2.5 通过首位估算进行小数加法

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  通过首位估算进行小数加法

  

  [Figure 1]

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  Kim is packaging up some books to send to her brother who is studying abroad in Europe. She learns that the weight limit for the flat  rate  box she is using from the post office is 20 pounds. She has 4 books that she wants to send to her brother. The books weigh 5.431 pounds, 3.713 pounds, 4.1325 pounds, and 3.98 pounds. How can Kim estimate the total weight of the books she wants to send? Will she be able to send them in the flat rate box?
  ::金正文正在整理一些书,以便寄给她正在欧洲留学的兄弟。她从邮局得知,她使用的平价箱的重量限为20磅。她有四本书想寄给她的兄弟。书重5.431磅,3.713磅,4.1325磅和3.98磅。金如何估计她想寄出的书的总重量?她能否用平价箱寄出?

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  In this concept, you will learn how to estimate decimal sums using  front-end estimation .
  ::在此概念下,您将学会如何使用前端估计来估计小数总和。

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  Adding Decimals Using Front-End Estimation
  ::使用前端前端估计方法添加十进制

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  To  estimate  means to find an approximate solution to a problem.
  ::估计找到一个问题大致解决办法的手段。

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  You can estimate a solution when you don’t need an exact answer, when you need to quickly get an idea of what an answer will be, or when you want to check if your exact answer is reasonable.
  ::如果您不需要确切的答案, 需要快速了解答案会是什么, 或想知道答案是否合理, 可以估算解决方案 。

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  There are many different methods for  estimation . One method is  front-end estimation . Front-end estimation relies on adding the front-end digits (the left-most digits) of the numbers.
  ::估算方法有很多不同。 一种方法是前端估算。 前端估算依赖于添加数字的前端位数( 最左边位数 ) 。

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  Here are the steps for front-end estimation with decimal number addition.
  ::这是前端估计步骤,加上小数数。

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  1. Add the digits to the left of the  decimal point  (the whole numbers).
     ::将数字添加到小数点左边(整个数字)。
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  2. Add the digits directly to the right of the decimal point (the digits in the tenths place).
     ::将数字直接添加到小数点右侧(十位数中的位数)。
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  3. Add the results from steps 1 and 2.
     ::加上步骤1和步骤2的结果。

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  Here is an example.
  ::举一个例子。

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  Use front-end estimation to estimate the  sum  of 6.819 and 4.621.
  ::使用前端估计来估计6.819和4.621的总额。

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  First, arrange the numbers vertically, lining up the decimal points.
  ::首先,垂直排列数字,将小数点排成一行。

  $$\begin{array}{r}6.819\\ 4.621\end{array}$$

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  Now, add the  whole numbers .
  ::现在,加上全部数字。

  $$\begin{array}{r}6+4=10\end{array}$$

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  Next, add the digits in the tenths place.
  ::接下来,在十分位数中添加数字。

  $$\begin{array}{r}0.8+0.6=1.4\end{array}$$

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  Finally, add the results.
  ::最后,加上结果。

  $$\begin{array}{r}10+1.4=11.4\end{array}$$

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  The answer is 6.819 plus 4.621 is approximately 11.4.
  ::答案是6.819+4.621约为11.4。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Kim, who is packaging up some books to send to her brother.
  ::之前,你被问及金金的问题, 他正在整理一些书 寄给她哥哥。

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  The weight limit for the box she is using is 20 pounds. The 4 books she wants to send weigh 5.431 pounds, 3.713 pounds, 4.1325 pounds, and 3.98 pounds. Kim needs to see if her books weigh less than the 20 pound limit.
  ::她使用的盒子的重量限是20磅。她要寄的4本书是5.431磅、3.713磅、4.1325磅和3.98磅。Kim需要看看她的书重量是否低于20磅的限值。

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  First, arrange the numbers vertically, lining up the decimal points.
  ::首先,垂直排列数字,将小数点排成一行。

  $$\begin{array}{r}\begin{array}{rc}& 5.431\\ & 3.713\\ & 4.1325\\ & 3.98\end{array}\end{array}$$

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  Now, add the whole numbers.
  ::现在,加上全部数字。

  $$\begin{array}{r}5+3+4+3=15\end{array}$$

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  Next, add the digits in the tenths place.
  ::接下来,在十分位数中添加数字。

  $$\begin{array}{r}0.4+0.7+0.1+0.9=2.1\end{array}$$

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  Finally, add the results.
  ::最后,加上结果。

  $$\begin{array}{r}15+2.1=17.1\end{array}$$

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  The answer is that all together the books weigh about 17.1 pounds. Even though this is a slight underestimation of their weight, they definitely weigh under 20 pounds. Kim will be able to mail them in the box.
  ::答案是,所有的书体总重约17.1磅。尽管这是对书体重量的略微低估,但书体重量肯定低于20磅。金可以把它们寄到盒子里。

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  Example 2
  ::例2

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  Use front-end estimation to estimate the sum of 2.93474 and 9.72155.
  ::使用前端估计来估计2.93474和9.72155的总额。

