3. (7 points) The unit digit of the product $7 \times 17 \times 27 \times 37 \times 47 \times 57 \times 67 \times 77 \times 87 \times 97$ is
【Analysis】Since the unit digit of these 10 numbers in the equation is 7, we only need to determine the unit digit of the product of 10 sevens. First, we calculate the values of $7^{1} 、 7^{2} 、 7^{3} 、 7^{4} 、 7^{5} 、 7^{6}$ to identify the pattern in the unit digits, which will lead us to the answer.

【Solution】Solution: $7^{1}=7, 7^{2}=49, 7^{3}=343, 7^{4}=2401, 7^{5}=16807, 7^{6}=117649$, so the unit digits are $7, 9, 3, 1$ and they change in a cyclic pattern. Since $10 \div 4=2 \cdots 2$, the unit digit of the product $7 \times 17 \times 27 \times 37 \times 47 \times 57 \times 67 \times 77 \times 87 \times 97$ is 9; therefore, the answer is: 9.