What defines a rational number?

A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. This definition encompasses both fractions and repeating decimals.

For example, the number 1/2 is a clear representation of a fraction, and it is rational because it fits the criteria of being a ratio of two integers. Similarly, repeating decimals like 0.333... (which can be expressed as 1/3) are also classified as rational numbers since they can be converted into a fraction.

In contrast, non-repeating decimals, whole numbers, and negative numbers alone do not encompass all the aspects that rational numbers cover. While whole numbers and negative numbers can be rational (as they can be represented as fractions with a denominator of 1), they do not define the whole category. Non-repeating decimals can also include numbers like π or √2, which cannot be expressed as simple fractions and thus are not considered rational.

Thus, the combination of all fractions and repeating decimals accurately captures the full definition of rational numbers, making this choice the most appropriate.