Question

Without actual division, show that the following rational numbers is a terminating decimal. Express in decimal form.

`23/((2^3 xx 5^2))`

Answer 1

`23/((2^3 × 5^2)) = (23 × 5)/((2^3 × 5^3))`

= `115/((10^3))`

= `115/1000`

= 0.115

We know either 2 or 5 is not a factor of 23, so it is in its simplest form.

Moreover, it is in the form of (2^m × 5ⁿ). 

Hence, the given rational is terminating.