Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.

You are watching: What is a rational number but not an integer

Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4…

Integers include all whole numbers and their negative counterpart e.g. …-4, -3, -2, -1, 0,1, 2, 3, 4,…

All integers belong to the rational numbers. A rational number is a number

\$\$fracab,: b eq 0\$\$

Where a and b are both integers.

Example

The number 4 is an integer as well as a rational number. As it can be written without a decimal component it belongs to the integers. It is a rational number because it can be written as:

\$\$frac41\$\$

Or

\$\$frac82\$\$

Or even

\$\$frac-8-2\$\$

Whereas

\$\$frac15=0.2\$\$

is a rational number but not an integer.

A rational number written in a decimal form can either be terminating as in:

\$\$frac15=0.2\$\$

Or repeating as in

\$\$frac56=0.83333...\$\$

All rational numbers belong to the real numbers.

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## Video lesson

Write as rational numbers

More classes on this subject
Pre-AlgebraMore about the four rules of arithmetic: Calculating with decimals and fractionsPre-AlgebraMore about the four rules of arithmetic: Geometric sequences of numbersPre-AlgebraMore about the four rules of arithmetic: Scientific notation

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MORE ABOUT THE FOUR RULES OF ARITHMETIC – Learn how to estimate calculations
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