4.2估算十进制乘法

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  估算十进制乘法

  

  [Figure 1]

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  At the Science Museum, Kelly wants to buy a few books on dinosaurs. Each book costs $14.65. She has $46 that she has been saving. Kelly estimates that she will have enough to buy 3 books. Is she right?
  ::在科学博物馆,Kelly想买几本恐龙书 每本书花费14.65美元 她存了46美元

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  In this concept, you will learn how to find an estimated product by  rounding  decimals to the nearest whole number.
  ::在此概念中,您将学习如何通过四舍五入到最近的整数来找到估计产品。

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  Estimating When Multiplying Decimals
  ::乘进数乘以十进数时的估算

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  You can multiply a decimal with a whole number to find an exact answer. When an exact answer is not necessary, you can find an approximate product by  estimating .
  ::您可以将小数点乘以一个整数来找到准确的答案。如果不需要准确的答案,您可以通过估计找到大致的产品。

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  To find a reasonable estimate using decimal numbers,  round  the decimal to the nearest whole number. Remember to look at the number in the tenths place.
  ::要用小数点数找到合理的估计数字,请将小数点舍入小数点到最接近的整数点。请注意十分位数中的数字。

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  If the number is less than 5, round the number down to the nearest whole number.
  ::如果数字小于5,则将数字四舍五入到最近的整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 3.498\approx 3\\ & & \uparrow \end{array}\end{array}$$

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  If the number is equal to or greater than 5, round the number up to the nearest whole number.
  ::如果数字等于或大于5,则将数字四舍五入至最近的整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 3.741\approx 4\\ & & \uparrow \end{array}\end{array}$$

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  Let’s look at an  estimation  problem. Estimate  $\begin{array}{r}5(1.7)=\underset{\_}{}\end{array}$
  ::让我们来看看估算问题。 估计值 5 (1.7) = _

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  First, round the decimal to the nearest whole number.
  ::首先,从小数点到最接近的整数四舍五入。

  $$\begin{array}{r}\begin{array}{rcl}& & 1.7\approx 2\\ & & \uparrow \end{array}\end{array}$$

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  Then, rewrite the problem and multiply.
  ::然后,重写问题 并倍增。

  $$\begin{array}{r}5(2)=10\end{array}$$

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  An estimated product for  $\begin{array}{r}5(1.7)\end{array}$  is 10.
  ::估计5(1.7)的产值为10。

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  Here is another estimation problem. Estimate  $\begin{array}{r}7(4.3)=\underset{\_}{}\end{array}$
  ::还有另一个估算问题。估计值7 (4.3) = _

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  First, round the decimal to the nearest whole number.
  ::首先,从小数点到最接近的整数四舍五入。

  $$\begin{array}{r}\begin{array}{rcl}& & 4.3\approx 4\\ & & \uparrow \end{array}\end{array}$$

   

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  Then, rewrite the problem and multiply.
  ::然后,重写问题 并倍增。

  $$\begin{array}{r}7(4)=28\end{array}$$

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  An estimate product for  $\begin{array}{r}7(4.3)\end{array}$  is 28.
  ::估计7(4.3)的产值为28。

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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 Kelly at the Science Museum.
  ::早些时候,你在科学博物馆 遇到关于Kelly的问题

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  Kelly thinks that $46 is enough to buy 3 books that cost $14.65. Estimate the product to check if she is right.
  ::Kelly认为46美元足以买三本价14.65美元的书。

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  First, write a multiplication problem to find the cost of the books.
  ::首先,写一个乘法问题来找出帐本的成本。

  $$\begin{array}{r}3(14.65)=\underset{\_}{}\end{array}$$

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  Then, round the decimal to the nearest whole number.
  ::然后,将小数点到最近的整数点左右。

  $$\begin{array}{r}\begin{array}{rcl}& & 14.65\approx 15\\ & & \uparrow \end{array}\end{array}$$

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  Next, rewrite the problem and multiply.
  ::下一个,重写问题并倍增。

  $$\begin{array}{r}3(15)=45\end{array}$$

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  The books will cost approximately $45.00. Kelly is correct; $46 should be enough to purchase 3 books.
  ::Kelly是正确的;46美元应足以购买3本书。

