## Irrational Numbers

Irrational means not Rational

An Irrational Number is a real number that cannot be written as a simple fraction.

Example | |

Rational Number | 0.5 = ½ |

Irrational Number | √2 = 1.414213562373095… = ?/? |

Table of Contents

## Rational Numbers

A Rational Number can be written as a Ratio of 2 integers (ie a simple fraction).

2.5 is rational, because it can be written as the ratio 5/2

4 is rational, because it can be written as the ratio 4/1

0.666… (6 repeating) is also rational, because it can be written as the ratio 2/3

## Irrational Numbers

The numbers that cannot be written as a ratio of 2integers are called Irrational Numbers.

π = 3.14159265358979…

√3 = 1,732050807568877…

## Cannot Be Written as a Fraction

It is irrational because it cannot be written as a ratio (or fraction),

So we can tell if it is Rational or Irrational by trying to write the number as a simple fraction.

Number | Fraction Form | Rational or Irrational |

0.75 | ¾ | Rational |

0.4 | ⅖ | Rational |

√2 | ? | Irrational |

π | ? | Irrational |

## Famous Irrational Numbers

π | 3.14159265358979323… | People have calculated Pi to over a quadrillion decimal places and still there is no pattern |

e | 2.71828182845904523… | People have also calculated to lots of decimal places without any pattern showinge |

φ | 1.61803398874989484… | |

√ | Many roots (except perfect roots) are also irrational numbers |

## Multiplying Irrational Numbers

π × π = π^{2} is irrational

√3 × √3 = 3 is rational