Decimal expansion of a rational number couldn’t be

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terminating

non-terminating

non-terminating repeating

non-terminating, non-repeating

answer is D.

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Detailed Solution

Here, we have to find the decimal expansion of a rational number.
The decimal expansion of a number in the form

p q

always comes to an end or begins repeating the same finite series of digits after a certain number of digits.
Take the rational number

712

for example. When we divide 7 by 12, the decimal expansion of 0.58333333.
As a result, it has a repeating group that never terminates.
Also, consider the rational number

28

as well, which expands to a decimal as 0.25 and is referred to as terminating.
As a result, a rational number's decimal expansion is either terminating or non-terminating recurring.
Therefore, the decimal expansion of a rational number couldn’t be non-terminating and non-repeating.
Hence, option (4) is correct.

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