4.9十进制乘法

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  十进制乘法

  

  [Figure 1]

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  Micah is preparing to go on a climbing trip and needs to buy climbing rope. The cost of the rope is $1.59  per  foot. He wants to buy 195.5 feet of rope. How much will the rope cost?
  ::Micah正准备登山,需要购买攀爬绳子。绳子的成本是每英尺1.59美元。他想买195.5英尺的绳子。绳子的成本是多少?

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  In this concept, you will learn how to multiply a decimal number with another decimal number.
  ::在此概念中, 您将学习如何乘以一个十进制数字, 并乘以另一个十进制数字 。

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  Multiplying Decimals
  ::乘进数十进数

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  One way to multiply decimals is using area models. Another more efficient way to multiply two decimals is to ignore the decimal and multiply the numbers as if they were  whole numbers  first. Afterwards, add the  decimal point  back into the product. It is important to place the decimal point in the correct place.
  ::乘以小数点的一种方法是使用区域模型。乘以两个小数点的另一种更有效的方法是忽略小数点,然后将数字像整数一样先乘以数字。然后,在产品中加入小数点。重要的是将小数点放在正确的位置。

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  Here is another multiplication problem.
  ::还有一个乘法问题。

  $$\begin{array}{r}4.7\times 2.1=\underset{\_}{}\end{array}$$

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  First, ignore the decimal point and multiply the numbers as if they were two whole numbers.
  ::首先,忽略小数点,将数字乘以两个整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 4.7\\ & & \underset{\_}{\times 2.1}\\ & & 47\\ & & \underset{\_}{+940}\\ & & 987\end{array}\end{array}$$

    

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  Then, place the decimal point into the product. Count the number of decimal places both multipliers. 4.7 has 1 decimal place. 2.1 also has 1 decimal places. There are a total of 2 decimal places. Move the decimal point 2 places to the left. Remember that the decimal point is located to the right of the ones place in a whole number.
  If you need to move the decimal point more places than there are digits, you can always use  zero  placeholders.
  ::然后将小数点移到产品中。计算小数点数后,两个乘数都位。4.7小数点为小数点数。4.7小数点为小数点数后位数。2.1小数点数后位数为小数点数。总和为小数点数。将小数点 2 位数移到左边。记住小数点位数位于整个数字中各个位置的右侧。如果需要移动小数点数点数后,您总是可以使用零占位符。

  $$\begin{array}{r}9.\underset{\leftarrow }{87}\end{array}$$

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  The product of 4.7 times 2.1 is 9.87.
  ::4.7乘2.1的产物为9.87。

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  Check to see if the decimal point was placed correctly by estimating the product of 4.7 times 2.1.
  ::通过估计4.7乘2.1的产物,检查小数点是否正确。

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  First,  round  the decimal numbers to the nearest whole number.
  ::首先,四舍五入小数到最近的整数。

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  4.7 rounds to 5.
  ::4.7至5轮。

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  2.1 rounds to 2.
  ::2.1至2发子弹。

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  Then, multiply to find an estimate product.
  ::然后,乘以找到估计产品。

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

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  Next, compare the products. The actual product should be close to the estimate product. 9.87 is close to 10. The decimal point was placed in the right location.
  ::接下来,比较产品。实际产品应该接近估计产品。9.87接近10。小数点位于正确的地点。

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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 Micah on the climbing trip.
  ::早些时候,你在登山旅行时 遇到Micah的问题

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  Micah wants to buy 195.5 feet of rope that costs $1.59 per foot. Multiply 195.5 by $1.59 to find the total cost of the rope.
  ::Micah想买195.5英尺的绳索,每英尺1.59美元,乘以195.5乘1.59,以找出绳索的总成本。

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  First, ignore the decimal point and multiply the numbers as if they were two whole numbers.
  ::首先,忽略小数点,将数字乘以两个整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 195.5\\ & & \underset{\_}{\times 1.59}\\ & & 17595\\ & & 9775\\ & & \underset{\_}{+1995}\\ & & 310845\end{array}\end{array}$$

