8.16分数、小数和百分数的比较

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  分数、小数和百分数的比较

  

  [Figure 1]

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  Steve and Nickie are at the library. They are reading the same book for a class. They make a bet to see who is the farthest along after 1 hour of reading. The winner decides what to eat for lunch. After an hour, Steve says he has read  $\begin{array}{r}\frac{3}{5}\end{array}$  of the book. Nickie says she has read 65% of the book. Who will get to decide what to eat for lunch?
  ::Steve和Nickie在图书馆。 他们为一堂课读同一本书。 他们打赌看谁在读完一小时后是最远的。 获胜者决定午餐吃什么。 一小时后, Steve说, 他读了3-5本书。 Nickie说, 她读了65%的书。 谁来决定午餐吃什么?

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  In this concept, you will learn to compare and  order  fractions, decimals, and percents.
  ::在这个概念中,你会学习比较和排序分数、小数和百分比。

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  Comparing Fractions, Decimals, and Percents
  ::比较分数、十进制数和百分数

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  You can compare fractions, decimals and percents using greater than, less than or equal to. Convert fractions, decimals, and percents to the same form to compare the values. If you are comparing a fraction and a percent, write both of them either as fractions or percents to figure out which is greater. Use this information to write a set of numbers or quantities in order from least to greatest or from greatest to least.
  ::您可以使用大于、小于或等于的值来比较分数、小数和百分数。 将分数、 小数和百分数转换成相同的格式来比较数值。 如果您比较了分数和百分数, 请将两者都写成分数或百分数, 以找出哪个更大。 使用此信息来写入一组数字或数量, 从最小到最大或者从最大到最小。

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  Compare 45% and  $\begin{array}{r}\frac{4}{5}\end{array}$ .
  ::比较45%和4 5。

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  First, write 45% and  $\begin{array}{r}\frac{4}{5}\end{array}$  in the same form. Let’s change  $\begin{array}{r}\frac{4}{5}\end{array}$  to a percent. Find the equivalent fraction of  $\begin{array}{r}\frac{4}{5}\end{array}$  as a fraction out of 100. Multiply both  numerator  and  denominator  by 20.
  ::首先,以同样的形式写作45%和4/5。让我们将45%修改为1%。在100分之1中,将相当于4/5的分数乘以20乘以分子和分母的分数。

  $$\begin{array}{r}\frac{4\times 20}{5\times 20}=\frac{80}{100}\end{array}$$

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  Next, convert the fraction to a percent.
  ::接下来,将分数转换成百分之一。

  $$\begin{array}{r}\frac{80}{100}=80\mathrm{\%}\end{array}$$

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  Now, we can compare 45% and 80%.
  ::现在,我们可以比较45%和80%。

  $$\begin{array}{r}45\mathrm{\%}<80\mathrm{\%}\end{array}$$

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  45% is less than 80%.
  ::45%低于80%。

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  Let’s compare percents and decimals.
  ::让我们比较百分比和小数点。

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  Compare 18% and 0.9.
  ::比较18%和0.9。

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  First, write 18% and 0.9 in the same form. Let’s change 0.9 to a percent. Move the  decimal point  two places to the right and add the percent sign.
  ::首先,以同样的形式写出18%和0.9。让我们将0.9修改为1%。将小数点两点移到右边,并添加百分比符号。

  $$\begin{array}{r}0.9=90\mathrm{\%}\end{array}$$

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  Now, compare 18% and 90%.
  ::现在,比较18%和90%。

  $$\begin{array}{r}18\mathrm{\%}<90\mathrm{\%}\end{array}$$

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  18% is less than 90%.
  ::18%低于90%。

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  Write 0.56, 34%,  $\begin{array}{r}\frac{9}{10}\end{array}$ , and  $\begin{array}{r}\frac{1}{2}\end{array}$  in order from least to greatest.
  ::写0.56, 34%, 9 10, 和12, 从最少到最大的顺序。

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  First, rewrite them in the same form. Let’s convert all of them to percents. 34% is already in percent form.
  ::首先,以同样的形式重写它们。让我们把它们全部转换为百分比。 34%已经以百分比的形式出现。

