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Q.


Classify 0.3796 as rational or irrational:

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a

Rational

b

Irrational

c

Both of these

d

None of the above 

answer is A.

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Detailed Solution

Given number is 0.3796.
Rational numbers:
The numbers which can be expressed in the form of p q  , where p, q integers, and q ≠ 0, are known as rational numbers.
On dividing p by q, if the remainder becomes zero then the decimal expansion is terminating and if the remainder never becomes zero and Set of digits repeats periodically then the decimal expansion is non terminating repeating. It is also known as non-terminating recurring decimal expansion.
0.3796
Write 0.3796 in p q   form:
3796 10000  
Applying decimal expansion of real numbers:
The value of   0.3796  is,
3796 10000  
Since the number 3796 10000  can be represented in p q   form so, it is a rational number.
Hence, 0.3796 is a rational number.
Therefore, the correct option is 1.
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Classify 0.3796 as rational or irrational: