8.10将小数和分数转换为百分比

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• 选择节将小数和分数转换为百分比

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  将小数和分数转换为百分比

  

  [Figure 1]

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  Stan is filling out applications for a scholarship. Some of the forms ask for his grade point average as a percent. Other forms ask for his GPA as a fraction out of 100. Stan’s GPA is 3.20. What should he write in the forms?
  ::斯坦正在填写奖学金申请表。 有些表格要求他的年级点平均百分比为%。 另一些表格则要求他的GPA占100 %的一小部分,斯坦的GPA是3.20。 他应该写什么表格?

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  In this concept, you will learn how to write a ratio as a fraction, decimal, and percent.
  ::在这个概念中,你将学会如何以小数、小数和百分比来写一个比率。

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  Writing Ratios as Fractions, Decimals, and Percents
  ::作为分数、十进数和百分数的书写比率

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  Decimals and fractions are used to express parts of a whole.  Percents  also describe parts of a whole. A  percent  is a ratio that describes a quantity out of 100. The symbol for percent is %. The ratio 56 out of 100 is written as 56%. Percents are ratios and can also be written as a fraction or decimal.
  ::十进制和分数用于表示整体的部位。 百分数还描述整体的部位。 百分数是100中的比例。 百分数的符号是%。 百分数的符号是56%。 百分数中的56是56%。 百分数是比率,也可以写成小数或小数。

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  Here is a percent: 14%.
  ::这是百分之一:14%。

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  14% describes 14 out of 100. It is written as 14 in the  numerator  and 100 in the  denominator  of a fraction. A percent is always written as the number over 100 as a fraction.
  ::14%表示100分之14, 分子数为14, 分数分母为100。 百分比总是以百分数超过100表示。

  $$\begin{array}{r}14\mathrm{\%}=\frac{14}{100}\end{array}$$

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  “Out of 100” refers to the decimal place “hundredths.” 14% is 14 hundredths. You can also take the number and move the decimal two spaces to the left.
  ::“百分百”是指小数位的“百分百”。14%是一千四百。您也可以将小数位数移到左边,然后将小数点后的两个空格移到左边。

  $$\begin{array}{r}14\mathrm{\%}=0.14\end{array}$$

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  The table below shows a ratio expressed as a fraction, decimal, and percent.
  ::下表显示了以小数、小数和百分比表示的比率。

  

  [Figure 2]

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  Let’s look at the first ratio in the table, 33 out of 100. It is written  $\begin{array}{r}\frac{33}{100}\end{array}$  as a fraction or 33% as a percent. Find 33 out of 100 as a decimal.
  ::让我们看看表中的第一位比例,即100人中有33人,其中33人以分数表示33 100人,或以百分比表示33%。 将100人中的33人以小数表示。

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  First, think about “out of 100.” 33 out of 100 is also 33 hundredths.
  ::首先,想一想“在100人中”。 100人中有33人也是3300人。

  $$\begin{array}{r}33\text{ out of }100=0.33\end{array}$$

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  Let’s look at the second ratio 55 out of 100. It is written as 55 hundredths or 0.55. Find 55 out of 100 as a fraction and percent.
  ::让我们看看每100人中有55人占第二位, 写成5500人或0.55人, 将每100人中有55人作为分数和百分比。

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  First, think about the ratio. 55 out of 100 is written as 55 in the numerator and 100 in the denominator.
  ::首先,想想这个比例。 一百分之五十五的写法是55在分子中,100在分母中。

  $$\begin{array}{r}55\text{ out of }100=\frac{55}{100}\end{array}$$

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  Next, write the ratio as a percent. The percent symbol means “out of 100.”
  ::接下来,将比例写成%。 百分数符号表示“ 超过100 ” 。

  $$\begin{array}{r}55\text{ out of }100=55\mathrm{\%}\end{array}$$

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  Let’s look at the third ratio 12 out of 100. It is written  $\begin{array}{r}\frac{12}{100}\end{array}$  as a fraction. Find 12 out of 100 as a decimal and percent.
  ::让我们看看100人中有12人占12人占第三位的比例。 将12 100人作为一个分数来写。 将100人中的12人作为小数和百分数来查。

