5.15 极小和大比例问题

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  极小和大比例问题

  

   

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  Wembley Stadium in London, England, has a seating capacity of 90,000. In contrast, The Georgia Dome in Atlanta, Georgia, has a seating capacity of 71,250. How much larger is Wembley Stadium than the Georgia Dome?
  ::英国伦敦温布利体育场的座位容量为90 000人,而佐治亚亚州亚特兰大佐治亚多多的座位容量为71 250人。 文布利体育场比佐治亚多多?

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  In this concept, you will learn how to solve statistics-based problems involving percent greater than 100 and less than one.
  ::在这个概念中,你将学会如何解决以统计数字为基础的问题,涉及百分率大于100和不到1。

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  Statistics
  ::统计统计统计统计统计

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  Statistics refers to mathematics involved with data and its interpretation.
  ::统计数据是指数据及其解释所涉及的数学。

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  You can accumulate large sets of data like from a survey, a poll, an experiment, formal observations, etc. In order to draw any conclusion from the data, you must be able to interpret it. You have seen some statistical measures like mean, median, and mode. You have also used to work with large and small numbers. Based on these statistical measures, you might make inferences that reach beyond the set of data or experiment. As you make inferences, percent calculations will be useful. Sometimes percent will be greater than 100 or less than 1 so you need to perform operations carefully.
  ::您可以从调查、民意测验、实验、正式观察等中收集大量的数据。为了从数据中得出任何结论, 您必须能够解释这些数据。 您已经看到了一些统计尺度, 如中位数、 中位数和模式。 您也曾经使用过大数和小数的统计尺度。 根据这些统计尺度, 您可能会做出超越数据集或实验的推断。 您的推断是, 百分比的计算是有用的。 有时百分比会超过100或1, 所以您需要小心操作 。

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  Let’s start with percent that are greater than one hundred.
  ::让我们从百人以上的百分比开始。

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  Percent is a ratio with a denominator of 100 that represents a part of a whole. One-hundred percent represent one whole. If you have 100% of a pizza, you have an entire pizza. What if you have 200% of a pizza? Then that is 2 whole pizzas. 300% would be 3 whole pizzas. 1000% is 10 times 100% so that would be 10 whole pizzas. You can see, then, that percentages do not stop at 100. Whenever percentages represent more than a whole, they will be greater than 100%.
  ::百分率是百分位数的百分位数,它代表整体的一部分。百分之一百代表一个整体。如果你拥有100%的比萨饼,你拥有完整的比萨饼。如果你拥有200%的比萨饼,那又如何?这是2个整份比萨饼。3个整份比萨饼是3个整份的3倍。1000%是10倍的100倍,也就是10个整份比萨。你可以看到,当百分率代表一个以上时,百分率不会停留在100,它们就会超过100%。

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  Let’s look at an example.
  ::让我们举个例子。

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  A nation-wide survey found that the average home in 1907 had 1.2 bathrooms. A hundred years later, the average home had 2.6 bathrooms. What was the in the number of bathrooms per home?
  ::一项全国范围的调查发现,1907年平均住家有1.2个卫生间,100年后,平均住家有2.6个卫生间,每个家庭有多少卫生间?

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}2.6-1.2=1.4\end{array}$$

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  Next, divide by the original amount and multiply by 100.
  ::下一步,除以原来的数额,乘以100。

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  $$\begin{array}{r}\begin{array}{rcl}\text{percent of increase}& =& \frac{\text{amount of increase}}{\text{original amount}}\times 100\\ \text{percent of increase}& =& \frac{1.4}{1.2}\times 100\\ \text{percent of increase}& =& 1.167\times 100\\ \text{percent of increase}& =& 116.7\end{array}\end{array}$$

  
  ::增加的百分率=增加的百分率×增加的100%=1.41.2×增加的100%=1.167×增加的100%=116.7

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  The answer is 116.7.
  ::答案是116.7。

