Irrational numbers are those which cannot be written as a fraction. These numbers include non-terminating, non-repeating decimals and the transcendental numbers such as e, pi, and the golden ratio.
A number is either rational
or irrational, it can never be both. If you put all the rational and irrational
numbers together, you get the set of all real numbers. This makes
up the set of numbers that we normally use everyday. Other kinds of numbers
besides real numbers include the imaginary and complex numbers.