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1964年新编初中代数课(第三册,第一分册)中,有效数字是近似计算一章中基本概念之一。它是以后讲解乘、除、乘方、开方运算的基础。课本中给出定义:一个近似数的绝对誤差,如果不超过它最末一位的半个单位,那么这个近似数从左边第一个不是零的数字起,到末位数字止,所有的数字都叫做这个近似数的有效数字。如何利用学生已有的知识和具体例子引出有效数字这一新概念,确实是值得研究的问题。下面谈谈我在教学上是如何安排的,请大家指正。 (1) 复习绝对誤差,相对誤差等有关概念。 (2) 在复习的基础上,计算四舍五入得来的近似数0.304,0.00304,0.3040,0.003040的绝对誤差和相对誤差。把计算结果列成下表:
In the 1964 New Junior High Algebra Course (Volume 3, Volume 1), the effective figure is one of the basic concepts in the chapter on approximate calculation. It is the basis for explaining the multiplication, division, power, and square root calculations later. The definition is given in the textbook: The absolute error of an approximate number, if it does not exceed its last half-unit, then the approximate number starts from the first number on the left, which is not zero, to the last digit, all numbers Both are called valid figures for this approximate number. How to use the existing knowledge and concrete examples of students to elicit the new concept of effective numbers is indeed a question worthy of study. Now let’s talk about how I arranged for teaching. Please correct me. (1) Review concepts such as absolute error and relative error. (2) On the basis of the review, the absolute and relative errors of the approximate numbers 0.304, 0.00304, 0.3040, and 0.003040 rounded off are calculated. The calculation results are listed in the following table: