Question

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

`17 /320`

Answer 1

`17/320 = 17/(2^6 xx 5)`

= `(17 xx 5^5)/(2^6 xx 5^6)`

= `53125/1000000`

= 0.053125

We know either 2 or 5 is not a factor of 17, so it is in its simplest form.

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

Hence, the given rational is terminating.