question

Without actually performing the long division, find if 987\10500 will have terminating or nonterminating repeating decimal expansion. Give reason for your answer.

Answer 1

formula: 2^n x 5^m
non terminating

Answer 2

When we are able to represent the denominator in the form 2^n 5^m then it is a terminating decimal expansion.

987/10500
It is a non terminating decimal expansion since it has factors other than 2 and 5. This denominator ha factors 2, 5, 3 and 7.