Mathematics divides numbers into two big categories: real numbers and complex numbers. Previously known as "imaginary".

Real numbers:

Real numbers are ones that you could (in theory) count. All of these rational and irrational numbers, including fractions, are considered real numbers. They are denoted by the symbol “R”.

Rational Numbers:

Numbers that can be written in the form of \frac{p}{q}, where q \neq 0 .Examples of rational numbers are [math] \frac{1}{2}[[/math], \frac{6}{7} and \frac{16}{8} etc.

Rational numbers:

i) Natural numbers

ii) whole numbers

iii) Integers

Irrational numbers:

Irrational number cannot be expressed in the form of \frac{p}{q}, where p and q are integers (q > 0 and q not equal to 0).

[NOTE: the decimal expansion of a irrational number is non terminating non recurring.]

EXAMPLE: 4\pi, \sqrt{2}, \sqrt{7}, \sqrt{\frac{3}{5}}, -\sqrt{11}, \sqrt{1.6},......etc