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  First, think about the ratio. 12 out of 100 is also 12 hundredths.
  ::首先,想想这个比例。 12在100中也是1200。

  $$\begin{array}{r}12\text{ out of }100=0.12\end{array}$$

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  Next, write the ratio as a percent. Replace the words “out of 100” with the percent symbol.
  ::接下来,将比率写成百分比。用百分数符号替换“在100之间”等字。

  $$\begin{array}{r}12\text{ out of }100=12\mathrm{\%}\end{array}$$

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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 Stan’s scholarship applications.
  ::先前, Stan的奖学金申请给您带来了问题。

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  He needs to convert his GPA of 3.20 into a percent and a fraction out of 100. To convert his GPA, Stan can convert his GPA into a ratio.
  ::他需要将其3.20的《政府采购协定》转换为3.20的百分率和100的分数。

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  First, write his GPA as a ratio in fraction form.
  ::首先,将其《政府采购协定》以分数形式写成比例。

  $$\begin{array}{r}\frac{3.20}{4.00}\end{array}$$

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  Next, convert the fraction to a decimal by dividing 3.20 by 4.00.
  ::下一步,将分数转换为小数点后一位,除以3.20除以4.00。

  $$\begin{array}{r}3.20÷4.00=0.80\end{array}$$

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  Eighty-hundredths is the same as saying 80 out of 100. 80 out of 100 is  $\begin{array}{r}\frac{80}{100}\end{array}$  and 80%
  ::八百分百和百分之八十一样 百分之八十八十 百分之八十八十是八十 百八十是八十,八十是八十,八十是八十,八十是八十

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  Stan can write that his GPA is  $\begin{array}{r}\frac{80}{100}\end{array}$  or 80%.
  ::Stan可以写到他的GPA是80 100%或80%。

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  Example 2
  ::例2

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  Write the ratio as a fraction, decimal, and percent: 18 out of 100.
  ::以小数、小数和百分数来写这个比率:100分之18。

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  First, write the ratio as a fraction. A percent as a fraction is the number over 100.
  ::首先,将比率写成一个分数。一个分数是100以上。一个分数是100以上。

  $$\begin{array}{r}18\text{ out of }100=\frac{18}{100}\end{array}$$

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  Next, write the ratio as a decimal. 18 out of 100 is also 18 hundredths.
  ::接下来,以小数记下这个比率。 每100人中有18人也是1800人。

  $$\begin{array}{r}18\text{ out of }100=0.18\end{array}$$

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  Then, write the ratio as a percent. Replace the words “out of 100” with the percent symbol.
  ::然后,将比率写成百分比。用百分数符号替换“在100之间”等字。

  $$\begin{array}{r}18\text{ out of }100=18\mathrm{\%}\end{array}$$

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  Write the following ratios as a percent.
  ::将以下比率写成百分比。

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  Example 3
  ::例3

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  Write the ratio as a percent: 67 out of 100.
  ::将比率写成百分比:100人中有67人。

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  Replace the words “out of 100” with the percent
  ::将“在100人中”改为“在100人中”

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  The ratio is 67%.
  ::比率为67%。

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  Example 4
  ::例4

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  Write the ratio as a percent: 23 out of 100.
  ::将比率写成百分比:100人中有23人。

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  Replace the words “out of 100” with the percent symbol.
  ::以百分数符号取代“百分数”等字。

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  The ratio is 23%.
  ::比率为23%。

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  Example 5
  ::例5

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  Write the ratio as a percent: 10 out of 100.
  ::将比例写成百分比:100人中有10人。

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  Replace the words “out of 100” with the percent symbol.
  ::以百分数符号取代“百分数”等字。

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  The ratio is 10%.
  
  ::比率为10%。

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  Review
  ::回顾

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  Find the missing ratio, fraction, decimal, or percent.
  ::查找缺失的比例、分数、小数或百分比。

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  Fill in the sections of the below chart numbered 1-13.
  ::填写下图编号1-13的各节。

  

  [Figure 3]

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  14. Write .12 as a percent.
      ::写12成百分率。
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  15. Write 15 out of 100 as a percent.
      ::百分之十五写成百分之十五

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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