Question

Without actually performing the long division, state whether 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.