# 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… = ?/?

## Rational Numbers

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

Example

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.

Example

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 e to lots of decimal places without any pattern showing φ 1.61803398874989484… √ Many roots (except perfect roots) are also irrational numbers

## Multiplying Irrational Numbers

π × π = π2 is irrational

√3 × √3 = 3 is rational