Question

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

`171/800`

Answer 1

`171/800 = 171/(2^5 xx 5^2)`

= `(171 xx 5^3)/(2^5 xx 5^5)`

= `21375/100000`

= 0.21375

We know either 2 or 5 is not a factor of 171, so it is in its simplest form.

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

Hence, the given rational is terminating.