4.14用十的幂除以的心算

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  用十的幂除以的心算

  

  [Figure 1]

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  Kailey needs to decide on a science project. She wants to make a model of the Earth for science class. The Earth’s diameter is about 12,756.3 kilometers. She thinks that a model 10,000 times smaller than the actual Earth might work. Would this be a reasonable size model for a class project?
  ::凯利需要决定一个科学项目。 她想为科学类制作一个地球模型。 地球直径约为12,756.3公里。 她认为一个比实际地球小10,000倍的模型可能有效。 这是否是一个合理规模模型?

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  In this concept, you will learn to  divide  decimals by  powers of ten  using mental math.
  ::在此概念中,您将学会使用心理数学将十位数除以十位数的功率。

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  Dividing by Powers of Ten
  ::十国强权的分裂

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  You have already learned how to use mental math to multiply decimal numbers by  powers of ten .
  ::您已经学会了如何使用心理数学 乘以十位数乘以十位数的功率。

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  • When multiplying by whole number powers of ten, the number will become larger. Move the decimal to the  right  once for every  zero  in the power of ten.
    ::当乘以十的整数功率乘以十时, 数字会变大。 在十时的功率为每零时, 将小数点向右移动一次 。
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  • When multiplying by decimal powers of ten, the number will become smaller. Move the decimal to the  left  once for every decimal  place value .
    ::当乘以十位数的十位数乘以十位数时,数字会变小。将小数数位数移到左位数时,每个小数点位数的位数都会移动一次。

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  You can also use mental math to divide by powers of ten. The process is similar to multiplying powers of ten, except you move the  decimal point  the opposite direction.
  ::您也可以使用心理数学来除以 10 的功率。这一过程类似于乘以 10 的功率,但将小数点向相反方向移动时除外。

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  Let’s look at a decimal number divided by power of ten numbers.
  ::让我们看看十位数除以十位数的功率。

  $$\begin{array}{r}\begin{array}{rcl}& & 2.5÷1\underset{\_}{0}=0.\underset{\leftarrow }{2}5\\ & & 2.5÷1\underset{\_}{0}\underset{\_}{0}=0.\underset{\leftarrow }{02}5\\ & & 2.5÷1\underset{\_}{0}\underset{\_}{0}\underset{\_}{0}=0.\underset{\leftarrow }{002}5\end{array}\end{array}$$

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  The decimal point is moved to the left once for every 10 multiplied or the number of zeros in the power of ten number. In the first example, 10 has one zero and the decimal point is moved one place to the left. In the second example, 100 has two zeros and the decimal point is moved two places to the left. The third example has three zeros and the decimal point is moved three places to the left.
  ::小数点向左移动一次,每10乘10,或十位数为零。在第一个例子中,10是零,小数点向左移动1 个。在第二个例子中,100是2个零,小数点向左移动2个。第三个例子为3个零,小数点向左移动3个。

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  Let’s look at a decimal number divided by decimal power of ten numbers.
  ::让我们看看十位数除以十位数的十位数。

  $$\begin{array}{r}\begin{array}{rcl}& & 2.5÷0.\underset{\_}{1}=2\underset{\to }{5}\\ & & 2.5÷0.\underset{\_}{0}\underset{\_}{1}=2\underset{\to }{50}\\ & & 2.5÷0.\underset{\_}{0}\underset{\_}{0}\underset{\_}{1}=2,\underset{\to }{500}\end{array}\end{array}$$

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  The decimal point in the product is moved to the right for every decimal place in the power of ten number. In the first example, there is one decimal place in 0.1 and the decimal point is moved one place to the right. In the second example, there are two decimal places in 0.01 and the decimal point is moved two places to the right. The third example has three decimal places in 0.001 and the decimal point is moved three places to the right.
  ::产品中的小数点在十位数的功率下移动到右侧。 在第一个例子中,小数点在 0.1 中有一个小数点,小数点向右移动一个。在第二个例子中,0.01 中有两个小数点,小数点向右移动两个位。第三个例子在0.001 中有三个小数点,小数点向右移动三个位。

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  Depending on what type of power of ten is the  divisor , you can calculate the  quotient  using mental math.
  ::取决于十分之一的功率是什么类型, 你可以用心理数学来计算商数。

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  • When dividing by whole number powers of ten, the number will become smaller. Move the decimal to the  left  once for every zero in the power of ten.
    ::当整数除以十的全数功率时, 数字会变小。 在十的功率为十时, 将小数点向左移动一次, 每零位的小数点向左移动一次 。
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  • When dividing by decimal powers of ten, the number will become larger. Move the decimal to the  right  once for every decimal place value.
    ::当除以十位十位数的十位数时,数字会变大。将每个十位数的十位数移到右边一次。

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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 Kailey’s science project.
  ::先前,你曾因Kailey的科学项目而遇到问题。

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  Kailey wants to make a model of the earth that is 10,000 times smaller of the Earth. To find the diameter of the model, divide the actual diameter by 10,000.
  ::Kailey 想要制作一个比地球小一万倍的地球模型。 要找到模型的直径, 请将实际直径除以一万。

