Irrational Numbers – Definition & Examples

 Irrational Numbers 

Definition: 

An “Irrational Number” is a Real Number that cannot be expressed as a simple fraction for any Integers.

Simply Irrational means not Rational.

   2.5 =  5/2  is a ratio or fraction, but

      𝝅 = 3.1415926…is not a ratio or fraction.

Decimal expansions of irrational Numbers does not repeat or terminate.

Example: √2 and √2 are famous Irrational Numbers.

𝝅 = 3.14159265358979323846264338327950…(etc).

We cannot write 𝝅 into a simple fraction form, approximate value of 𝝅 is 22/7.

22/7 = 3.14159265358979323846264338327950…
is closed but not accurate value of 𝝅.

𝝅 cannot be written in a fractional or rational form so, it is Irrational.

√2 = 1.4142135623730950488016887242096…(etc).

√2 is also cannot be written in a fractional or rational form so, it is Irrational.

Some more examples;

Number           Fraction          Rational or Irrational

  1.25                 5/4                          Rational

  .003               1/3000                       Rational

    𝝅                22/7(approximate)        Irrational

√2                  ?                               Irrational