Concept of Irrational Numbers - Class 9th - R D Sharma and R S Aggarwal Book Solutions
Channel: Math Solutions Foundation
Date: 09/03/2021

What is an irrational number? What is the definition of irrational number? These questions has been discussed in this video. We have seen that a rational number can either be expressed as terminating or non-terminating repeating decimal expression. A natural question arises. Are there decimal numbers other than terminating or non terminating repeating decimals? In order to answer this, let us consider the following decimal number
x = 0.202002000200002 ...
We observe that in the decimal number x, there are either 2's or 0's and that 2's are separated respectively by one zero, then two zeros, then three zeros and so on. Clearly, the number of zeros separating two successive 2's goes on increasing successively by one. So, we can go writing this number endlessly. Consequently, the decimal representation of number x is non-terminating. Thus, we have numbers whose decimal representation is neither terminating nor repeating. 
It follows from the above discussion that a number can have decimal representation in one of the following forms:
(i) Terminating
(ii) Non-terminating but repeating (recurring)
(iii) Non-terminating and non-repeating.
Irrational numbers : A number is an irrational number, if it has a non-terminating and non-repeating decimal representation.

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