8.3作为小数的比率

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  作为小数的比率

  

  [Figure 1]

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  Daniel is in charge of the tennis club. Before the season starts, the coach asks Daniel to sort through all of the equipment and to remove the flat tennis balls. There are 100 tennis balls. He finds that 80 are still good and 20 are flat. The coach wants Daniel to make a report of his findings using decimals. Compare the ratio of flat tennis balls to good tennis balls. Compare the ratio of good tennis balls to flat tennis balls.
  ::丹尼尔负责网球俱乐部。 赛季开始前, 教练请丹尼尔整理所有设备, 并清除平板网球。 有100个网球。 他发现80个仍然不错, 20个是平板球。 教练希望丹尼尔用小数来报告他的调查结果。 比较平板网球与好网球的比率。 比较好网球与平板网球的比率 。

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  In this concept, you will learn how to convert ratios to decimal form.
  ::在此概念中,您将学习如何将比率转换为小数位数。

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  Writing Ratios as Decimals
  ::作为十进制书写比率

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  The value of a ratio can be written as a decimal number. A  ratio  is the quotient of the first quantity divided by the second quantity. This value tells us how many of the first quantity there are for every 1 of the second quantity.
  ::比率值可以以小数数表示。 A 比率是第一个数量除以第二个数量的商数。 这个数值可以告诉我们第二个数量中每一个数量的第一个数量有多少。

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  Fractions can help convert ratios to decimal numbers.
  ::小数可以帮助将比率转换为小数点数字。

  

  [Figure 2]

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  Consider the ratio of apples to oranges at the local fruit stand. The ratio 12 :24. Convert 12: 14 into a decimal.
  ::考虑当地水果摊点苹果对橙子的比例。12:24。12:14转换为小数点。

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  First, write the ratio as a fraction. Remember that the first quantity, the number of apples, goes into the numerator and the second quantity, the number of oranges, goes into the denominator.
  ::首先,将比率写成一个分数。 记住第一个数量, 苹果的数量, 进入分子中, 第二个数量, 橙子的数量, 进入分母中 。

  $$\begin{array}{r}12:24=\frac{12}{24}\end{array}$$

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  Next, simplify the fraction if possible.
  ::接下来,尽可能简化分数。

  $$\begin{array}{r}\frac{12÷12}{24÷12}=\frac{1}{2}\end{array}$$

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  Finally, convert the fraction to a decimal by dividing the numerator by the denominator.
  ::最后,通过将分子除以分母,将分数转换成小数点。

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

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  The ratio 12 : 24 in decimal form is 0.5. This tells us that for every orange, there is 0.5 apples. Check to see if this is correct:
  ::比例 12:小数点为 0. 5 : 24, 小数点为 0. 5。 这表明每橙色有0. 5 苹果。 请检查是否正确 :

  $$\begin{array}{r}24\times 0.5=12\end{array}$$

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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 Daniel and all the tennis balls he had to sort through.
  ::早些时候,你得到一个问题 关于丹尼尔 和所有网球 他不得不理清。

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  Out of 100 tennis balls, 80 were good and 20 were flat. To find the decimal value of the ratio, convert the ratio to a fraction and divide.
  ::在100个网球中,80个是好的,20个是平的。为了找到该比率的小数点值,将该比率转换成一个分数和分数。

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  Let’s compare the ratio of flat tennis balls to good tennis balls. First, write the ratio as a fraction.
  ::让我们比较平板网球和好网球的比例。 首先,将比例写成一个小数。

  $$\begin{array}{r}\frac{20}{80}\end{array}$$

   

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  Then, simplify the fraction to its simplest form.
  ::然后,将碎片简化为最简单的形式。

  $$\begin{array}{r}\frac{20÷20}{80÷20}=\frac{1}{4}\end{array}$$

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  Next, convert the fraction to a decimal by dividing the numerator by the denominator.
  ::下一步,将分数转换为小数,将分子除以分母。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.25}{4\overline{)1.00}}\\ & & \underset{\_}{-100}\\ & & 0\end{array}\end{array}$$

