An irrational number is any number that is not a rational number.

In other words, an irrational number cannot be expressed as a fraction ratio of two integers.

Famous examples of irrational numbers include pi (π), Euler's number (*e*), and the golden ratio (φ).

For example, pi is often shortened to 3.14159, but is actually an infinite series of numbers. And unlike a rational repeating decimal number such as 0.3333333..., pi does not end with a series of repeating numbers.

Also, almost all square roots of natural numbers are irrational. Only perfect squares are not irrational numbers.

For instance, unlike the perfect square root of 4 (2^{2}), the square root of 3 is 1.7320508..., or about 1.73.