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  The number of bathrooms in the average home increased by 116.7% in 100 years. This indicates that the number of bathrooms per home more than doubled.
  ::平均家庭浴室的数量在100年中增加了116.7%,这表明每个家庭浴室的数量增加了一倍多。

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  Percentages can also be very small. The operations do not change but you must be more careful in using decimal places correctly. Scientists often work with very small percentages.
  ::百分比也可能非常小。 操作没有改变, 但您必须更小心正确使用小数点位数。 科学家工作的百分比往往很低 。

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  Let’s look at an example.
  ::让我们举个例子。

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  A researcher was interested in the truth about lucky four-leaf clovers. He surveyed 34,810 clover plants and found that only 18 of them actually had four leaves. All of the others had only 3 leaves. What percent of the plants had four leaves?
  ::一位研究人员对幸运的四叶叶三叶草的真相感兴趣。他调查了34,810个三叶草植物,发现其中只有18个植物实际有4个叶子。其他所有植物只有3个叶子。哪些植物有4个叶子?

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  First, find the ratio of four-leaf plants to all of the plants.
  ::首先,找到四叶工厂与所有工厂的比率。

  $$\begin{array}{r}\frac{18}{34810}=0.0005\end{array}$$

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  Next, multiply by 100 to get percent.
  ::下一个,乘以百 获得百分之百。

   

  $$\begin{array}{r}0.0005\times 100=0.05\mathrm{\%}\end{array}$$

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  The answer is 0.05%.
  ::答案是0.05%。

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  Therefore, four-leaf plants occur only 0.05% of the time.
  ::因此,四叶工厂只出现0.05%的时间。

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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  the sizable stadiums.
  ::早些时候,有人给了你一个问题 关于巨大的体育场。

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  Wembley Stadium seats 90,000 people and the Georgia Dome seats 71,250 people. How much bigger is Wembley Stadium than the Georgia Dome?
  
  First, find the difference between the seating capacities of the two stadiums.
  ::温布利体育场有90,000人座席,佐治亚穹顶有71,250人座席。 温布利体育场比佐治亚穹顶大多少? 首先,发现两个体育场的座位能力有区别。

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  $$\begin{array}{r}90,000-71,250=18,750\end{array}$$

  
  
  Next, divide by the original amount and multiply by 100.
  ::90,000 - 71,250=18,750 下一个,除以原来的数额,再乘以100。

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  $$\begin{array}{r}\begin{array}{rcl}\text{percent of increase}& =& \frac{\text{amount of increase}}{\text{original amount}}\times 100\\ \text{percent of increase}& =& \frac{18750}{90000}\times 100\\ \text{percent of increase}& =& 0.2083\times 100\\ \text{percent of increase}& =& 20.83\end{array}\end{array}$$

  
  ::增加的%=增加的%x 增加的100%= 1875090000× 增加的100%= 0.2083× 增加的100%= 2083。

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  The answer is 20.83%.
  ::答案是20.83%。

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  Therefore, Wembley Stadium is 20.83% larger than the Georgia Dome.
  ::因此,温布利体育场比佐治亚穹顶大20.83%。

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  Example 2
  ::例2

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  What percent of 75 is 0.3?
  ::75分中0.3是多少?

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  First, find the ratio of four-leaf plants to all of the plants.
  ::首先,找到四叶工厂与所有工厂的比率。

  $$\begin{array}{r}\frac{0.3}{75}=0.004\end{array}$$

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  Next, multiply by 100 to get percent. 
  ::下一个,乘以百 获得百分之百。

  $$\begin{array}{r}0.004\times 100=0.4\mathrm{\%}\end{array}$$

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  The answer is 0.4%.
  ::答案是0.4%。

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  Example 3
  ::例3

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  Figure out each or decrease from 3.4 to 6.9.
  ::从3.4到6.9不等的下降。

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}6.9-3.4=3.5\end{array}$$

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  Next, divide by the original amount and multiply by 100.
  ::下一步,除以原来的数额,乘以100。

