Question

Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:

(v) $\frac{64}{455}$

Answer 1

Solution:

When the denominator of a fraction has a factor other than the factors of the form $2^m\times 5^n$(Where ‘m’ and ‘n’ are positive integers), then rational numbers is a non-terminating repeating decimal.

For the given rational number, we will factorize numerator and denominator as follow,

$\frac{64}{455}$$=\frac{2^6}{5\times 7\times 13}$

As the denominator has the factors $\text{'}13\text{'}$and $\text{'}7\text{'}$other than the factors of the form $2^m\times 5^n$.

Therefore, $\frac{\mathbf{64}}{\mathbf{455}}$is a non-terminating repeating decimal.