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Qus: Which among the following options is irrational?


A. 3.1415926535… (non-repeating and non-terminating)
B. 10.2
C. (0.2)2
D. 0.2


Solution
A. 3.1415926535… (non-repeating and non-terminating)



Explanation

Non-terminating and non-repeating decimals are irrational.


If the denominator of a rational number is in the form of  where n and m are non-negative integers, then the rational number is terminating.


0.2 = 2/ 10 = 2/ (2 x 5)


∴ 0.2 has terminating decimal and is a rational number.


3.1415926535… is non-terminating and non-repeating.


∴ 3.1415926535… is irrational.


1/0.2 = 10/2


∴ 1/ 0.2 has terminating decimal and is a rational number.

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