Decimal representation of a rational number cannot be(A) terminating(B) non-terminating(C) non-terminating repeating(D) non-terminating non-repeating
Question
Decimal representation of a rational number cannot be(A) terminating(B) non-terminating(C) non-terminating repeating(D) non-terminating non-repeating
Solution
The decimal representation of a rational number cannot be (D) non-terminating non-repeating.
Here's why:
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
(A) Terminating decimals are certainly possible. For example, the fraction 1/2 is 0.5 in decimal form, which is a terminating decimal.
(B) Non-terminating decimals are also possible. For example, the fraction 1/3 is 0.3333... in decimal form, which is a non-terminating decimal.
(C) Non-terminating repeating decimals are possible too. The same example of 1/3 is a non-terminating repeating decimal.
(D) However, non-terminating non-repeating decimals are not possible for rational numbers. These are numbers like Pi or the square root of 2, which go on forever without repeating. These are known as irrational numbers. Therefore, the decimal representation of a rational number cannot be non-terminating non-repeating.
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