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  • Which of the following is irrational?

Which of the following is irrational?

(A) 0.14

(B) 0.14\overline{16}

(C) 0.\overline{1416}

(D) 0.4014001400014

Answers (1)

Answer: [D]

Solution.

Irrational numbers are real numbers which cannot be represented as simple fractions.
Examples: \sqrt{2},\sqrt{3},\pi
Irrational cannot be expressed in form of p/q form and its decimal expansion is non- terminating non-recurring decimal expansions.
Non-Recurring non terminating decimals do not have a particular pattern/sequence after the decimal point. They are also called non repeating decimals.
Examples:
\sqrt{2}=1.414213562373
\sqrt{3}=1.732050807568
\pi =3.14159265359
In the given options, only option D is non-terminating non-recurring decimal as it satisfies the above definition.
Therefore option (D) is correct.

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infoexpert26

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