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  $$\begin{array}{r}\begin{array}{rcl}\text{percent of increase}& =& \frac{\text{amount of increase}}{\text{original amount}}\times 100\\ \text{percent of increase}& =& \frac{3.5}{3.4}\times 100\\ \text{percent of increase}& =& 1.029\times 100\\ \text{percent of increase}& =& 102.9\end{array}\end{array}$$

  
  ::增加的%=增加的%x 增加的100%=3.53.4× 增加的100%=1.029× 增加的100%=102.9

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  The answer is 103%.
  ::答案是103%。

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  Example 4
  ::例4

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  Figure out each percent of increase or decrease from 8.7 to 20.2.
  ::说明从8.7到20.2之间增加或减少的每一个百分比。

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}20.2-8.7=11.5\end{array}$$

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  Next, divide by the original amount and multiply by 100.
  ::下一步,除以原来的数额,乘以100。

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  $$\begin{array}{r}\begin{array}{rcl}\text{percent of increase}& =& \frac{\text{amount of increase}}{\text{original amount}}\times 100\\ \text{percent of increase}& =& \frac{11.5}{8.7}\times 100\\ \text{percent of increase}& =& 1.322\times 100\\ \text{percent of increase}& =& 132.2\end{array}\end{array}$$

  
  ::增加的百分比=增加的%×增加的100%=11.58.7×增加的100%=1.322×增加的100%=132.2

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  The answer is 132%.
  ::答案是132%。

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  Example 5
  ::例5

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  Figure out each percent of increase or decrease from 450,000 to 200,000.
  ::找出增加或减少的每一个百分比,从45万增加到20万。

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  First, find the amount of change.
  ::首先,找到变化的金额。

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  $$\begin{array}{r}45,000-200,000=250,000\end{array}$$

  
  
  Next, divide by the original amount and multiply by 100.
  ::下一步,除以原来的数额,再乘以100。

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  $$\begin{array}{r}\begin{array}{rcl}\text{percent of decrease}& =& \frac{\text{amount of decrease}}{\text{original amount}}\times 100\\ \text{percent of decrease}& =& \frac{250,00}{450,000}\times 100\\ \text{percent of decrease}& =& 0.5556\times 100\\ \text{percent of decrease}& =& 55.56\end{array}\end{array}$$

  
  ::减少的百分比=减少的%x 原数x减少的100%=250 00450,000× 减少的100%=0.5556× 减少的100%=55.56。

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  The answer is 55.56%.
  ::答案是55.56%。

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  Review
  ::回顾

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  Answer each question and round your answers to the nearest tenth.
  ::回答每个问题,然后把答案绕到最近的十分之一。

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  1. What percent of 110 is 450?
  ::110的百分之一是450?

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  2. What percent of 32 is 100?
  ::32%是100?

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  3. What percent of 50 is 200?
  ::50的百分之三是200是多少?

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  4. What percent of 88 is 400?
  ::百分之八十八的百分之四是四百吗?

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  5. What percent of 10 is 18?
  ::10分之5是18是多少?

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  6. What percent of 2 is 4?
  ::两分之六是四?

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  7. What percent of 45 is 60?
  ::45分之七是60?

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  Answer each question and round your answers to the nearest hundredth.
  ::回答每个问题,然后把答案绕到最近的第一百个

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  8. What percent of 50,980 is 325?
  ::5,980是325?

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  9. What percent of 85 is .25?
  ::85分的百分之九是多少? 25分是多少?

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  10. What percent of 90 is 15?
  ::百分之十是百分之十是百分之十五吗?

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  11. What percent of 10 is 4?
  ::11. 10%是4%是多少?

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  12. What percent of 30 is 6?
  ::30的12 %是6?

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  13. What percent of 385 is 25?
  ::385的13%是25?

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  14. What percent of 400 is 3?
  ::400的14%是3?

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  15. What percent of 595 is 18?
  ::595分的15分是18分?

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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 。