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  Example 2
  ::例2

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  Estimate the product.
  ::估计产品。

  $$\begin{array}{r}4(7.82)=\underset{\_}{}\end{array}$$

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  First, round the decimal to the nearest whole number.
  ::首先,从小数点到最接近的整数四舍五入。

  $$\begin{array}{r}\begin{array}{rcl}& & 7.82\approx 8\\ & & \uparrow \end{array}\end{array}$$

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  Then, rewrite the problem and multiply.
  ::然后,重写问题 并倍增。

  $$\begin{array}{r}4(8)=32\end{array}$$

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  An estimate product for  $\begin{array}{r}4(7.82)\end{array}$  is 32.
  ::估计4(7.82)的产值为32。

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  Example 3
  ::例3

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  Estimate the product.
  ::估计产品。

  $$\begin{array}{r}4(3.2)=\underset{\_}{}\end{array}$$

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  First, round the decimal to the nearest whole number.
  ::首先,从小数点到最接近的整数四舍五入。

  $$\begin{array}{r}\begin{array}{rcl}& & 3.2\approx 3\\ & & \uparrow \end{array}\end{array}$$

   

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  Then, rewrite the problem and multiply.
  ::然后,重写问题 并倍增。

  $$\begin{array}{r}4(3)=12\end{array}$$

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  An estimate product for  $\begin{array}{r}4(3.2)\end{array}$  is 12.
  ::估计4(3.2)的产值为12。

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  Example 4
  ::例4

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  Estimate the product.
  ::估计产品。

  $$\begin{array}{r}6(2.8)=\underset{\_}{}\end{array}$$

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  First, round the decimal to the nearest whole number.
  ::首先,从小数点到最接近的整数四舍五入。

  $$\begin{array}{r}\begin{array}{rcl}& & 2.8\approx 3\\ & & \uparrow \end{array}\end{array}$$

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  Then, rewrite the problem and multiply.
  ::然后,重写问题 并倍增。

  $$\begin{array}{r}6(3)=18\end{array}$$

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  An estimate product for  $\begin{array}{r}6(2.8)\end{array}$  is 18.
  ::估计6(2.8)的产值为18。

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  Example 5
  ::例5

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  Estimate the product.
  ::估计产品。

  $$\begin{array}{r}7(5.3)=\underset{\_}{}\end{array}$$

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  First, round the decimal to the nearest whole number.
  ::首先,从小数点到最接近的整数四舍五入。

  $$\begin{array}{r}\begin{array}{rcl}& & 5.3\approx 5\\ & & \uparrow \end{array}\end{array}$$

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  Then, rewrite the problem and multiply.
  ::然后,重写问题 并倍增。

  $$\begin{array}{r}7(5)=35\end{array}$$

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  An estimate product for  $\begin{array}{r}7(5.3)\end{array}$  is 35.
  ::估计7(5.3)的产值为35。

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  Review
  ::回顾

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  Estimate the product for the following problems.
  ::估计以下各问题的产品。

  1. $\begin{array}{r}4(3.2)=\underset{\_}{}\end{array}$
  2. $\begin{array}{r}5(1.8)=\underset{\_}{}\end{array}$
  3. $\begin{array}{r}6(2.3)=\underset{\_}{}\end{array}$
  4. $\begin{array}{r}9(1.67)=\underset{\_}{}\end{array}$
  5. $\begin{array}{r}8(4.5)=\underset{\_}{}\end{array}$
  6. $\begin{array}{r}9(6.7)=\underset{\_}{}\end{array}$
  7. $\begin{array}{r}4(8.1)=\underset{\_}{}\end{array}$
  8. $\begin{array}{r}8(3.2)=\underset{\_}{}\end{array}$
  9. $\begin{array}{r}9(9.7)=\underset{\_}{}\end{array}$
  10. $\begin{array}{r}7(1.1)=\underset{\_}{}\end{array}$
  11. $\begin{array}{r}8(3.5)=\underset{\_}{}\end{array}$
  12. $\begin{array}{r}5(8.4)=\underset{\_}{}\end{array}$
  13. $\begin{array}{r}12(9.1)=\underset{\_}{}\end{array}$
  14. $\begin{array}{r}9(11.9)=\underset{\_}{}\end{array}$
  15. $\begin{array}{r}6(12.3)=\underset{\_}{}\end{array}$
  16. $\begin{array}{r}9(13.8)=\underset{\_}{}\end{array}$
  17. $\begin{array}{r}8(14.3)=\underset{\_}{}\end{array}$

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源