Comparing and Ordering Rational Numbers

A rational number is any number that can be written as a fraction of two integers, including whole numbers, fractions, and terminating or repeating decimals. To compare two rational numbers means to decide which is greater, and to order a list means to arrange them from least to greatest (or the reverse).

The most reliable way to compare rational numbers is to put them in the same form — usually decimals, since they line up naturally. Converting −¾ to −0.75 makes it easy to see it sits between −1.5 and 0. The rule that matters most is direction: on a number line, numbers get larger moving right and smaller moving left, so any negative number is always less than any positive number.

To order several rational numbers, convert them all to the same form, then read their positions from left (least) to right (greatest) on a number line, as in the example above: −1½ < −¾ < 0 < ½ < 1¼.

Negative numbers can be the trickiest part: −1½ is less than −¾, even though 1½ looks like the "bigger" number, because −1½ sits farther to the left. The number closer to zero on the negative side is always the greater value — the same reasoning used when finding the square root of a rational number.

Related lessons

• Basic Math