3.15 将分数转换为小数

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• 选择节 将分数转换为小数

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  将分数转换为小数

  

  [Figure 1]

  Erik is making Italian bread to go with his mom's lasagna for dinner tonight. Instead of using measuring cups to measure his ingredients by volume, he is using a scale to measure his ingredients by weight. Erik’s recipe calls for   $\begin{array}{r}10\frac{5}{8}\end{array}$  ounces of water. The numbers on Erik’s scale are shown in decimal form. How can Erik figure out what number his scale should show when he has added the correct  amount  of water?

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  In this concept, you will learn how to write fractions and mixed numbers as terminating decimals.
  ::在此概念中,您将学习如何将分数和混合数字写成终止小数。

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  Writing Fractions and Mixed Numbers as Decimals
  ::小数和混合数字作为十进制

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  Fractions and decimals are both ways of describing numbers that are not  whole numbers . Every fraction is equivalent to some decimal. To write a fraction as a decimal, remember that a fraction is really just a division expression. For example,  $\begin{array}{r}\frac{3}{4}\end{array}$  is the same as  $\begin{array}{r}3÷4\end{array}$ .
  ::分数和小数点是描述数字的两种方式,它们不是整数。每个分数都相当于一些小数点。如果将一个分数写为小数点,请记住一个分数实际上只是一个分割表达式。例如,3 4和3 + 4相同。

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  Here are the steps for writing a fraction as a decimal.
  ::这是将分数写为十进制的步数 。

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  1. Rewrite your fraction as a division problem.
     ::将您的分数重写为分裂问题 。
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  2. Divide  using long division. Add a  decimal point  and zeros to the  dividend  as needed.
     ::使用长除法除法。根据需要,在红利中加上小数点和零。

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  Here is an example.
  ::举一个例子。

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  Convert  $\begin{array}{r}\frac{3}{4}\end{array}$  to a decimal.
  ::将3 4转换为小数。

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  First, write  $\begin{array}{r}\frac{3}{4}\end{array}$  as a division problem.
  ::首先,写34,作为一个分裂问题。

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  $\begin{array}{r}\frac{3}{4}\end{array}$  is the same as  $\begin{array}{r}3÷4\end{array}$ .
  ::3是3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于3等于4等于4等于3等于3等于4等于4等于3等于4等于4等于3等于3等于4等于3等于4等于4等于4等于3等于3等于4等于4等于3等于3等于4等于4等于3等于3等于4等于4等于3等于4等于3等于3等于4等于3等于4等于3等于4等于4等于3等于3等于4等于3等于4等于4等于3等于3等于4等于4等于3等于3等于4等于4等于3等于4等于3等于4等于4等于3等于4等于4等于3等于4等于3等于4等于4等于3等于4等于3等于4等于3等于4等于4等于4等于4等于3等于4等于4等于3等于4等于4等于4等于3等于4等于4等于4等于3等于4等于4等于4等于4等于4等于3等于4等于4等于4等于4等于4等于4等于4等于4等于3等于4等于4等于4等于4等于4等于4等于3等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于3等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于4等于3

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  Next, use long division to divide. You will need to add a decimal point and zeros to the 3.
  ::下一步,使用长除法进行分隔。您需要在 3 中加上小数点和零。

  $$\begin{array}{rl}& \stackrel{0.75}{4\overline{)3.00}}\\ & \underset{\_}{-28}\\ & 20\\ & \underset{\_}{-20}\\ & 0\end{array}$$

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  The answer is  $\begin{array}{r}\frac{3}{4}=0.75\end{array}$ .
  ::答案是3 4 = 0.75。

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  You can also  . Here are the steps for writing mixed numbers as decimals.
  ::您也可以。这里是将混合数字写成小数的阶梯。

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  1. Convert the fractional part of the  mixed number  to a decimal using long division.
     ::使用长分割法将混合数字的分数部分转换为小数。
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  2. Add the whole number part of the mixed number to the result from step 1.
     ::将混合数字的整个编号部分加上第1步的结果。

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  Here is an example.
  ::举一个例子。

