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  • Decimal representation of a rational number cannot be : (A)Terminating (B)non-terminating (C)non-terminating repeating (D)non-terminating non-repeating

Decimal representation of a rational number cannot be :

(A)Terminating
(B)non-terminating
(C)non-terminating repeating
(D)non-terminating non-repeating

Answers (1)

Answer: [D]

Solution.

Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. So it is basically a fraction with non-zero denominator.
Examples: 4/5, 2/3, -6/7
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 = 0.3333..., 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 by the above definitions we can see that the decimal representation of a rational number cannot be non-terminating non repeating because decimal expansion of rational number is either terminating or non-terminating recurring (repeating).
Therefore option (D) is correct.

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infoexpert26

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