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Irrational Numbers

Real numbers can be divided into rational and irrational numbers. Here, we are going to discuss about irrational numbers.
The numbers which can not be represented as rational numbers are known as irrational numbers. We can say that these numbers can not be written in the form of $\frac{p}{q}$, where p and q are integers and $q\neq 0$.

The decimal representation of rational numbers can either be terminating or non-terminating or recurring, but the decimal representation of an irrational number is non-terminating as well as non-recurring.

What is Non-terminating?
By non-terminating number, we mean that a number that never ends after decimal. For example: 4.5 and 37.86 are terminating numbers, while 8.159768.... and 1.33333.... are examples of non-terminating numbers.

What is Non-recurring?
By non-recurring number, we imply a number that, after decimal, does not repeat its numbers in a particular fashion. For example: In above example, 1.33333.... is recurring, while 8.159768.... is non-recurring.

An irrational number is always non-terminating and non-recurring, when represented as decimal.

Following tree diagram gives a better understanding about the position and nature of irrational numbers among all the numbers:

Number Tree
Examples of Irrational Numbers:

  • Pi ($\pi $) is a well known and most popular irrational number. $\pi = 3.1415926535.....$.
  • The number "e (Euler's number)" is an irrational number. It value is 2.71828182845904...
  • All surds $\sqrt{2}$, $\sqrt{3}$, $\sqrt{11}$, $\sqrt{7}$ etc are irrational numbers.
  • All non-terminating and non-recurring decimal representations are irrational, e.g. 23.783802... etc.

Related Calculators
Irrational Number Calculator Number Rounding
5 Number Summary Calculator Adding Binary Numbers Calculator

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