A rational number can be written as a fraction of two integers (like 1/2 or 4), while an irrational number cannot — its decimal expansion goes on forever without repeating, like π or √2.
Rational numbers include whole numbers, fractions, and terminating or repeating decimals — anything expressible as p/q where p and q are integers and q isn't zero. Examples: 3, -5, 0.75, and 0.333... (which equals 1/3).
Irrational numbers cannot be written as a simple fraction. Famous examples include π (pi, roughly 3.14159...), e (Euler's number, roughly 2.71828...), and the square root of any number that isn't a perfect square, like √2 (roughly 1.41421...). Their decimal digits continue infinitely with no repeating pattern.
Together, rational and irrational numbers make up the full set of real numbers.
Last reviewed: September 2026