Question

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

(i) ${\displaystyle \frac{19}{3125}}$

Answer 1

${\displaystyle \frac{19}{3125}=\frac{19}{5^5}=\frac{19\times 2^5}{5^5\times 2^5}=\frac{608}{100000}=0.00608}$
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.