Define a rational number.

A rational number is defined as any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero. This means that any number in the form ( \frac{a}{b} ) fulfills this criterion, with ( a ) being any integer (which can be positive, negative, or zero) and ( b ) being any non-zero integer.

This definition encompasses not only whole numbers but also fractions and certain decimal numbers that either terminate or repeat. For example, the number ( 1 ) can be expressed as ( \frac{1}{1} ), and the decimal ( 0.75 ) can be represented as ( \frac{3}{4} ). This inclusivity emphasizes that rational numbers are a broad category of numbers that can be finitely represented as fractions, hence making the provided definition comprehensive and accurate.

Other definitions mentioned, such as a whole number or a number that cannot be written as a fraction, either limit the scope of rational numbers or describe concepts outside this classification, confirming that the choice correctly represents the essential characteristic of rational numbers.