# Rational Numbers

A **Rational Number** can be made by dividing an integer by an integer.

*(An integer itself has no fractional part.)*

### Example:

**1.5 is a rational number** because 1.5 = 3/2 (3 and 2 are both integers)

Most numbers we use in everyday life are Rational Numbers.

You can make a few rational numbers yourself using the sliders below:

Here are some more examples:

Number | As a Fraction | Rational? |
---|---|---|

5 | 5/1 | Yes |

1.75 | 7/4 | Yes |

1000 | 1000/1 | Yes |

.001 | 1/1000 | Yes |

−0.1 | −1/10 | Yes |

0.111... | 1/9 | Yes |

√2 (square root of 2) |
? | NO ! |

Oops! The square root of 2 cannot be written as a simple fraction! And there are many more such numbers, and because they are **not rational** they are called Irrational.

Another famous **irrational** number is Pi (π):

## Formal Definition of Rational Number

More formally we say:

*A rational number is a number that can be in the form p/q
where p and q are integers and q is not equal to zero.*

So, a rational number can be:

where q is not zero.

### Examples:

p | q | p / q | = |
---|---|---|---|

1 | 1 | 1/1 | 1 |

1 | 2 | 1/2 | 0.5 |

55 | 100 | 55/100 | 0.55 |

1 | 1000 | 1/1000 | 0.001 |

253 | 10 | 253/10 | 25.3 |

7 | 0 | 7/0 | No! "q" can't be zero! |

Just remember: q can't be zero.

## Using Rational Numbers

If a rational number is still in the form "p/q" it can be a little difficult to use, so I have a special page on how to: |

### Fun Facts ....

The ancient greek mathematician * Pythagoras* believed that all numbers were rational, but one of his students

*proved (using geometry, it is thought) that you could*

**Hippasus****not**write the square root of 2 as a fraction, and so it was

*irrational*.

But followers of Pythagoras could not accept the existence of irrational numbers, and it is said that Hippasus was drowned at sea as a punishment from the gods!