Question

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

`19/3125`

Answer 1

`19/3125 = 19/5^5`

= `(19 xx 2^5)/(5^5 xx 2^5)`

= `608/100000`

= 0.00608

We know either 2 or 5 is not a factor of 19, so it is in its simplest form.

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

Hence, the given rational is terminating.