“Moses said [to Pharaoh] ‘So said Hashem, Around midnight, I will go out in the midst of Egypt. Every firstborn in the land of Egypt shall die…’” 11:4-5
Our Sages explained that Moshe used a word which implies at about midnight, either slightly before or after, and he did not say at midnight, lest Pharaoh's stargazers make a mistake [in calculating the exact time] and say, "Moshe is a liar!" But Hashem, who knows exact times and moments, actually said, "At midnight." - Rashi
Moshe knew the Egyptians and their capacity to deny the obvious all too well. Therefore, he deliberately left the exact time of the Plague of the Firstborn slightly vague, knowing that the Egyptians might well attribute the sudden passing of every firstborn in Egypt[!] to a mere coincidence. They would never for a moment consider the possibility that they had erred in their calculations of the exact moment of midnight. Man’s capacity to reject the obvious is so strong that when he wishes to do so, no amount of proof can ever suffice.