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  Convert 0.56 to a percent. Move the decimal point two places to the right and add the percent sign.
  ::将0.56%转换为1%。将小数点 2 位移到右边,并添加百分数符号 。

  $$\begin{array}{r}0.56=56\mathrm{\%}\end{array}$$

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  Next, find the   of  $\begin{array}{r}\frac{9}{10}\end{array}$  and  $\begin{array}{r}\frac{1}{2}\end{array}$  as fractions over 100 and convert them to percents. Multiply the numerator and denominator of  $\begin{array}{r}\frac{9}{10}\end{array}$  by 10. Multiply the numerator and denominator of  $\begin{array}{r}\frac{1}{2}\end{array}$  by 50.
  ::接下来, 将 9 10 和 12 的 分数作为 100 以上的分数, 并将其转换为百分数 。 乘以 9 10 乘以 9 10 乘以 10 乘以 1 乘以 2 乘以 50 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{9\times 10}{10\times 10}& =& \frac{90}{100}=90\mathrm{\%}\\ \frac{1\times 50}{2\times 50}& =& \frac{50}{100}=50\mathrm{\%}\end{array}\end{array}$$

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  Then, compare the percents.
  ::然后,比较百分比。

  $$\begin{array}{r}56\mathrm{\%},34\mathrm{\%},90\mathrm{\%},50\mathrm{\%}\end{array}$$

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  Finally, write them in the order from least to greatest.
  ::最后,写成从最少到最大的顺序。

  $$\begin{array}{r}\begin{array}{rcl}& & 34\mathrm{\%},50\mathrm{\%},56\mathrm{\%},90\mathrm{\%}\\ & & \text{or}\\ & & 34\mathrm{\%},\frac{1}{2},0.56,\frac{9}{10}\end{array}\end{array}$$

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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 Steve and Nickie and their bet.
  ::之前,你得到一个问题 关于史蒂夫和尼基 和他们的赌注。

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  Steve has read  $\begin{array}{r}\frac{3}{5}\end{array}$  of the book and Nickie has read 65% of the book. To find out who has read the farthest, compare the quantities.
  ::史蒂夫读了这本书的三十五本,尼基读了65%的书。要知道谁读了最远的书,比较数量。

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  First, rewrite  $\begin{array}{r}\frac{3}{5}\end{array}$  as a percent. Find the equivalent fraction of  $\begin{array}{r}\frac{3}{5}\end{array}$  as a fraction over 100 and convert to a percent. Multiply the numerator and denominator by 20.
  ::首先, 将 3 5 重写为百分比 。 将 3 5 的等值分数作为 100 以上的分数, 然后转换为 1% 。 乘以 20 乘以 分子和分母 20 。

  $$\begin{array}{r}\frac{3\times 20}{5\times 20}=\frac{60}{100}=60\mathrm{\%}\end{array}$$

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  Next, compare the percents.
  ::接下来,比较百分比。

  $$\begin{array}{r}60\mathrm{\%}<65\mathrm{\%}\end{array}$$

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  60% is less than 35%. Nickie is farther along than Steve and will get to decide on lunch.
  ::60%不到35%,尼克比史蒂夫走得更远,可以决定午餐时间。

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  Example 2
  ::例2

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  Write the values in order from least to greatest.
  ::将值从最小到最大顺序写入 。

  $$\begin{array}{r}\frac{83}{100},0.16,33\mathrm{\%},\frac{4}{5}\end{array}$$

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  First, rewrite then in the same form. Let’s write them as decimals. 0.16 is already in decimal form.
  ::首先, 重写后以同样的形式写。 让我们把它们写成小数。 0. 16 已经以小数形式出现 。

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  Convert  $\begin{array}{r}\frac{83}{100}\end{array}$  and  $\begin{array}{r}\frac{4}{5}\end{array}$  to decimals. The fraction is 83 out of 100 or 83 hundredths. Convert  $\begin{array}{r}\frac{4}{5}\end{array}$  to a decimal by dividing 4 by 5.
  ::转换 83 100 和 4 5 到 小数点。 分数是 100 或 8300 的 83 。 转换 4 5 到 小数点, 将 4 除以 5 。

  $$\begin{array}{r}\begin{array}{rcl}& & \frac{83}{100}=0.83\\ & & \stackrel{0.8}{5\overline{)4.0}}\end{array}\end{array}$$

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  Next, convert 33% to a decimal. Move the decimal point two places to the left and remove the percent sign.
  ::下一步, 将 33% 转换为小数点。 将小数点 2 位移到左边, 并删除百分数符号 。

  $$\begin{array}{r}33\mathrm{\%}=0.33\end{array}$$

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  Then, compare the decimals.
  ::然后,比较小数点。

  $$\begin{array}{r}0.83,0.16,0.33,0.8\end{array}$$

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  Finally, write them in the order from least to greatest.
  ::最后,写成从最少到最大的顺序。

  $$\begin{array}{r}\begin{array}{rcl}& & 0.16,0.33,0.8,0.83\\ & & \text{or}\\ & & 0.16,33\mathrm{\%},\frac{4}{5},\frac{83}{100}\end{array}\end{array}$$

