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Example of Irrational Number

An irrational number is a number which can't be expressed as a simple fraction, like 1.23. In arithmetic, these numbers are also commonly called 'repeating' numbers after division, like 3.33 repeating, as a result of dividing 10 by 3. Although irrational numbers aren't entirely efficient, they're sufficiently accurate for some uses, like basic measurements. New mathematical methods are progressively removing these issues with irrational numbers.

Examples of Irrational Numbers:

Pi, expressed as 22/7 or 3.142etc., which until comparatively recently was the method of finding the area of a circle, etc. The square root of 2, which is 1.41421356etc.
http://www.math.utah.edu/online/1010/irrational/
http://www.personal.psu.edu/jxt18/Math4_WEB/Math4%20Math%20Assignments/Irrational%20Numbers.htm
http://www.sci.ccny.cuny.edu/~chemwksp/Intro_Algebra_WN_06/PLTL_Math_Module-2-IrrationalNumbers.pdf

Image Example of Irrational Number:

The number 2 is irrational.