Irrational Numbers

Irrational means not Rational

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

 Example
Rational Number0.5 = 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.

NumberFraction FormRational or Irrational
0.75¾Rational
0.4Rational
√2?Irrational
π?Irrational

Famous Irrational Numbers

π3.14159265358979323…People have calculated Pi to over a quadrillion decimal places and still there is no pattern
e2.71828182845904523…People have also calculated e to lots of decimal places without any pattern showing
φ1.61803398874989484… 
 Many roots (except perfect roots) are also irrational numbers

Multiplying Irrational Numbers

π × π = π2 is irrational

√3 × √3 = 3 is rational

Learn More

Rationalize the Denominator

Dividing Fractions By Whole Numbers

Even and Odd Numbers

Reciprocal of a Fraction

Numbers Index

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