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  Example 3
  ::例3

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  Compare the values.
  ::比较数值 。

  $$\begin{array}{r}0.19\text{ and }19\mathrm{\%}\end{array}$$

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  First, rewrite them in the same form. Convert 19% to a decimal. Move the decimal two places to the left and remove the percent sign.
  ::首先, 重写相同的表格。 将19% 转换为小数点。 将小数点后的两个位移到左边, 并删除百分数符号 。

  $$\begin{array}{r}19\mathrm{\%}=0.19\end{array}$$

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  Next, compare the decimals.
  ::接下来,比较小数点。

  $$\begin{array}{r}0.19=0.19\end{array}$$

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  0.19 and 19% are equal values.
  ::0.19和19%是等值。

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  Example 4
  ::例4

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  Compare the values.
  ::比较数值 。

  $$\begin{array}{r}\frac{2}{5}\text{ and }45\mathrm{\%}\end{array}$$

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  First, rewrite them in the same form. Let’s convert both  $\begin{array}{r}\frac{2}{5}\end{array}$  and 45% to decimals.  Divide  2 by 5.
  ::首先, 重写它们相同的格式。 让我们将 2 5% 和 45 % 转换为小数。 除以 2 乘以 5 。

  $$\begin{array}{r}\stackrel{0.4}{5\overline{)2.0}}\end{array}$$

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  Move the decimal place two places to the left and remove the percent sign.
  ::将小数点位移到左边两个位子,并删除百分数符号。

  $$\begin{array}{r}45\mathrm{\%}=0.45\end{array}$$

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  Next, compare the decimals.
  ::接下来,比较小数点。

  $$\begin{array}{r}0.4<0.45\end{array}$$

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  $\begin{array}{r}\frac{2}{5}\end{array}$  is less than 45%.
  ::2 5 不到45%。

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  Example 5
  ::例5

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  Compare the values.
  ::比较数值 。

  $$\begin{array}{r}56\mathrm{\%}\text{ and }21\mathrm{\%}\end{array}$$

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  First, these values are in the same form. Compare the two percents.
  ::首先,这些数值的形式相同。比较2%。

  $$\begin{array}{r}56\mathrm{\%}>21\mathrm{\%}\end{array}$$

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  56% is greater than 21%.
  
  ::56%高于21%。

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  Review
  ::回顾

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  Write the following values in order from least to greatest.
  ::写下以下值, 以从最小到最大顺序排列 。

  1. $\begin{array}{r}\frac{16}{100},.27,53\mathrm{\%},\frac{1}{5}\end{array}$  
  2. $\begin{array}{r}\frac{99}{100},.30,68\mathrm{\%},\frac{9}{10}\end{array}$  
  3. $\begin{array}{r}\frac{18}{100},.99,87\mathrm{\%},\frac{10}{20}\end{array}$  
  4. $\begin{array}{r}\frac{88}{100},.18,23\mathrm{\%},\frac{1}{5}\end{array}$  
  5. $\begin{array}{r}\frac{93}{100},.98,6\mathrm{\%},\frac{1}{2}\end{array}$  
  6. $\begin{array}{r}\frac{77}{100},.37,93\mathrm{\%},\frac{2}{5}\end{array}$  
  7. $\begin{array}{r}\frac{12}{100},.76,13\mathrm{\%},\frac{1}{3}\end{array}$  
  8. $\begin{array}{r}\frac{9}{100},.2,67\mathrm{\%},\frac{4}{5}\end{array}$  
  9. $\begin{array}{r}\frac{88}{100},.29,35\mathrm{\%},\frac{2}{10}\end{array}$  

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  Compare the following values using <, > or =.
  ::比较以下使用 <, > 或= 的数值。

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  10.   $\begin{array}{r}\frac{6}{7}\end{array}$  and 35%
      ::6%、7%和35%
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  11. $\begin{array}{r}\frac{3}{4}\end{array}$  and 75%
      ::3%和75%
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  12. $\begin{array}{r}\frac{1}{2}\end{array}$  and 55%
      ::1%和55%
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  13. $\begin{array}{r}\frac{9}{10}\end{array}$  and 25%
      ::9%和25%
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  14. $\begin{array}{r}\frac{1}{4}\end{array}$  and 25%
      ::1% 4% 和25%
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  15. $\begin{array}{r}\frac{1}{5}\end{array}$  and 15%
      ::1%、5%和15%

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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