Home > Pre-Algebra > Number Theory > Classifying Rational Numbers

## Classifying Rational Numbers

#### Introduction

Rational numbers are numbers that can be written as a fraction containing two integers. For example, $0.overline{3}$ is a rational number, because it can be expressed as $rac{1}{3}$. Working out how rational numbers relate to whole numbers and integers is important, as each of the terms means something different, but similar.

## Lesson

To classify the relationship between Rational Numbers, Whole Numbers, and Integers, we need to think about examples of each.

Every integer can be expressed as a fraction, simply by putting the number as the numerator, and 1 as the denominator. For example, 754 can be written as $rac{754}{1}$.

Therefore, all integers are rational numbers.

Since whole numbers are positive integers, then all whole numbers are rational numbers.

All whole numbers are also integers.

To demonstrate out point, let's look at some examples:

Rational Number?Integer?Whole Number?
$rac{15}{2}$XX
-7X
1

Therefore, all whole numbers are integers and are also rational numbers. All integers are rational numbers. Rational numbers are not always integers or whole numbers, but sometimes can be.

Irrational numbers are a totally separate category. No integers, whole numbers, or rational numbers are irrational numbers.

## Examples

$-4$
$-4 is in \mathbb{Z} - Integers$
$-4 is in \mathbb{Q} - Rational Numbers$