Question

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

(i) `19/3125`

Answer 1

`19/3125 = 19/5^5 = (19 × 2^5)/(5^5 × 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.