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  First, arrange the numbers vertically, lining up the decimal points.
  ::首先,垂直排列数字,将小数点排成一行。

  $$\begin{array}{r}2.93474\\ 9.72155\end{array}$$

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  Now, add the whole numbers.
  ::现在,加上全部数字。

  $$\begin{array}{r}2+9=11\end{array}$$

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  Next, add the digits in the tenths place.
  ::接下来,在十分位数中添加数字。

  $$\begin{array}{r}0.9+0.7=1.6\end{array}$$

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  Finally, add the results.
  ::最后,加上结果。

  $$\begin{array}{r}11+1.6=12.6\end{array}$$

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  The answer is 2.93474 plus 9.72155 is approximately 12.6.
  ::答案是2.93474加9.72155约为12.6。

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  Example 3
  ::例3

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  Use front-end estimation to estimate the sum of 3.5137 and 2.34.
  ::使用前端估计来估计3.5137和2.34的总额。

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  First, arrange the numbers vertically, lining up the decimal points.
  ::首先,垂直排列数字,将小数点排成一行。

  $$\begin{array}{r}\begin{array}{rc}& 3.5137\\ & 2.34\end{array}\end{array}$$

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  Now, add the whole numbers.
  ::现在,加上全部数字。

  $$\begin{array}{r}3+2=5\end{array}$$

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  Next, add the digits in the tenths place.
  ::接下来,在十分位数中添加数字。

  $$\begin{array}{r}0.5+0.3=0.8\end{array}$$

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  Finally, add the results.
  ::最后,加上结果。

  $$\begin{array}{r}5+0.8=5.8\end{array}$$

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  The answer is 3.5137 plus 2.34 is approximately 5.8.
  ::答案是3.5137加2.34,大约为5.8。

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  Example 4
  ::例4

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  Use front-end estimation to estimate the sum of 12.67194 and 8.1232.
  ::使用前端估计来估计12.67194和8.1232的总额。

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  First, arrange the numbers vertically, lining up the decimal points.
  ::首先,垂直排列数字,将小数点排成一行。

  $$\begin{array}{r}\begin{array}{rc}& 12.67194\\ & 8.1232\end{array}\end{array}$$

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  Now, add the whole numbers.
  ::现在,加上全部数字。

  $$\begin{array}{r}12+8=20\end{array}$$

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  Next, add the digits in the tenths place.
  ::接下来,在十分位数中添加数字。

  $$\begin{array}{r}0.6+0.1=0.7\end{array}$$

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  Finally, add the results.
  ::最后,加上结果。

  $$\begin{array}{r}20+0.7=20.7\end{array}$$

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  The answer is 12.67194 plus 8.1232 is approximately 20.7.
  ::答案是12.67194加8.1232约为20.7。

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  Example 5
  ::例5

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  Use front-end estimation to estimate the sum of 15.67018 and 9.34523.
  ::使用前端估计来估计15.67018和9.34523的总额。

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  First, arrange the numbers vertically, lining up the decimal points.
  ::首先,垂直排列数字,将小数点排成一行。

  $$\begin{array}{r}15.67018\\ 9.34523\end{array}$$

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  Now, add the whole numbers.
  ::现在,加上全部数字。

  $$\begin{array}{r}15+9=24\end{array}$$

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  Next, add the digits in the tenths place.
  ::接下来,在十分位数中添加数字。

  $$\begin{array}{r}0.6+0.3=0.9\end{array}$$

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  Finally, add the results.
  ::最后,加上结果。

  $$\begin{array}{r}24+0.9=24.9\end{array}$$

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  The answer is 15.67018 plus 9.34523 is approximately 24.9.
  ::答案是15.67018+9.34523约为24.9。

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  Review
  ::回顾

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  Use front-end estimation to estimate the following sums.
  ::使用前端估计来估计以下数额。

  1. $\begin{array}{r}4.57+2.34\end{array}$
  2. $\begin{array}{r}2.123+4.136\end{array}$
  3. $\begin{array}{r}8.913+2.047\end{array}$
  4. $\begin{array}{r}8.7651+2.345\end{array}$
  5. $\begin{array}{r}2.436+4.567\end{array}$
  6. $\begin{array}{r}8.127+9.431\end{array}$
  7. $\begin{array}{r}8.214+7.3214\end{array}$
  8. $\begin{array}{r}12.137+2.456\end{array}$
  9. $\begin{array}{r}18.671+20.41\end{array}$
  10. $\begin{array}{r}21.643+22.123\end{array}$
  11. $\begin{array}{r}18.012+19.367\end{array}$
  12. $\begin{array}{r}21.456+18.023\end{array}$
  13. $\begin{array}{r}0.48218+0.61927\end{array}$
  14. $\begin{array}{r}6.7765+6.421192\end{array}$
  15. $\begin{array}{r}0.5075412+0.859931+0.373462\end{array}$

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  Review (Answers)
  ::回顾(答复)