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Q.

Identify the true statement(s) from the given two statements about rational and irrational numbers and choose the option which follows.


Statement 1: Irrational numbers are those which cannot be expressed either as a terminating decimal or as a


                     recurring decimal.


Statement 2: Rational numbers differ from irrational numbers as they can be expressed as a fraction which is                                          either terminating or repeating or both.


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a

Statement 1 and statement 2 are both correct.

b

Statement 1 and statement 2 are both incorrect.

c

Statement 1 is correct and statement 2 is incorrect.

d

Statement 1 is incorrect and statement 2 is correct.  

answer is A.

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Detailed Solution

Here, we are given two statements and we have to determine which of them is true.
Now, according to the first statement, irrational numbers cannot be expressed either as a terminating decimal, or a recurring decimal.
So, this is a true statement because irrational numbers cannot be expressed as a ratio of two integers, while both terminating and recurring decimals can be expressed as a ratio of two integers.
Now, as per the next statement, the difference between a rational and an irrational number is that a rational number can be expressed as a fraction which is either terminating, or repeating or both, while an irrational number can’t.
This is also a true statement as per the definition of rational and irrational numbers.
So, both statement 1 and 2 are true.
Hence, the correct option is (1).
 
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Identify the true statement(s) from the given two statements about rational and irrational numbers and choose the option which follows.Statement 1: Irrational numbers are those which cannot be expressed either as a terminating decimal or as a                     recurring decimal.Statement 2: Rational numbers differ from irrational numbers as they can be expressed as a fraction which is                                          either terminating or repeating or both.