Question

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

\[\frac{125}{441}\]

Answer 1

The given number is \[\frac{125}{441}\]

Here, \[441 = 3^2 \times 7^2\] and none of 3 and 7 is a factor of 125.

So, the given number is in its simplest form.

Now,

\[441 = 3^2 \times 7^2\] is not of the form

\[2^m \times 5^n\]

So, the given number has a non-terminating repeating decimal expansion.