This question is taken from real numbers in which we have given a rational number 64/455 and we have to prove that the given rational number is a non terminating decimal without actual division.

Kindly solve the above problem in detail

RS Aggarwal, Class 10, chapter 1C, question no 2(viii)

64/455

=64/5×7×13

## 5,7 or 13 is not factor of 64 so given fraction is in its simplest form.

and, (5×7×13)≠(2^m×5^n) in denominator

hence given fraction is non-terminating repeating decimal.