Question

Without actually performing the long division method, state whether the $\frac{64}{455}$ will have a terminating decimals expansion or a non terminating repeating decial expansion.

Answer 1

Question:

Without actually performing the long division method, state whether the $\frac{64}{455}$ will have a terminating decimals expansion or a non terminating repeating decial expansion.

Solution:

$\frac{64}{455}$

$\implies \frac{64}{{5}^{1} \times{7}^{1} \times{13}^{1}}$

It's denominator is not a form of ${2}^{n} \times{5}^{m}$

So, the given Rational Number is non-terminating but repeating.