章节大纲

  • 常规

    全部折叠 展开全部

  • 重要数字

    Sign welcoming to Jacinto City, Texas, displaying population and speed limit of 30 mph.

    How fast do you drive?
    ::你开多快?

    As you enter the town of Jacinto City, Texas, the sign below tells you that the speed limit is 30 miles per hour. But what if you happen to be driving 31 miles an hour? Are you in trouble? Probably not, because there is a certain amount of leeway built into enforcing the regulation. Most speedometers do not measure the vehicle speed very accurately and could easily be off by a mile or so (on the other hand, radar measurements are much more accurate). So, a couple of miles/hour difference won’t matter that much. Just don’t try to stretch the limits any further unless you want a traffic ticket.
    ::当你进入得克萨斯州Jacinto市时,下面的标志告诉你,时速限制是30英里/小时。 但如果你恰好驾驶31英里/小时? 你是否遇到麻烦? 可能没有,因为执行条例需要一定的回旋余地。 大部分速度计并不精确地测量车辆速度,而且很容易降低一英里左右(另一方面,雷达测量则更准确 ) 。 因此,几英里/小时差异并不重要。 只是不要试图进一步拉开限制范围,除非您想要交通票。

    Significant Figures
    ::重要数字

    The significant figures in a measurement consist of all the certain digits in that measurement plus one uncertain or estimated digit. In the ruler illustration below, the bottom ruler gave a length with 2 significant figures, while the top ruler gave a length with 3 significant figures. In a correctly reported measurement, the final digit is significant but not certain. Insignificant digits are not reported. With either ruler, it would not be possible to report the length as 2.553 cm as there is no possible way that the thousandths digit could be estimated. The 3 is not significant and would not be reported.
    ::测量中的重要数字包含该测量中的所有特定数字,加上一个不确定的数字或估计数字。在下文标尺图解中,底线标尺给出了2个重要数字的长度,而顶线标尺给出了3个重要数字的长度。在正确报告的测量中,最后数字是显著的,但不确定。没有报告无足轻重的数字。在任何一个标尺中,不可能将长度报告为2.553厘米,因为无法估计千位数字。3个数字并不重要,也不会报告。

    Two rulers showing length measurements with different counts of significant figures.

    Measurement with two different rulers.
    ::用两种不同的标尺进行测量。

    When you look at a reported measurement, it is necessary to be able to count the number of significant figures.  Table   details the rules for determining the number of significant figures in a reported measurement. For the examples in the table, assume that the quantities are correctly reported values of a measured quantity.
    ::当您查看所报告的测量时,必须能够计算重要数字的数量。表格详细说明了用于确定所报告测量中重要数字数量的规则。对于表中的例子,假设所报告数量是某一计量数量的正确报告值。

    Significant Figure Rules
    Rule Examples
    1. All nonzero digits in a measurement are significant

    A. 237 has three significant figures.
    ::A.237有三个重要数字。

    B. 1.897 has four significant figures.
    ::B. 1.897有四个重要数字。

    2. Zeros that appear between other nonzero digits are always significant.

    A. 39,004 has five significant figures.
    ::A. 39 004有5个重要数字。

    B. 5.02 has three significant figures
    ::B5.02有三个重要数字

    3. Zeros that appear in front of all of the nonzero digits are called left-end zeros.  Left-end zeros are never significant

    A. 0.008 has one significant figure.
    ::A0.008有一个重要数字。

    B. 0.000416 has three significant figures.
    ::B0.000416有三个重要数字。

    4. Zeros that appear after all nonzero digits are called right-end zeros.  Right-end zeros in a number that lacks a decimal point are not significant.

    A. 140 has two significant figures.
    ::A. 140有两个重要数字。

    B. 75,210 has four significant figures.
    ::B 75 210有四个重要数字。

    5. Right-end zeros in a number with a decimal point are significant.  This is true whether the zeros occur before or after the decimal point.

    A. 620.0 has four significant figures.
    ::A. 620.0有四个重要数字。

    B. 19.000 has five significant figures
    ::19.000 B19.000有5个重要数字

    It needs to be emphasized that to say a certain digit is not significant does not mean that it is not important or can be left out. Though the zero in a measurement of 140 may not be significant, the value cannot simply be reported as 14. An insignificant zero functions as a placeholder for the decimal point. When numbers are written in , this becomes more apparent. The measurement 140 can be written as 1.4 × 10 2 with two significant figures in the coefficient . For a number with left-end zeros, such as 0.000416, it can be written as 4.16 × 10 −4 with 3 significant figures. In some cases, scientific notation is the only way to correctly indicate the correct number of significant figures. In order to report a value of 15,000,000 with four significant figures, it would need to be written as 1.500 × 10 7 . The right-end zeros after the 5 are significant. The original number of 15,000,000 only has two significant figures. 
    ::需要强调的是,说某一位数不重要并不重要,并不意味着它不重要或可以被遗漏。虽然测量140时的零可能并不重要,但数值不能简单地报告为14。作为小数点的占位符,一个微不足道的零函数不能作为小数点的占位符报告。当数字写入时,这一点就更加明显了。测量140可以写成1.4×102,系数中有两个重要数字。对于左端0的数字,如0.00416,可以写成4.16×10-4,3个重要数字。在某些情况下,科学标记是正确显示重要数字正确数字的唯一方法。为了报告15 000 000美元的价值,4个重要数字,它需要写为1.500×107。在5个数字大之后,右端零,最初的数字为15 000 000 000,只有两个重要数字。

     

    Practice using significant figures in this simulation: 
    ::在模拟中使用重要数字的做法:

    Summary
    ::摘要

    • Significant figures give an indication of the certainty of a measurement.
      ::重要数字表明衡量的确定性。
    • Rules allow decisions to be made about how many digits to use in any given situation.
      ::规则允许就任何特定情况下使用多少位数作出决定。

    Review
    ::回顾

    1. What does a significant figure tell us?
      ::一个重要人物告诉我们什么?
    2. What is a left-end zero?
      ::什么是左端零?
    3. What is a right-end zero?
      ::右端零是什么?
    4. What does an insignificant zero do?
      ::一个微不足道的零能做什么?