Significant figures are one of the basic starting steps in natural science, even for high school students. The convenient rule-of-thumb on handling significant figures comes from the top constraint that the answer you obtain should not be more precise than the numbers you measured with. Recently, we found a kind of ‘significant error’ in the conventional use of the rule-of-thumb for handling significant figures. Here, we show that the application of the convenient rule-of-thumb can easily and widely violate the top constraint of significant figures when calculating the areas of squares and the volumes of cubes. We believe that this ‘significant error’ should be taught in the elementary physics courses for most freshmen in the science/engineering colleges.

中文翻译：

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有效数字有重大错误？

重要人物是自然科学的基本起点之一，即使对于高中生也是如此。处理重要数字的便捷经验法则来自于最高约束，即您获得的答案不应比您测量的数字更精确。最近，我们发现在处理有效数字的经验法则的常规使用中存在一种“重大错误”。在这里，我们表明，在计算正方形面积和立方体体积时，方便的经验法则的应用可以轻松且广泛地违反有效数字的顶部约束。我们认为，对于大多数理科/工程学院的新生来说，这个“重大错误”应该在基础物理课程中教授。