3.13 十进制、分数和百分数转换

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  十进制、分数和百分数的转换

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  Conversion of Decimals, Fractions, and Percents
  ::十进制、分数和百分数的转换

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  A percent is simply a ratio with a base unit of 100. When we write a ratio as a fraction, the percentage we want to represent is the numerator , and the denominator is 100. For example, 43% is another way of writing $\begin{array}{r}\frac{43}{100}\end{array}$ . $\begin{array}{r}\frac{43}{1000}\end{array}$ , on the other hand, is equal to $\begin{array}{r}\frac{4.3}{100}\end{array}$ , so it would be equivalent to 4.3%. $\begin{array}{r}\frac{2}{5}\end{array}$ is equal to $\begin{array}{r}\frac{40}{100}\end{array}$ , or 40%. To convert any fraction to a percent, just convert it to an equivalent fraction with a denominator of 100, and then take the numerator as your percent value.
  ::A%仅仅是一个基本单位为100的比例,当我们以分数来写一个比例时,我们希望代表的百分比是分子,而分母是100。例如,43%是写43100的另一种方式。431000,另一方面,等于4.3100,相当于4.3100,因此相当于4.3%。25等于40100,或40%。要将任何分数转换成一个百分比,只需将其转换成一个等分数,分母为100,然后将分子当作你的百分比值。

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  To convert a percent to a decimal, just move the decimal point two spaces to the right:
  ::要将百分比转换为十进制,只需将小数点的两个空格移到右边:

  $$\begin{array}{rl}67\mathrm{\%}& =0.67\\ 0.2\mathrm{\%}& =0.002\\ 150\mathrm{\%}& =1.5\end{array}$$

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  And to convert a decimal to a percent, just move the decimal point two spaces to the left:
  ::要将小数点转换为百分比,只需将小数点两个空格移到左边:

  $$\begin{array}{rl}2.3& =230\mathrm{\%}\\ 0.97& =97\mathrm{\%}\\ 0.00002& =0.002\mathrm{\%}\end{array}$$

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  Finding and Converting Percentages
  ::查找和转换百分比

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  Before we work with percentages, we need to know how to convert between percentages, decimals and fractions.
  ::在我们研究百分比之前,我们需要知道如何在百分比、小数和分数之间转换。

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  Converting percentages to fractions is the easiest. The word “percent” simply means “ per 100”—so, for example, 55% means 55 per 100, or $\begin{array}{r}\frac{55}{100}\end{array}$ . This fraction can then be simplified to $\begin{array}{r}\frac{11}{20}\end{array}$ .
  ::将百分数转换成分数最为容易。 “ 百分数”一词仅指“ 每100人”-例如,55%指每100人55%,或55100人。 然后,这一分数可以简化为1120人。

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  Converting Percents to Fractions 
  ::将百分比转换成分数

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  Convert 32.5% to a fraction.
  ::将32.5%转换成一个分数。

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  32.5% is equal to 32.5 per 100, or $\begin{array}{r}\frac{32.5}{100}\end{array}$ . To reduce this fraction, we first need to multiply it by $\begin{array}{r}\frac{10}{10}\end{array}$ to get rid of the decimal point. $\begin{array}{r}\frac{325}{1000}\end{array}$ then reduces to $\begin{array}{r}\frac{13}{40}\end{array}$ .
  ::32.5%等于32.5%/100,或32.5100。为了减少这一分数,我们首先需要将其乘以1010,才能除去小数点。3251000然后降至1340。

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  Converting fractions to percentages can be a little harder. To convert a fraction directly to a percentage, you need to express it as an equivalent fraction with a denominator of 100.
  ::将分数转换成百分比可能有点困难。 要直接将分数转换成百分比, 您需要将分数表达为等值分数, 分数为100。

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  Converting Fractions to Percents 
  ::将分数转换成百分比

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  Convert $\begin{array}{r}\frac{7}{8}\end{array}$ to a percent.
  ::78%转换成百分之七十八

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  To get the denominator of this fraction equal to 100, we have to multiply it by 12.5. Multiplying the numerator by 12.5 also, we get $\begin{array}{r}\frac{87.5}{100}\end{array}$ , which is equivalent to 87.5%.
  ::要获得这个分数分母的分母等于 100, 我们必须乘以 12.5 。 将分子乘以 12.5, 我们得到87.5100, 相当于 87.5% 。

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  But what about a fraction like $\begin{array}{r}\frac{1}{6}\end{array}$ , where there’s no convenient number to multiply the denominator by to get 100? In a case like this, it’s easier to do the division problem suggested by the fraction in order to convert the fraction to a decimal, and then convert the decimal to a percent. 1 divided by 6 works out to 0.166666.... Moving the decimal two spaces to the right tells us that this is equivalent to about 16.7%.
  ::但是,像16这样的分数如何呢? 16这样的分数没有方便的数乘以分母以获得100。 在这样的情况中,使用分数建议的分数问题比较容易,这样可以将分数转换成小数,然后将小数转换成小数,然后将小数转换成一个百分数。 1除以6等于0.166666.。 将小数点的两个空格移到右边告诉我们,这相当于16.7%。

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  Why can we convert from decimals to percents just by moving the decimal point? Because of what decimal places represent. 0.1 is another way of representing one tenth, and 0.01 is equal to one hundredth—and one hundredth is one percent. By the same logic, 0.02 is 2 percent, 0.35 is 35 percent, and so on.
  ::为什么我们仅仅通过移动小数点就能从小数点转换为百分点?因为小数点代表什么。0.1是代表十分之一的另一种方法,0.01等于十分之一,而百分之一等于百分之一。按照同样的逻辑,0.02是2%,0.35是35%,等等。

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  Converting Decimals to Percents 
  ::将十进制转换为百分比

