Rational Numbers

The history of numbers is a history of expanding systems to fill gaps. Natural numbers (1, 2, 3, ...) were extended to whole numbers (0, 1, 2, 3, ...) to include zero. Whole numbers were extended to integers (..., −2, −1, 0, 1, 2, ...) to include negatives. But even integers leave gaps. What number represents 750m below sea level if we use kilometres? It would be −3/4, which is neither an integer nor an ordinary fraction (which requires a positive denominator). This need leads us to rational numbers.

A rational number is any number that can be expressed in the form $\frac{p}{q}$, where p and q are integers and $q \neq 0$.