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  Convert  $\begin{array}{r}3\frac{1}{2}\end{array}$  to a decimal.
  ::将312转换为小数。

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  First, set aside the 3.  $\begin{array}{r}\frac{1}{2}\end{array}$  is the same as  $\begin{array}{r}1÷2\end{array}$ . Convert the  $\begin{array}{r}\frac{1}{2}\end{array}$  to a decimal using long division.
  ::首先,搁置3,12和1,%2相同。用长分法将12转换为小数。

  $$\begin{array}{rl}& \stackrel{0.5}{2\overline{)1.0}}\\ & \underset{\_}{-10}\\ & 0\end{array}$$

  
  

  $$\begin{array}{r}\frac{1}{2}=0.5\end{array}$$

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  Next, add the 3 from the original mixed number.
  ::下面加上原来的混合数字中的3。

  $$\begin{array}{r}3.5\end{array}$$

  
  

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  The answer is  $\begin{array}{r}3\frac{1}{2}=3.5\end{array}$ .
  ::答案是3 1 2 = 3.5 。

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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 Erik and his Italian bread.
  ::早些时候,你被问及 Erik 和他的意大利面包的问题。

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  He needs  $\begin{array}{r}10\frac{5}{8}\end{array}$  ounces of water to make his bread dough, but his scale only shows numbers in decimal form. Erik needs to figure out what number his scale should show when he has added the correct amount of water.
  ::他需要10,5,8盎司的水来做面包面团,但他的规模只以小数表示数字。 Erik需要弄清楚当他添加了正确的水量时,他的规模应该显示多少。

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  Erik needs to convert  $\begin{array}{r}10\frac{5}{8}\end{array}$  to a decimal.
  ::Erik需要转换10 -5 -8到小数点

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  First, he should set aside the 10.  $\begin{array}{r}\frac{5}{8}=5÷8\end{array}$ . He needs to convert the  $\begin{array}{r}\frac{5}{8}\end{array}$  to a decimal using long division.
  ::首先,他应该搁置10,5,8=5,8。他需要用长分法将5,8小数转换为小数。

  $$\begin{array}{rl}& \stackrel{0.625}{8\overline{)5.000}}\\ & \underset{\_}{-48}\\ & 20\\ & \underset{\_}{-16}\\ & 40\\ & \underset{\_}{-40}\\ & 0\end{array}$$

  $$\begin{array}{r}\frac{5}{8}=0.625\end{array}$$

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  Next, he should add the 10 from the original mixed number.
  ::其次,他应从原来的混合数字中加上10。

  $$\begin{array}{r}10.625\end{array}$$

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  The answer is Erik should look for his scale to show 10.625 when he has added the correct amount of water.
  ::答案是Erik应该寻找他的尺码 显示10.625 当他添加了正确的水量时

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  Example 2
  ::例2

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  Convert  $\begin{array}{r}4\frac{3}{5}\end{array}$  to a decimal.
  ::将4 3 5转换为小数。

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  First, set aside the 4.  $\begin{array}{r}\frac{3}{5}\end{array}$  is the same as  $\begin{array}{r}3÷5\end{array}$ . Convert the  $\begin{array}{r}\frac{3}{5}\end{array}$  to a decimal using long division.
  ::首先,搁置4,3,5和3,5相同。用长分法将3,5小数转换为小数。

  $$\begin{array}{rl}& \stackrel{0.6}{5\overline{)3.0}}\\ & \underset{\_}{-30}\\ & 0\end{array}$$

  $$\begin{array}{r}\frac{3}{5}=0.6\end{array}$$

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  Next, add the 4 from the original mixed number.
  ::下面加上原来的混合数字中的4。

  $$\begin{array}{r}4.6\end{array}$$

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  The answer is  $\begin{array}{r}4\frac{3}{5}=4.6\end{array}$ .
  ::答案是4 3 5 = 4.6。

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  Example 3
  ::例3

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  Convert  $\begin{array}{r}\frac{1}{5}\end{array}$  to a decimal.
  ::将15转换为小数点后一位。

