Rational and Irrational Numbers
Rational and Irrational Numbers
Rational Numbers:
The word rational number comes from the word ratio. Numbers of the form are called rational numbers, where p and q are integers and p and q are co-prime.on converting them into decimals they can be expressed either in the terminating decimal form or in the non-terminating repeating (recurring) decimal form
Irrational Numbers:
There are certain decimal number which neither terminating nor repeating such as
x = 0.202002000200002...
We observe that in the decimal number x, there are either 2,s or 0,s and that the 2,s are separated respectively by one zero, then 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 on writing this decimal endlessly. Consequently, the decimal representation of number x is non-terminating. We also observe that no group of digits repeats. So, the decimal representation of x is non-repeating. Thus, we have numbers whose decimal representation is neither terminating nor repeating. In fact, there a lots of non-terminating non-repeating decimals such as 0.12112111211112...,0.3000300003000003..., 0.10100100010001....and so on.
Decimal Expansion of | |||
| Right Option : A | |||
| View Explanation | |||
Decimal Representation of rational number | |||
| Right Option : A | |||
| View Explanation | |||
Out of the following, the irrational number is | |||
| Right Option : D | |||
| View Explanation | |||
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