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在实际计算题中,所遇到的数字多数都含有误差。所谓误差就是一个量的真值减去它的近似值。如果以A代表真值,α代表近似值,那末误差△A与A及α之关系是: △A=A-α。(1) 误差一般都是很小,但是不能不加注意。我们很容易看到对于含有误差的数字进行运算,其结果,除了少数特殊情形外,还是含有误差的。并且这一误差,比起原先数字上的误差,可能来得大,也可能来得小。因此我们在计算实际问题时,决不能满足于求得了答数就算了,必须进一步查问这一答数的误差有多少,以便了解它的准确程度。
In actual calculations, most of the numbers encountered contain errors. The so-called error is the true value of a quantity minus its approximate value. If A represents the true value and α represents the approximate value, then the relationship between the error ΔA and A and α is: ΔA=A-α. (1) Errors are generally small, but they cannot be ignored. It is easy to see that the calculations are performed on numbers that contain errors. The results, apart from a few special cases, still contain errors. And this error may be larger or smaller than the original numerical error. Therefore, when we calculate actual problems, we must not be satisfied with obtaining the answers. We must further investigate the error of this answer in order to understand its accuracy.