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在中等技术学校教材試用本代数学教程中第40頁§29“按預定准确度的計算法”一节,我認为作者所应用的方法是不正确的;因为应用这种方法去解决問題时,在很多情况下並不能保証預定的精确度。(書上的方法是应用了“存疑的概念去确定結果所应有几位有效数字,从而确定原来的数字的准确度)。为了說明問題,我們从書上的二个例子中之一来加以討論。問題1:要使圓柱的体积能計算得准确到1％,問它的底的直徑及它的高应当以怎样准确度来量? 已知直徑的粗近似值d≈20(公分),高的粗近似值h≈30(公分)。 現在来求定圓柱体积的粗近似值:
In the section on “Calculation of Predetermined Accuracy” on page 40 of the textbook for the trial of mathematics textbooks for secondary technical schools, I believe that the method applied by the author is not correct; as this method is used to solve problems In many cases, the predetermined accuracy cannot be guaranteed. (The method in the book is to apply “the concept of doubt to determine the number of valid figures to determine the accuracy of the original number.” To illustrate the problem, we use one of the two examples in the book. Question 1: To make the cylinder’s volume calculate to be accurate to 1%, ask how its bottom diameter and its height should be measured with accuracy. The approximate diameter of the known diameter is d≈20 (cm), high The rough approximation h≈30 (cm). Now let’s find the approximate value of the cylinder volume: