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.

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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.

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