Rationals vs. irrationals

Rational numbers are numbers that can be expressed exactly as a fraction of two integers (like 1/2 or 3/4), meaning their decimal expansion either terminates or repeats. Irrational numbers, on the other hand, cannot be written as such fractions; their decimal expansions go on forever without repeating or settling into a pattern (like π or √2). Both sets are real numbers, but rationals are "countable" and have a predictable pattern, while irrationals are "uncountable" and more complex in their decimal form.