章节大纲

  • Police tape indicating a crime scene, blurred city lights in the background.

    How do police officers identify criminals?
    ::警察如何识别罪犯?

    After a bank robbery has been committed, police will ask witnesses to describe the robbers. They will usually get some answer such as “medium height.” Others may say “between 5 foot 8 inches and 5 foot 10 inches.” In both cases, there is a significant amount of uncertainty about the height of the criminals.
    ::银行抢劫案发生后,警方会要求证人描述劫匪,通常会得到一些答案,比如“中等高度 ” 。 其他人可能会说“5英尺8英寸到5英尺10英寸之间 ” 。 在这两种情况下,罪犯的高度都有很大的不确定性。

    Measurement Uncertainty
    ::不确定性

    Some error or uncertainty always exists in any measurement . The amount of uncertainty depends both upon the skill of the measurer and upon the quality of the measuring tool. While some balances are capable of measuring masses only to the nearest 0.1 g, other highly sensitive balances are capable of measuring to the nearest 0.001 g or even better. Many measuring tools such as rulers and graduated cylinders have small lines which need to be carefully read in order to make a measurement. The figure below shows two rulers making the same measurement of an object (indicated by the blue arrow).
    ::在任何测量中总是存在某些错误或不确定性。 不确定性的程度取决于测量器的技巧和测量工具的质量。 虽然有些平衡只能测量质量到最接近的0.1克,但其他高度敏感的平衡能够测量到最接近的0.001克或甚至更好。 许多测量工具,如标尺和毕业圆筒,有小条线需要仔细阅读,以便进行测量。下图显示两个标尺对一个对象进行相同的测量(由蓝箭头标明 ) 。

    Two rulers measuring an object's length, showing variations in precision and uncertainty.

    Uncertainty in measurement.
    ::测量的不确定性。

    With either ruler, it is clear that the length of the object is between 2 and 3 cm. The bottom ruler contains no millimeter markings. With that ruler, the tenths digit can be estimated and the length may be reported as 2.5 cm.  However, another person may judge that the measurement is 2.4 cm or perhaps 2.6 cm. While the 2 is known for certain, the value of the tenths digit is uncertain. 
    ::标尺两处的天体长度显然在2厘米至3厘米之间。 底线无毫米标记。 使用该标尺,可以估计十位数,长度可报告为2.5厘米。 但是, 另一人可以判断测量值为2.4厘米或2.6厘米。 虽然已知2厘米是肯定的,但十分位数的价值不确定。

    The top ruler contains marks for tenths of a centimeter (millimeters). Now the same object may be measured as 2.55 cm. The measurer is capable of estimating the hundredths digit because he can be certain that the tenths digit is a 5. Again, another measurer may report the length to be 2.54 cm or 2.56 cm. In this case, there are two certain digits (the 2 and the 5), with the hundredths digit being uncertain. Clearly, the top ruler is a superior ruler for measuring lengths as precisely as possible.
    ::顶层标尺含有10厘米(毫米)的标记。 现在, 同一对象可以测量为2.55厘米。 测量器能够估计第100位数字, 因为他可以确定第10位数字是5。 另外, 另一个测量器可以报告长度为2.54厘米或2.56厘米。 在这种情况下, 有两个特定的位数( 2 和 5) , 而第100位数字是不确定的。 显然, 顶层标尺是尽可能精确测量长度的高级标尺 。

     

     

    Summary
    ::摘要

    • Uncertainty exists in all measurements.
      ::所有测量都存在不确定性。
    • The degree of uncertainty is affected in part by the quality of the measuring tool.
      ::不确定性的程度部分受到衡量工具质量的影响。

    Review
    ::回顾

    1. What is uncertainty in measurements?
      ::测量的不确定性是什么?
    2. Why is the top ruler more reliable in measuring length than the bottom ruler?
      ::为什么顶级标尺比底层标尺更可靠?
    3. How could the top ruler be made more accurate?
      ::如何使最高标尺更准确?