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有些数学规律可以在运算中发现,当然,这要一边算一边想才能实现.下面以求一个整数的个位数为例加以说明.例1求3~(2002)的个位数.分析与解从计算3~1,3~2,3~3,3~4的个位数,发现3~4=81的个位数是1.显然,两个自然数乘积的个位数等于这两个自然数的个位数之积的个位数,而2002=4×500+2,于是,求3~(2002)的个位数就转化为求(3~4)~(500)×3~2,或3~2的个位数.因此,3~(2002)的个位数等于9.
Some mathematical laws can be found in the operation, of course, this should be considered while working to achieve the following order to find an integer single digits as an example to illustrate Example 1 seeking 3 ~ (2002) single digits analysis and solution From the calculation of the digits of 3 ~ 1, 3 ~ 2, 3 ~ 3, and 4 ~, we find that the number of digits of 3 ~ 4 = 81 is 1. Obviously, the unit of the product of two natural numbers is equal to these two natural numbers (2002) = 4 × 500 + 2, then the unit digit of 3 ~ (2002) is transformed into (3 ~ 4) ~ (500) × 3 ~ 2, Or a single digit of 3 to 2. Therefore, the unit digit of 3 to (2002) is equal to 9.