Irrational Number

Irrational numbers are real numbers that cannot be expressed exactly as a fraction or integer. The two most famous examples of such numbers are pi (~3.1416) and the golden ratio (~1.6180). These numbers are not crazy, they just cannot be represented as an exact ratio, but they can be approximated as pi and phi have been above. (It is important to note that pi can be expressed as an approximation as 22/7.) Some irrational numbers are easy to compute such as the golden ratio, some are kind of easy like pi, and some are hard.