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 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