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  First, write  $\begin{array}{r}\frac{1}{5}\end{array}$  as a division problem.
  ::首先,写15,作为一个分裂问题。

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  $\begin{array}{r}\frac{1}{5}\end{array}$  is the same as  $\begin{array}{r}1÷5\end{array}$ .
  ::1 5和1 5相同。

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  Next, use long division to divide. You will need to add a decimal point and a  zero  to the 1.
  ::下一步,使用长除法进行分隔。您需要在 1 中添加小数点和零。

  $$\begin{array}{rl}& \stackrel{0.2}{5\overline{)1.0}}\\ & \underset{\_}{-10}\\ & 0\end{array}$$

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  The answer is  $\begin{array}{r}\frac{1}{5}=0.2\end{array}$ .
  ::答案是15=0.2

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  Example 4
  ::例4

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  Convert  $\begin{array}{r}\frac{3}{6}\end{array}$  to a decimal.
  ::将3 6转换为小数点后一位。

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  First, write  $\begin{array}{r}\frac{3}{6}\end{array}$  as a division problem.
  ::首先,写36,作为一个分裂问题。

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  $\begin{array}{r}\frac{3}{6}\end{array}$  is the same as  $\begin{array}{r}3÷6\end{array}$ .
  ::3 6 与 3 + 6 相同 。

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  Next, use long division to divide. You will need to add a decimal point and a zero to the 3.
  ::下一步,使用长除法进行分隔。您需要在三点后加上小数点和零。

  $$\begin{array}{rl}& \stackrel{0.5}{6\overline{)3.0}}\\ & \underset{\_}{-30}\\ & 0\end{array}$$

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  The answer is  $\begin{array}{r}\frac{3}{6}=0.5\end{array}$ .
  ::答案是3 6=0.5

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  Example 5
  ::例5

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  Convert  $\begin{array}{r}4\frac{4}{5}\end{array}$  to a decimal.
  ::4 4 5 转换为小数。

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  First, set aside the 4.  $\begin{array}{r}\frac{4}{5}=4÷5\end{array}$ . Convert the  $\begin{array}{r}\frac{4}{5}\end{array}$  to a decimal using long division.
  ::首先,搁置4 4 5 = 4 5 = 4 5 。使用长分法将4 5 转换为小数。

  $$\begin{array}{rl}& \stackrel{0.8}{5\overline{)4.0}}\\ & \underset{\_}{-40}\\ & 0\end{array}$$

  $$\begin{array}{r}\frac{4}{5}=0.8\end{array}$$

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  Next, add the 4 from the original mixed number.
  ::下面加上原来的混合数字中的4。

  $$\begin{array}{r}4.8\end{array}$$

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  The answer is  $\begin{array}{r}4\frac{4}{5}=4.8\end{array}$ .
  ::答案是4 4 5 = 4.8。

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  Review
  ::回顾

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  Convert each fraction or mixed number to a decimal.
  ::将每个分数或混合数转换为小数。

  1. $\begin{array}{r}\frac{3}{5}\end{array}$  
  2. $\begin{array}{r}\frac{1}{2}\end{array}$  
  3. $\begin{array}{r}\frac{4}{5}\end{array}$  
  4. $\begin{array}{r}\frac{3}{4}\end{array}$  
  5. $\begin{array}{r}\frac{3}{8}\end{array}$  
  6. $\begin{array}{r}\frac{7}{8}\end{array}$  
  7. $\begin{array}{r}2\frac{1}{4}\end{array}$  
  8. $\begin{array}{r}5\frac{2}{5}\end{array}$  
  9. $\begin{array}{r}6\frac{4}{8}\end{array}$  
  10. $\begin{array}{r}11\frac{5}{8}\end{array}$  
  11. $\begin{array}{r}10\frac{1}{2}\end{array}$  
  12. $\begin{array}{r}18\frac{3}{4}\end{array}$  
  13. $\begin{array}{r}12\frac{4}{5}\end{array}$  
  14. $\begin{array}{r}19\frac{3}{4}\end{array}$  
  15. $\begin{array}{r}22\frac{1}{4}\end{array}$  

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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