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  • 乘数和司数的显著数字

    A calculator displaying the number 314.159 on a wooden surface.

    Who should report the numbers - you or your calculator?
    ::谁应该报告数字 - 你和你的计算器?

    Calculators do just what you ask of them, no more and no less.  However, they sometimes can get a little out of hand.  If I multiply 2.48 times 6.3, I get an answer of 15.687, a value that ignores the number of in either number. Division with a calculator is even worse. When I divide 12.2 by 1.7, the answer I obtain is 7.176470588. Neither piece of data is accurate to nine decimal places, but the calculator doesn’t know that. The human being operating the instrument has to make the decision about how many places to report.
    ::计算器只做你要求他们做的事, 不多也不少。 但是, 有时他们可能有点失控。 如果我乘以2.48乘以6.3, 我得到的答案是15.687, 这个数值忽略了任何一个数字中的数字。 使用计算器的分区更是糟糕。 当我将12.2除以1.7, 我得到的答案是7. 176470588。 任何数据都不准确到小数点9, 但计算器不知道这一点。 操作仪器的人必须决定要报告多少地方。

    Uncertainty in Multiplication and Division
    ::乘数和除法的不确定性

    The density of a certain object is calculated by dividing the mass by the volume . Suppose that a mass of 37.46 g is divided by a volume of 12.7 cm 3 . The result on a calculator would be:
    ::如果37.46克的质量除以12.7厘米3的体积,计算结果如下:

    D = m V = 37.46   g 12.7   cm 3 = 2.949606299   g / cm 3

    ::D=mV=37.46 g12.7 cm3=2.949606299 g/cm3

    The value of the mass measurement has four significant figures, while the value of the volume measurement has only three significant figures. The following rule is used to determine the correct number of significant figures present in the reported value.
    ::质量测量的价值有四个重要数字,而数量测量的价值只有三个重要数字。

    • For multiplication and division problems, the answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures. 
      ::对于乘数和分部问题,答案应四舍五入,四舍五入到与用数量最少的重要数字计量的相同数量的重要数字。

    Applying this rule to the example above results in a density of 2.95 g/cm 3 , with three significant figures – the same as the volume measurement.
    ::将这一规则适用于上述例子,其密度为2.95克/立方厘米,有三个重要数字,与量度相同。

     

     

    Sample Problem: Significant Figures in Calculations
    ::抽样问题:计算中的重要数字

    Perform the following calculations, the answers to the appropriate number of significant figures.
    ::进行以下计算,对适当数量的重要数字进行回答。

    1. 0.048 m × 32.97 m
      ::0.048米×32.97米
    2. 14,570 kg × 5.81 L
      ::14,570公斤x5.81升

    Step 1:  Plan the problem.
    ::第1步:规划问题。

    Analyze each of the measured values to determine how many significant figures should be in the result. Perform the calculation and round appropriately. Apply the correct units to the answer. When multiplying or dividing, the units are also multiplied or divided.
    ::分析每个测量值以确定结果中应包含多少重要数字。 适当进行计算和回合。 对答案应用正确的单位。 当乘或除时, 单位也会被乘或除。

    Step 2:  Calculate
    ::第2步:计算

    1. 0.048 m × 32.97 m = 1.6 m 2  Round to two significant figures because 0.0 48 has two.
      ::0.048 m × 32.97 m = 1.6 m2 圆到两个重要数字,因为 0.048 有两个。
    2. 14570 kg ÷ 5.81 L =  2510 kg/L Round to three significant figures because 5.81 has three.
      ::14570公斤 5.81 L = 2510公斤/升回合至3个重要数字,因为5.81有3个。

    Summary
    ::摘要

    • For multiplication and division problems, the answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures.
      ::对于乘数和分部问题,答案应四舍五入,四舍五入到与用数量最少的重要数字计量的相同数量的重要数字。

    Review
    ::回顾

    1. Perform the calculation and round your answer with the correct  number of significant figures.
      1. 78.2 ÷ 32 cm 3
        ::78.2 32厘米3
      2. 3.0 m/s × 9.21 s
        ::3.0 m/s × 9.21 s

      ::使用重要数字的正确数字进行计算和回合回答。 78.2 ° 32 cm3 3.0 m/s × 9.21 s
    1. What happens to units in multiplication and division problems?
      ::遇到乘数和分裂问题的单位会怎样?