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  • The decimal expansion of the number squareroot 2 is. (A) A finite decimal (B) 1.41421 (C) non-terminating recurring (D) non-terminating non-recurring.

The decimal expansion of the number \sqrt{2} is.

(A) A finite decimal
(B) 1.41421
(C) non-terminating recurring  
(D) non-terminating non-recurring

Answers (1)

best_answer

Answer: [D]

Solution.

Terminating decimals have a finite number of digits after decimal point, 
Examples: 1/2 = 0.5, 3/5 = 0.6
Non terminating decimals are the ones which keep on continuing after decimal point.
Examples: 1/3 = 0.33333...., 5/11 = 0.454545...
Recurring decimals are those non terminating decimals which have a particular pattern/sequence that keeps on repeating itself after the decimal point. They are also called repeating decimals.
Examples: 1/3 = 0.33333..., 4/11 = 0.363636....
Non-Recurring decimals are those non terminating decimals which 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
So, the decimal expansion of the number \sqrt{2}  is non-terminating non-recurring. It is an irrational number which is a non-terminating non-recurring decimal expansion.
Therefore option (D) is correct.

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