3.17 增加和减减方面的重要数字

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  增加和减减的重要数字

  

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  How old do you think this calculator is?
  ::你觉得这个计算器多大了?

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  Calculators are great devices. Their invention has allowed for quick computation at work, school, or other places where manipulation of numbers needs to be done rapidly and accurately. But they are only as good as the numbers put into them. The calculator cannot determine how accurate each of a set of numbers is and the answer given on the screen must be assessed by the user for reliability.
  ::计算器是很棒的装置。 它们的发明允许在工作、学校或其他需要快速和准确操作数字的地方快速计算数字。 但是它们只和数字输入的一样好。计算器无法确定每组数字的准确性,屏幕上给出的答案必须由用户评估是否可靠。

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  Uncertainty in Addition and Subtraction
  ::增加和减减中的不确定性

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  Consider two separate mass measurements: 16.7 g and 5.24 g. The first mass measurement (16.7 g) is known only to the tenths place or to one digit after the decimal point. There is no information about its hundredths place and so that digit cannot be assumed to be zero. The second measurement (5.24 g) is known to the hundredths place or to two digits after the decimal point.
  ::考虑两个独立的质量测量:16.7克和5.24克。 第一次质量测量(16.7克)只为十分位或小数点后一位数。没有关于第一百位的资料,因此不能假定数字为零。 第二次测量(5.24克)为百位数,小数点后两位数。

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  When these masses are added together, the result on a calculator is 16.7 + 5.24 = 21.94 g. Reporting the answer as 21.94 g suggests that the sum is known all the way to the hundredths place. However that cannot be true because the hundredths place of the first mass was completely unknown. The calculated answer needs to be rounded in such a way as to reflect the certainty of each of the measured values that contributed to it. The following rule can be used:
  ::当将这些质量加在一起时,计算结果为16.7+5.24=21.94g。将答案报告为21.94g。将答案报告为21.94g表明,总和直到第100个地方都是已知的。然而,这不可能是真实的,因为第一个质量的第100个位置是完全未知的。计算的结果需要四舍五入,以便反映每个测量值的确定性。可以使用以下规则:

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  • For addition and subtraction problems, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places. 
    ::对于添加和减法问题,答案应四舍五入到小数位数与小数位数最少的计量相同的小数位数。

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  The sum of the above masses would be properly rounded to a result of 21.9 g. Let's take a look at another example below.
  ::上述质量的总和将适当四舍五入到21.9克的结果。

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  Example 1
  ::例1

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  Determine the combined molecular mass of a glucose molecule and a  maltose molecule.
  ::确定葡萄糖分子和麦芽分子的混合分子质量。

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  Glucose molecule = $\begin{array}{r}180.156\frac{g}{mol}\end{array}$  
  ::甘糖分子=180.156gmol

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  Maltos e molecule =  $\begin{array}{r}342.3\frac{g}{mol}\end{array}$  
  ::马尔塔斯分子=342.3gmol

  $\begin{array}{r}180.156+342.4=522.456\end{array}$  

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  When adding and subtracting we know to look at  the least number of decimals in our starting values; in this case 342.3 has only 1 digit after the decimal, so we need to round our answer to the same place.
  ::当增减时,我们知道要查看我们起始值中最小的十进制数;在此情况下,342.3在小数后只有1位数,所以我们需要将答案舍入到同一个位置。

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  $\begin{array}{r}522.456\to 522.5\end{array}$   $\begin{array}{r}\frac{g}{mol}\end{array}$  
  ::522.456522.5gmol

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  When working with whole numbers, determine where to round your answer in the same way. For example, consider the subtraction: 78,500 m – 362 m. The calculated result is 78,138 m. Because both of these numbers have no decimal places we will round the answer to the nearest whole number, which means our answer  remains  78,138 m.
  ::当使用整数工作时, 请以同样的方式决定您答案的圆周点。 例如, 考虑减法: 78, 500米 - 362米。 计算结果为78, 138米。 因为这两个数字没有小数点位数, 我们将将答案四舍五入到最近的整数, 这意味着我们的答案是78, 138米 。

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  Example 2
  ::例2

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  What is  $\begin{array}{r}4200+540=?\end{array}$  
  ::什么是4200+540=?

  $\begin{array}{r}4200+540=4740\end{array}$  

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  To determine where to round our answer, we look at our starting numbers to see which has the fewest number of decimal places. They both have 0 so we round to the nearest whole number , 4740.  
  ::为了决定我们答案的圆周位置, 我们查看我们的起始数, 看看小数位数中位数最少的位数。 它们都有0位, 因此我们四舍五入到最近的整位数, 即4740 位数 。

   

   

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  Summary
  ::摘要

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  • For addition and subtraction problems, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places.
    ::对于添加和减法问题,答案应四舍五入到小数位数与小数位数最少的计量相同的小数位数。
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    The number of significant figures in starting numbers does not matter when rounding after addition or subtraction, only the decimal places in those numbers matter.
    ::在加或减后四舍五入时,起始数字中的重要数字数量并不重要,只有这些数字的小数点位数重要。

    
    ::在加或减后四舍五入时,起始数字中的重要数字数量并不重要,只有这些数字的小数点位数重要。

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  Review
  ::回顾

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  1. What is the basic principle to use in working with addition and subtraction?
     ::在增加和减法工作中使用的基本原则是什么?
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  2. What do you pay attention to when working with whole numbers?
     ::你用全数计算时会注意什么?