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Correct option is D)

Option $B,$ $0.1416ˉ$ is non-terminating recurring decimal, hence it is a rational number.

Option $C,$ $0.41ˉ$ is non-terminating recurring decimal, hence it is a rational number.

Option $D,$ $0.4014001400014...$ is non-terminating non-recurring decimal, hence it is an irrational number.

Therefore, option $D$ is correct.

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