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Mathematics

Assertion (A): 0.36‾0.\overline{36} is an irrational number.

Reason (R): Any real number that can be expressed in the form of pq\dfrac{p}{q} where p, q are integers, q ≠ 0 and p, q have no common factor except 1 is a rational number.

  1. Assertion (A) is true, Reason (R) is false.

  2. Assertion (A) is false, Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Rational Numbers

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Answer

Let x = 0.36‾0.\overline{36}

x = 0.363636…..      ………(1)

Multiplying both side by 100, we get

100x = 36.363636…     ………(2)

Subtracting equation (1) from equation (2), we get

⇒ 100x - x = 36.363636….. - 0.363636……

⇒ 99x = 36

⇒ x = 3699=411\dfrac{36}{99} = \dfrac{4}{11}.

Thus, 0.36‾0.\overline{36} is a rational number.

∴ Assertion (A) is false.

By definition,

Any real number that can be expressed in the form of pq\dfrac{p}{q} where p, q are integers, q ≠ 0 and p, q have no common factor except 1 is a rational number.

∴ Reason (R) is true.

∴ Assertion (A) is false, Reason (R) is true.

Hence, option 2 is the correct option.

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