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題名 | 論乘除運算中有效數字之處理規則=On the Rounding Rules for Multiplication and Division |
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作者 | 陳韋達; 李偉; Chen, Wei-da; Lee, Wei; |
期刊 | 科學教育研究與發展季刊 |
出版日期 | 20041200 |
卷期 | 37 2004.12[民93.12] |
頁次 | 頁81-93 |
分類號 | 311.11 |
語文 | chi |
關鍵詞 | 數學教育; 理化教育; 自然科學; Mathematics education; Physics and chemistry education; Natural science; |
中文摘要 | 乘除運算是十分常見的四則運算,在吾人求學過程中,多數教科書上都提供一標準規則來處理乘除運算中之結果的有效數字。然而,教科書奉為圭臬的標準規則的數學基礎為何?該規則真的合理嗎?其成功率又是幾成呢?是否有其他更好的規則存在?針對以上的問題,我們利用簡單的數學分析並透過蒙地卡羅模擬,仔細研究了乘除運算中三種有效數字的處理規則,並找出了最適切的取捨規則以供乘除運算之需。 |
英文摘要 | Multiplication and division are commonly encountered as two of the four fundamental operations. Most textbooks provide a standard rounding rule for multiplication and division, allowing students in schools to follow to deal with the significant figure of the results. However, what is the fundamental basis of the standard rule? Is the rule reasonably accurate? How good is the standard rule? Do there exist any other superior rules? A detailed investigation of three different rounding rules for multiplication and division is presented including statistical analyses via Monte-Carlo simulations as well as a mathematical derivation. We compare carefully different rounding rules for multiplication and division and suggest a best one to be adopted as the standard. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。