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  The ratio  $\begin{array}{r}\frac{20}{80}\end{array}$  in decimal form is 0.25 . We can say that for every good tennis ball, there is 0.25 flat tennis balls. Check to see if this is correct:
  ::小数点时的2080比0.25。我们可以说,每个好的网球都有0.25个平板网球。检查一下,看这是否正确:

  $$\begin{array}{r}80\times 0.25=20\end{array}$$

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  Now let’s compare the ratio of good tennis balls to flat tennis balls. First, write the ratio as a fraction.
  ::现在让我们比较一下好网球与平板网球的比率。 首先,将比率写成一个分数。

  $$\begin{array}{r}\frac{80}{20}\end{array}$$

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  Next, simplify the fraction to its simplest form.
  ::接下来,将分数简化为最简单的形式。

  $$\begin{array}{r}\frac{80÷20}{20÷20}=\frac{4}{1}=4\end{array}$$

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  In this situation, we know that a number divided by 1 will always be that number. So, the ratio of  $\begin{array}{r}\frac{80}{20}\end{array}$  is 4. We can say that for every flat tennis ball, there are 4 good tennis balls. Check to see if this is correct:
  ::在这种情况下,我们知道数字除以1将永远是这个数字。因此,80 20的比率是4。我们可以说,每个平板网球都有4个好的网球。看看这是否正确:

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

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  Example 2
  ::例2

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  Write the ratio as a decimal:  $\begin{array}{r}2\text{ out of }25\end{array}$ . 
  ::将比率写为小数点:25人中有2人。

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  First, write 2 out of 25 as a fraction.
  ::首先,在25个中写2个作为一个分数。

  $$\begin{array}{r}\frac{2}{25}\end{array}$$

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  This fraction is already in its simplest form. Then, convert this fraction to a decimal by dividing the numerator by the denominator.
  ::此分数已经处于最简单的形式中。 然后, 通过将分子除以分母, 将该分数转换为十进制 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.08}{25\overline{)2.00}}\\ & & \underset{\_}{-200}\\ & & 0\end{array}\end{array}$$

    

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  The ratio  $\begin{array}{r}\frac{2}{25}\end{array}$  in decimal form is 0.08.
  ::小数点时的25岁比率是0.08。

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  Example 3
  ::例3

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  Write the ratio as a decimal:  $\begin{array}{r}4\text{ to }5\end{array}$ .
  ::将比率写为小数点:4至5。

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  First, write 4 to 5 as a fraction.
  ::首先,写4到5作为一个分数。

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

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  Next, divide the numerator by the denominator.
  ::下一步,将分子除以分母。

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

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  The ratio 4 to 5 in decimal form is 0.8.
  ::小数点时的4比5比率为0.8。

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  Example 4
  ::例4

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  Write the ratio as a decimal:  $\begin{array}{r}\frac{5}{20}\end{array}$ .
  ::将比率写为小数点:5 20。

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  First, simplify the fraction
  ::首先,简化分数

  $$\begin{array}{r}\frac{5÷5}{20÷5}=\frac{1}{4}\end{array}$$

   

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  Next, divide the numerator by the denominator.
  ::下一步,将分子除以分母。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.25}{4\overline{)1.00}}\\ & & \underset{\_}{-100}\\ & & 0\end{array}\end{array}$$

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  The ratio  $\begin{array}{r}\frac{5}{20}\end{array}$  in decimal form is 0.20.
  ::小数点时的5 20比0.20。

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  Example 5
  ::例5

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  Write the ratio as a decimal:  $\begin{array}{r}6\text{ to }10\end{array}$ .    
  ::将比率写为小数点:6至10。

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  First, write 6 to 10 as a fraction.
  ::首先,写6到10作为一个分数。

  $$\begin{array}{r}\frac{6}{10}\end{array}$$

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  Next, simplify the fraction.
  ::接下来,简化分数。

  $$\begin{array}{r}\frac{6÷2}{10÷2}=\frac{3}{5}\end{array}$$

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  Then, divide the numerator by the denominator.
  ::然后,将分子除以分母。

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

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  The ratio 6 to 10 in decimal form is 0.6.
  ::小数点表6至10的比率为0.6。

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  Review
  ::回顾

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  Convert the following ratios into decimals.
  ::将下列比率转换为小数点。

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  1. 3 to 4
     ::3至4
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  2. 2 to 4 
     ::2 至 4
  3. $\begin{array}{r}\frac{1}{5}\end{array}$
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  4. 25 to 100
     ::25至100
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  5. 16 to 32
     ::16至32岁
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  6. 4 out of 5
     ::5人中有4人
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  7. 6 out of 20
     ::20个中的6个
  8. $\begin{array}{r}\frac{1}{4}\end{array}$
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  9. 5 to 6
     ::5至6项
  10. 1:2
  11. 4:10
  12. 10:50
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  13. 75 to 100
      ::75至100
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  14. 1 to 3
      ::1至3
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  15. 6 to 8
      ::6至8项

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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