Explain how irrational numbers differ from rational numbers?

Rational Numbers:

A number ‘s’ is called rational if it can be written in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $𝑞≠0$.

For example, $2,\ \frac{1}{2}$ are rational numbers. $\sqrt{2}$ cannot be written in $\frac{p}{q}$ form. Therefore, it is not a  rational number.

Irrational Numbers:

A number that cannot be expressed in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q$ is not equal to zero is an irrational number.

For example

$\sqrt{3}, \sqrt{7}, \pi$

The main difference is a rational number can be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers and $q≠0$ whereas an irrational number cannot be expressed in $\frac{p}{q}$ form.

 Also, a rational number can be expressed in either terminating decimal or non-terminating recurring decimals but an irrational number can only be expressed in non-terminating non-recurring decimals.