We learned earlier that rational numbers can be written as a positive or negative fraction. For example, and are both rational numbers. A complicated-looking numerical expression can also be a rational number as long as the value of the expression is a positive or negative fraction. For example,  and  are rational numbers because  and .

Rational numbers can also be written using decimal notation. Some have finite decimal expansions, like 0.75, -2.5, or -0.5. Other rational numbers have infinite decimal expansions, like 0.7434343 . . . , where the 43s repeat forever. This is called a repeating decimal. A repeating decimal has digits that keep going in the same pattern over and over, and these repeating digits are marked with a line above them. For example, we would write 0.7434343 . . . as . The bar tells us which part repeats forever.

The decimal expansion of a number helps us plot it accurately on a number line divided into tenths. For example, should be between 0.7 and 0.8. Each additional decimal digit increases the accuracy of our plotting. So the number is between 0.743 and 0.744.