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  Convert 2.64 to a percent.
  ::将2.64%转换成百分之二百六十四

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  To convert to a percent, simply move the decimal two places to the right. $\begin{array}{r}2.64=264\mathrm{\%}\end{array}$ .
  ::要转换为百分比,只需将小数点后两个位移到右边。 2.64=264%。

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  Does a percentage greater than 100 even make sense? Sure it does, percentages greater than 100 come up in real life all the time. For example, a business that made 10 million dollars last year and 13 million dollars this year would have made 130% as much money this year as it did last year.
  ::超过100 % 的百分率是否有意义? 当然,超过100的百分率总是在现实生活中出现。 比如,去年创造1000万美元,今年创造1300万美元的企业今年将比去年创造130 % 。

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  The only situation where a percentage greater than 100 doesn’t make sense is when you’re talking about dividing up something that you only have a fixed amount of. For example, if you took a survey and found that 56% of the respondents gave one answer and 72% gave another answer (for a total of 128%), you’d know something went wrong with your math somewhere, because there’s no way you could have gotten answers from more than 100% of the people you surveyed.
  ::唯一一个百分率超过100的人没有意义的情况是,你谈论的是分割你只有固定数量的东西。 比如,如果你进行了调查,发现56%的受访者给出了一个答案,72%的受访者给出了另一个答案(总共128 % ) , 你就会知道你的数学哪里出了问题,因为你不可能从超过100%的受访者那里得到答案。

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  Converting percentages to decimals is just as easy as converting decimals to percentages, simply move the decimal to the left instead of to the right.
  ::将百分比转换为小数点与将小数点转换为小数点一样容易,只需将小数点移到左边,而不是向右即可。

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  Converting Percents to Decimals 
  ::将百分比转换为十进制

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  Convert 58% to a decimal.
  ::将58%转换为十进制。

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  The decimal point here is invisible, it’s right after the 8. So moving it to the left two places gives us 0.58.
  ::这里的小数点是隐形的, 就在8点之后, 所以移动到左边两个地方, 给我们0.58。

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  It can be hard to remember which way to move the decimal point when converting from decimals to percents or vice versa. One way to check if you’re moving it the right way is to check whether your answer is a bigger or smaller number than you started out with. If you’re converting from percents to decimals, you should end up with a smaller number, just think of how a number like 50 percent, where 50 is greater than 1, represents a fraction like $\begin{array}{r}\frac{1}{2}\end{array}$ (or 0.50 in decimal form), where $\begin{array}{r}\frac{1}{2}\end{array}$ is less than 1. Conversely, if you’re converting from decimals to percents, you should end up with a bigger number.
  ::很难记住当从小数点转换到百分比时,小数点会以什么方式移动,反之亦然。 检查您移动小数点是否正确的方法之一是检查您的回答是大于还是小于您最初的回答。 如果您从百分数转换到小数点, 最终的结果应该是小数点, 只要想想一个像50%这样的数字, 其中50大于1, 代表一个像12的分数(或者小数点为0.50), 其中12代表一个小数点小于1。 相反, 如果您从小数转换到百分数, 最终的结果应该是更大的数字 。

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  One way you might remember this is by remembering that a percent sign is bigger than a decimal point, so percents should be bigger numbers than decimals.
  ::你可能记得的一个方法 就是记住一个百分数符号大于小数点, 所以百分数应该大于小数点。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Convert 3.4 to a percent.
  ::3.4%转换为1%。

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  If you move the decimal point to the left, you get a 0.034%. That's a smaller number than you started out with, but you're moving from decimals to percents, so you want the number to get bigger, not smaller. Move it to the right instead to get 340%. 
  ::如果将小数点移到左侧,就会得到0.034%的数值。这是一个小于你最初的数值,但从小数点移到百分数,所以你希望数字变得更大,而不是更小。将其移到右边,取340%。

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  Example 2
  ::例2

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  Convert $\begin{array}{r}\frac{2}{7}\end{array}$ to a percent.
  ::将27%转换成百分之二十七

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    $\begin{array}{r}\frac{2}{7}\end{array}$ doesn’t convert easily unless you change it to a decimal first. 2 divided by 7 is approximately 0.285714..., and moving the decimal and rounding gives us 28.6%.
  ::27 除非将小数点改为小数点后, 否则不容易转换。 2除以7等于0.285714, 移动小数点和四舍五入后,

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  Review 
  ::回顾

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  Express the following decimals as a percent.
  ::以百分比表示以下小数点。

  1. 0.011
  2. 0.001
  3. 0.91
  4. 1.75
  5. 20

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  Express the following percentages in decimal form
  ::以下百分数以小数数表示:

  6. 15%
  7. 0.08%
  8. 222%
  9. 3.5%
  10. 341.9%

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  Express the following fractions as a percent (round to two decimal places when necessary)
  ::以百分比表示下列分数(必要时小数点后数位数将至小数点后两位数)

  11. $\begin{array}{r}\frac{1}{6}\end{array}$
  12. $\begin{array}{r}\frac{5}{24}\end{array}$
  13. $\begin{array}{r}\frac{6}{7}\end{array}$
  14. $\begin{array}{r}\frac{11}{7}\end{array}$
  15. $\begin{array}{r}\frac{13}{97}\end{array}$

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  Express the following percentages as a reduced fraction.
  ::将下列百分比作为减少的分数表示。

  16. 11%
  17. 65%
  18. 16%
  19. 12.5%
  20. 87.5%

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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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  Texas Instruments Resources
  ::得克萨斯州工具资源

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  In the CK-12 Texas Instruments Algebra I FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See .
  ::在CK-12得克萨斯州仪器代数I FlexBook资源中,有图表计算活动,旨在补充本章某些经验教训的目标。