    

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  Then, place the decimal point into the product. There are a total of 3 decimal places in the multiplicands. Move the decimal point 3 places to the left.
  ::然后将小数点移到产品中。在多个倍数中,总小数点为3位。将小数点3位移到左边。

  $$\begin{array}{r}310.\underset{\leftarrow }{845}\end{array}$$

   

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  The cost of the rope should be $310.845, but remember that dollars are only calculated to the hundredths place. Round the decimal to the nearest hundredths place.
  ::绳索的成本应该是310.845美元, 但记住美元只计算到第一百位。 将小数点的十进制到最近的一百位 。

  $$\begin{array}{r}\begin{array}{rcl}& & 310.8\underset{\_}{4}5\approx 310.85\\ & & \uparrow \end{array}\end{array}$$

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  Micah will spend $310.85 on climbing rope.
  ::Micah会花310.85美元用于攀爬绳子

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  Example 2
  ::例2

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  Multiply the decimals.
  ::乘以小数。

  $$\begin{array}{r}0.134\times 0.567=\underset{\_}{}\end{array}$$

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  First, ignore the decimal point and multiply the numbers as if they were two whole numbers.
  ::首先,忽略小数点,将数字乘以两个整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 0.134\\ & & \underset{\_}{\times 0.567}\\ & & 938\\ & & 804\\ & & \underset{\_}{+670}\\ & & 75978\end{array}\end{array}$$

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  Then, place the decimal point into the product. Count the number of decimal places both multipliers. 0.134 has 3 decimal places. 0.567 also has 3 decimal places. There are a total of 6 decimal places. Move the decimal point 6 places to the left. Remember that the decimal point is located to the right of the ones place in a whole number. Use a zero placeholder if needed.
  ::然后将小数点移到产品中。计算小数点数后,两个乘数都位。0.134是小数点数,3位是小数点数。0.567还有3位小数点数。总小数点数为6位数。将小数点 6 位数移到左边。记住小数点位于整个数字中位数的右侧。如果需要,请使用 0 占位符 。

  $$\begin{array}{r}0.\underset{\leftarrow }{075978}\end{array}$$

   

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  The product of 0.134 times 0.567 is 0.075978
  ::0.134乘以0.567为0.075978

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  Example 3
  ::例3

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  Multiply the decimals.
  ::乘以小数。

  $$\begin{array}{r}3.1\times 4.9=\underset{\_}{}\end{array}$$

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  First, ignore the decimal point and multiply the numbers as if they were two whole numbers.
  ::首先,忽略小数点,将数字乘以两个整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 3.1\\ & & \underset{\_}{\times 4.9}\\ & & 279\\ & & \underset{\_}{+124}\\ & & 1519\end{array}\end{array}$$

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  Then, place the decimal point into the product. There are a total of 2 decimal places in the multiplicands. Move the decimal point 2 places to the left.
  ::然后将小数点移到产品中。在多个倍数中总共有两个小数点位。将小数点 2 位移到左边。

  $$\begin{array}{r}15.\underset{\leftarrow }{19}\end{array}$$

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  The product of 3.1 times 4.9 is 15.19.
  ::3.1乘以4.9是15.19。

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  Example 4
  ::例4

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  Multiply the decimals.
  ::乘以小数。

  $$\begin{array}{r}1.2\times 5.1=\underset{\_}{}\end{array}$$

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  First, ignore the decimal point and multiply the numbers as if they were two whole numbers.
  ::首先,忽略小数点,将数字乘以两个整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 1.2\\ & & \underset{\_}{\times 5.1}\\ & & 12\\ & & \underset{\_}{+60}\\ & & 612\end{array}\end{array}$$

   

