## 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.

#### Terms

## 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? | |
---|---|---|---|

$rac{15}{2}$ | ✓ | X | X |

-7 | ✓ | ✓ | X |

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.**