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  First, write an equation to find the diameter of the model. The Earth’s diameter is about 12,756.3 kilometers.
  ::首先,写一个方程以找到模型的直径。地球的直径约为12,756.3公里。

  $$\begin{array}{r}12,756.3÷10,000=\underset{\_}{}\end{array}$$

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  Then, use mental math to find the quotient. Count the number of zeros in the power of ten number. There are four zeros.
  ::然后,运用心理数学来找到商数。 计算十位数的零数。 有四位数 。

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  Next, move the decimal point four places to the left.
  ::下一步,将小数点四移到左边。

  $$\begin{array}{r}12,756.3\to 1.27563\end{array}$$

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  A model 10,000 times smaller than the Earth will have a diameter of 1.27563 kilometers. It would be far too big for a science class project.
  ::比地球小一万倍的模型直径将为1.27563公里。对于科学类项目来说,这个模型太大了。

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  Example 2
  ::例2

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  Use mental math to find the quotient.
  ::运用心理数学来找到商数。

  $$\begin{array}{r}67.89÷100=\underset{\_}{}\end{array}$$

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  First, count the number of zeros in the power of ten number. There are two.
  ::首先,在十位数的功率下计数零数。有两个。

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  Then, move the decimal point two places to the left.
  ::然后,将小数点两点移到左边。

  $$\begin{array}{r}67.89\to 0.6789\end{array}$$

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  The quotient of 67.89 divided by 100 is 0.6789.
  ::67.89除以100的商数为0.6789为0.6789。

  $$\begin{array}{r}0.7893÷0.001=\underset{\_}{}\end{array}$$

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  First, count the number of decimal place values in the power of ten number. There are three.
  ::首先,以十位数的功率计算十位数的小数位数。有三位。

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  Then, move the decimal point three places to the right.
  ::然后,将小数点三移到右边。

  $$\begin{array}{r}0.7893\to 789.3\end{array}$$

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  The quotient for 0.7893 divided by 0.001 is 789.3.
  ::0.7893除以0.001后除以0.001的商数为789.3。

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  Use mental math to find the quotient for the following problems.
  ::使用心理数学来寻找以下问题的商数。

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  Example 3
  ::例3

  $$\begin{array}{r}4.5÷10=\underset{\_}{}\end{array}$$

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  First, count the number of zeros in the power of ten number. There is one.
  ::首先,在十位数的功率下计数零数。有一个。

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  Then, move the decimal point once to the left.
  ::然后,将小数点移到左边。

  $$\begin{array}{r}4.5\to 0.45\end{array}$$

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  The quotient of 4.5 divided by 10 is 0.45.
  ::4.5的商数除以10为0.45。

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  Example 4
  ::例4

  $$\begin{array}{r}12.3÷0.01=\underset{\_}{}\end{array}$$

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  First, count the number of decimal place values in the power of ten number. There are two.
  ::首先,以十位数的功率计算十位数的小数位数。有两个。

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  Then, move the decimal point two places to the right.
  ::然后,将小数点两点移到右边。

  $$\begin{array}{r}12.3\to 1230.\end{array}$$

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  The quotient of 12.3 divided by 0.01 is 1230.
  ::12.3除以0.01除以1230的商数为1230。

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  Example 5
  ::例5

  $$\begin{array}{r}87.4÷1,000=\underset{\_}{}\end{array}$$

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  First, count the number of zeros in the power of ten number. There are three.
  ::首先,在十位数的功率下计数零数。有三位。

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  Then, move the decimal point three places to the left.
  ::然后,将小数点三移到左边。

  $$\begin{array}{r}87.4\to 0.0874\end{array}$$

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  The quotient of 87.4 divided by 1,000 is 0.0874.
  ::87.4除以1 000的商数为0.0874。

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  Review
  ::回顾

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  Use mental math to find the product for the following problems.
  ::使用心理数学来寻找产品,解决以下问题。

  1. $\begin{array}{r}3.4÷10=\underset{\_}{}\end{array}$
  2. $\begin{array}{r}8.91÷10=\underset{\_}{}\end{array}$
  3. $\begin{array}{r}67.89÷10=\underset{\_}{}\end{array}$
  4. $\begin{array}{r}67.89÷100=\underset{\_}{}\end{array}$
  5. $\begin{array}{r}32.1÷100=\underset{\_}{}\end{array}$
  6. $\begin{array}{r}4.545÷1000=\underset{\_}{}\end{array}$
  7. $\begin{array}{r}457.2÷1000=\underset{\_}{}\end{array}$
  8. $\begin{array}{r}1234.5÷1000=\underset{\_}{}\end{array}$
  9. $\begin{array}{r}6.7÷0.1=\underset{\_}{}\end{array}$
  10. $\begin{array}{r}2.1÷0.1=\underset{\_}{}\end{array}$
  11. $\begin{array}{r}0.987÷0.01=\underset{\_}{}\end{array}$
  12. $\begin{array}{r}456.8÷0.01=\underset{\_}{}\end{array}$
  13. $\begin{array}{r}0.08÷0.01=\underset{\_}{}\end{array}$  
  14. $\begin{array}{r}6.73÷0.001=\underset{\_}{}\end{array}$
  15. $\begin{array}{r}77.01÷0.001=\underset{\_}{}\end{array}$
  16. $\begin{array}{r}8.68÷0.0001=\underset{\_}{}\end{array}$

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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