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  Then, place the decimal point into the product. There are a total of 2 decimal places in the multiplicands. Move the decimal point 2 places to the left.
  ::然后将小数点移到产品中。在多个倍数中总共有两个小数点位。将小数点 2 位移到左边。

  $$\begin{array}{r}6.\underset{\leftarrow }{12}\end{array}$$

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  The product of 1.2 times 5.1 is 6.12.
  ::1.2乘以5.1的产物为6.12。

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  Example 5
  ::例5

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  Multiply the decimals.
  ::乘以小数。

  $$\begin{array}{r}3.21\times 6.7=\underset{\_}{}\end{array}$$

   

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  First, ignore the decimal point and multiply the numbers as if they were two whole numbers.
  ::首先,忽略小数点,将数字乘以两个整数。

  $$\begin{array}{r}\begin{array}{rcl}& & 3.21\\ & & \underset{\_}{\times 6.7}\\ & & 2247\\ & & \underset{\_}{+1926}\\ & & 21507\end{array}\end{array}$$

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  Then, place the decimal point into the product. There are a total of 3 decimal places in the multiplicands. Move the decimal point 3 places to the left.
  ::然后将小数点移到产品中。在多个倍数中,总小数点为3位。将小数点3位移到左边。

  $$\begin{array}{r}21.\underset{\leftarrow }{507}\end{array}$$

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  The product of 3.21 times 6.7 is 21.507.
  ::3.21乘以6.7是21.507的产物。

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  Review
  ::回顾

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  Multiply the following decimals.
  ::乘以以下小数。

  1. $\begin{array}{r}4.3\times 0.12=\underset{\_}{}\end{array}$
  2. $\begin{array}{r}2.3\times 3.4=\underset{\_}{}\end{array}$
  3. $\begin{array}{r}0.34\times 0.56=\underset{\_}{}\end{array}$
  4. $\begin{array}{r}2.7\times 3.2=\underset{\_}{}\end{array}$
  5. $\begin{array}{r}6.5\times 2.7=\underset{\_}{}\end{array}$
  6. $\begin{array}{r}0.23\times 0.56=\underset{\_}{}\end{array}$
  7. $\begin{array}{r}1.23\times 0.4=\underset{\_}{}\end{array}$
  8. $\begin{array}{r}0.5\times 0.76=\underset{\_}{}\end{array}$
  9. $\begin{array}{r}0.23\times 0.8=\underset{\_}{}\end{array}$
  10. $\begin{array}{r}3.45\times 1.23=\underset{\_}{}\end{array}$
  11. $\begin{array}{r}1.45\times 0.23=\underset{\_}{}\end{array}$
  12. $\begin{array}{r}0.89\times 0.9=\underset{\_}{}\end{array}$
  13. $\begin{array}{r}0.245\times 0.8=\underset{\_}{}\end{array}$  
  14. $\begin{array}{r}34.5\times 0.7=\underset{\_}{}\end{array}$
  15. $\begin{array}{r}18.7\times 0.9=\underset{\_}{}\end{array}$
  16. $\begin{array}{r}22.3\times 0.76=\underset{\_}{}\end{array}$
  17. $\begin{array}{r}21.7\times 0.4=\underset{\_}{}\end{array}$ .
  18. $\begin{array}{r}14.5\times 0.68=\underset{\_}{}\end{array}$
  19. $\begin{array}{r}20.1\times 0.3=\underset{\_}{}\end{array}$  
  20. $\begin{array}{r}34.23\times 0.18=\underset{\_}{}\end{array}$
  21. $\begin{array}{r}0.189\times 0.9=\underset{\_}{}\end{array}$  
  22. $\begin{array}{r}0.341\times 0.123=\underset{\_}{}\end{array}$
  23. $\begin{array}{r}0.451\times 0.12=\underset{\_}{}\end{array}$
  24. $\begin{array}{r}0.768\times 0.123=\underset{\_}{}\end{array}$
  25. $\begin{array}{r}0.76\times 0.899=\underset{\_}{}\end{array}$

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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