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

987/10500 is non-terminating repeating decimal
Reason:For a fraction to have terminating decimal the prime factorisation of denominator should contain factor 2 or factor 5 or both factors 2 & 5.
For a fraction to have non-terminating repeating decimal the prime factorisation of denominator should contain factor 2 & any other number or factor 5 & any other number or factors 2,5.& any other number.
since the prime factorisation of 10500 contain factors other than 2 and 5, i.e., 10500=2X2X5X5X5X21