# How to Visualize Fractions on a Number Line

Fractions help you fill in a lot of the spaces on the number line that fall between the counting numbers. For example, the figure shows a close-up of a number line from 0 to 1.

This number line may remind you of a ruler or a tape measure, with a lot of tiny fractions filled in. In fact, rulers and tape measures really are portable number lines that allow carpenters, engineers, and savvy do-it-yourselfers to measure the length of objects with precision.

Adding fractions to the number line expands the set of integers to the set of *rational numbers.*

In fact, no matter how small things get in the real world, you can always find a tiny fraction to approximate it as closely as you need. Between any two fractions on the number line, you can always find another fraction. Mathematicians call this trait the *density* of fractions on the real number line, and this type of density is a topic in a very advanced area of math called *real analysis.*