An irrational number is a number that cannot be expressed as the quotient or fraction of two integers, with the denominator not equal to zero. Irrational numbers are usually expressed as non-recurring, non-terminating decimals. They cannot be written as a simple fraction or ratio, and their decimal representation goes on forever without repeating. Common examples of irrational numbers include the square root of 2 (√2), pi (π), and the golden ratio (φ).