In mathematics, what is defined as any number that can be expressed as a fraction?

A rational number is defined as any number that can be expressed as a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. This definition encompasses not only simple fractions, such as 1/2 or 3/4, but also whole numbers and integers, as they can be represented as fractions with a denominator of 1 (e.g., 5 can be written as 5/1).

Whole numbers refer specifically to non-negative integers, including 0, and do not cover negative values or fractions. Integers include all positive and negative whole numbers, along with zero, but this does not encompass non-integer fractions. Irrational numbers, in contrast, cannot be expressed as fractions; they have non-terminating and non-repeating decimal representations, such as the square root of 2 or pi.

Thus, the broadest and most inclusive category that allows for expression as fractions is that of rational numbers.