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.