what makes a number irrational

A number is irrational if it cannot be expressed as the ratio of two integers (i.e., cannot be written as a simple fraction pq\frac{p}{q}qp​ where ppp and qqq are integers and q≠0q\neq 0q=0). Irrational numbers have decimal expansions that neither terminate nor repeat. Therefore, the decimal goes on forever without forming any repeating pattern. Examples include π\pi π, eee (Euler's number), the golden ratio ϕ\phi ϕ, and the square root of any natural number that is not a perfect square (e.g., 2\sqrt{2}2​).