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The real number system includes all values that can be placed on the number line, including both rational and irrational numbers.

Rational numbers include values that can be written as fractions. For example, cutting a fruit into two equal parts gives one-half, a rational number. These also include negative fractions, like negative three-fourths.

Rational numbers include decimals that terminate, like 0.5, or repeat, like 0.33, with a bar over the digits.

Within rational numbers lies the subset of integers. Integers include negative numbers, zero, and positive numbers. Counting fruits in a tray gives natural numbers: 1, 2, 3, and so on. Adding zero to natural numbers forms the whole numbers. Extending these to include negatives gives the full set of integers.

Another part of the real number system, irrational numbers, represents values like the square root of two, which gives the diagonal of a unit square.

These numbers have non-repeating decimals that go on forever and cannot be written as fractions.

The real number system includes all values used to count, measure, or compare.