About Irrational Numbers

An irrational number is a real number that cannot be expressed as a simple fraction of two integers p/q where q≠0. In decimal form, irrational numbers have non-repeating and non-terminating decimal expansions.

The most famous irrational numbers are π (pi), e (Euler's number), and √2. The ratio of a square's diagonal to its side is √2, famously the first number proven to be irrational by the ancient Greeks.

Rational numbers, on the other hand, can be written as a fraction of two integers. This includes all integers, terminating decimals, and repeating decimals. Every rational number has a decimal expansion that eventually repeats.

Note: This tool uses heuristics to determine rationality. For numbers like √2, it can give a definitive answer. For unknown decimals, it checks the expansion length and patterns. For a rigorous mathematical proof of irrationality, more advanced methods are required.