§3.近似数的四则运算在中学算术里教学近似计算,第二个任务是要使学生掌握近似数四则运算的法则。这里主要的问题是:怎样根据已知数的精确度合理地确定运算结果的精确度?具体一些说也就是:已经知道了原始数据精确有效数字(或可靠数字)的个数,或者它的最后一个精确有效数字(或可靠数字)所在的数位;怎样合理地确定运算结果中应该保留的可靠数字的个数,或者它的最后一个可靠数字所在的数位? 在理论上解决这个问题,需要用到代数方面的知识,这对学生现有的知识基础来说是力所不及的。因此在中学算术里我们并不提出这样的要求,而仅仅是通过一些例题的实际演算来导出有关的法则。这种法 §3. The arithmetic of approximation of numbers is teaching approximate calculations in middle school arithmetic. The second task is to make students master the rules of arithmetic of approximate numbers. The main question here is: how to reasonably determine the accuracy of the operation result based on the accuracy of the known number. Specifically, it means that the number of accurate and valid numbers (or reliable numbers) of the original data is known, or its final value. The number of digits where an exact significant number (or reliable number) is located; how to reasonably determine the number of reliable digits that should be retained in the result of the calculation, or the digit to which the last reliable digit lies? To solve this problem theoretically, it is necessary to use Algebraic knowledge is beyond the student’s existing knowledge base. Therefore, in the middle school grammar we do not make such a request, but merely derive the relevant laws through actual calculations of some examples. This method