Question

If p/q is a rational number (q not equal to 0), what is condition of q so that the decimal representation of p/q is terminating?

Answer 1

p/q is a rational q is not equal to zero

p/q is a terminating decimal ,
if q = 2^n *5^m where n ,m are positive integers

Answer 2

q should have any factor or multiple of 10 that is $q=2^{x} \times 5^{y}$where x and y are positive integers.

Given:

$\frac{p}{q}$ is the rational number  

To find:

The condition of q so that the decimal representation of $\frac{p}{q}$ is terminating

Solution:

Given, $\frac{p}{q}$ is a rational number where q not equal to 0.

So, for $\frac{p}{q}$  to be a terminating decimal, q should have any factor or multiple of 10.

This can be represented in the order of $\bold{q=2^{x} \times 5^{y}}$, where both x and y are positive integers.  

So, q must be any factor or multiple of 10 expressed in the form of $2^{x} \times 5^{y}$, for a fraction  

$\bold{\frac{p}{q}}$ to be a terminating fraction.