what is a irrarational number

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

Eg: 1.13577894561...

       7.89463148723...

An irrational number is a real number that cannot be represented as a ratio of \(\frac{a}{b}\)such that a and b are both integers.

 

Another way to know if a number is irrational is to notice if the decimal expansion does not terminate or repeat indefinitely. If it is, that number is irrational.

 

\(\pi\), for example, is irrational. \(\sqrt{2}\) is also irrational. \(\phi\) (known as the golden ratio) is irrational, too.

 

\(\frac{1}{3}\) is not irrational because it is a ratio of \(\frac{a}{b}\) where a=1 and b=3.

 

\(2.7551\) is not irrational because the decimal terminates.

 

\(1.3\overline{949494}\) is not irrational because the decimal repeats indefinitely.