3.17小数转化为分数

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  小数转化为分数

  

  [Figure 1]

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  Liam is making his great-grandmother's famous brownies. He has the recipe that his great-grandmother wrote down many years ago on an index card. As Liam looks through the ingredients he sees that he will need 1.25 cups of sugar. He takes out the measuring cups and notices that all the measurements on the cups are written as fractions. How can Liam convert 1.25 to a  mixed number  so that he can figure out what measuring cups to use to measure out the sugar for the brownies?
  ::Liam正在制作他曾祖母著名的布朗尼蛋糕。 他有他曾祖母多年前在索引卡上写下来的食谱。 正如Liam在查看他所看到的需要1. 25杯糖的成分时所看到的。 他拿出测量杯子, 并注意杯子上的所有测量数据都是分数。 Liam如何将1. 25转换成混合数, 以便他能弄清楚用什么量杯子来测量巧克力的糖量?

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  In this concept, you will learn to write terminating decimals as fractions.
  ::在此概念中,您将学习将终止小数小数作为分数写成。

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  Writing Decimals as Fractions
  ::将十进制写为分数

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  Decimals and fractions are different ways of expressing the same numbers. Every repeating and  terminating decimal  is equivalent to some fraction. To write a decimal as a fraction, you will need to think about the  place value  of the decimal digits.
  ::十进制数和分数是表达相同数字的不同方式。每次重复和终止小数数都相当于某些分数。要将小数数写成一个分数,需要考虑小数位数的位置值。

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  Here are the steps for writing a terminating decimal as a fraction.
  ::以下是将终止小数小数分数写成的步骤 。

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  1. Determine the  numerator  of the fraction. The numerator of the fraction will be the digits to the right of the  decimal point .
     ::确定分数的分子。分数的分子将是小数点右侧的数位。
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  2. Determine the  denominator  of the fraction. The denominator of the fraction will be the place value of the last digit of the decimal. For example, if the last digit of the decimal is in the thousandths place, the denominator will be 1000.
     ::确定分数的分母。 分数的分母将是小数点最后一位数的位值。 例如, 如果小数点最后一位数是千位数, 分母将是千位数 。
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  3. Simplify  the answer.
     ::简化答案 。

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  Here is an example.
  ::举一个例子。

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  Convert 0.35 to a fraction.
  ::将0.35转换为分数 。

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  First, read the decimal out loud. 0.35 is “35 hundredths”. The numerator of the fraction will be 35. The denominator of the fraction will be 100.
  ::首先,大声读出小数小数。0.35是“三百三百”,分数的分子数为35,分数的分母为100。

  $$\begin{array}{r}\frac{35}{100}\end{array}$$

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  Next, simplify your answer. Both the numerator and the denominator are divisible by 5.
  ::接下来,简化您的回答。 分子和分母的分母 均在 5 分辨 。

  $$\begin{array}{r}\frac{35÷5}{100÷5}=\frac{7}{20}\end{array}$$

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  The answer is  $\begin{array}{r}0.35=\frac{7}{20}\end{array}$ .
  ::答案是0.35=7 20

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  You can convert decimals greater than 1 to mixed numbers. Here are the steps for writing a terminating decimal as a mixed number.
  ::您可以将小数点大于 1 转换为混合数字。这里是将终止小数点写成混合数字的步骤。

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  1. Convert the portion of the number to the right of a decimal point to a fraction. The numerator of the fraction will be the digits to the right of the decimal point. The denominator of the fraction will be the place value of the last digit of the number.
     ::将数字的部位转换为小数点右侧的分数。分数的数位数将是小数点右侧的数位数。分数的分母将是数字最后一位数的位值。
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  2. Simplify the fraction.
     ::简化分数 。
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  3. Add the whole number part of the original decimal to the fraction.
     ::将原小数小数点的整个数字部分添加到分数中。

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  Here is an example.
  ::举一个例子。

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  Convert 2.4 to a mixed number.
  ::2.4转换成混合数字。

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  First, set aside the 2.
  ::首先,先把二号放下

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  Next, read the portion of the number to the right of the decimal point out loud. 0.4 is “4 tenths”. The numerator of the fraction will be 4. The denominator of the fraction will be 10.
  ::接下来,请大声读读小数点右侧的数字部分。0.4是“十分之四”。分数的分子数将是4。分数的分母将是10分。

  $$\begin{array}{r}\frac{4}{10}\end{array}$$

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  Now, simplify your fraction. Both the numerator and the denominator are divisible by 2.
  ::现在,简化您的分数。 分子和分母的分母 都可除以 2 。

  $$\begin{array}{r}\frac{4÷2}{10÷2}=\frac{2}{5}\end{array}$$

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  Finally, add the 2 from the original mixed number.
  ::最后,加上原来的混合数字中的2个。

  $$\begin{array}{r}2\frac{2}{5}\end{array}$$

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  The answer is  $\begin{array}{r}2.4=2\frac{2}{5}\end{array}$ .
  ::答案是2.4=2 2 5。

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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 Liam and his brownie recipe.
  ::早些时候,你得到一个问题 关于利亚姆和他的布朗尼配方。

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  The old recipe from his great-grandmother calls for 1.25 cups of sugar. Liam needs to convert this mixed number to a fraction so that he can use his measuring cups.
  ::他曾祖母的旧食谱需要1.25杯糖。 利亚姆需要将这个混合数转换成一小部分,以便他能用他的量杯。

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  First, Liam should set aside the 1.
  ::首先,利亚姆应该把一号放在一边

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  Next, he should read the portion of the number to the right of the decimal point out loud. 0.25 is “25 hundredths”. The numerator of the fraction will be 25. The denominator of the fraction will be 100.
  ::接下来,他应该大声读读小数点右侧的数字部分。0.25是“第25百位”。分数的分子数将是25。分数的分母将是100。分数的分母将是100。

  $$\begin{array}{r}\frac{25}{100}\end{array}$$

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  Now, he can simplify his fraction. Both the numerator and denominator are divisible by 25.
  ::现在,他可以简化他的分数。分子和分母的分数都可除以25。

  $$\begin{array}{r}\frac{25÷25}{100÷25}=\frac{1}{4}\end{array}$$

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  Finally, he can add the 1 from the original mixed number.
  ::最后,他可以加上原来的混合数字中的1。

  $$\begin{array}{r}1\frac{1}{4}\end{array}$$

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  The answer is Liam will need  $\begin{array}{r}1\frac{1}{4}\end{array}$  cups of sugar. He can use the 1 cup and the  $\begin{array}{r}\frac{1}{4}\end{array}$  cup measuring cups to measure out the sugar.
  ::答案是利亚姆需要14杯糖,他可以用1杯和14杯量的杯子测量糖量。

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  Example 2
  ::例2

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  Convert 5.25 to a mixed number.
  ::5.25转换成混合数字。

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  First, set aside the 5.
  ::首先,先把五号放下

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  Next, read the portion of the number to the right of the decimal point out loud. 0.25 is “25 hundredths”. The numerator of the fraction will be 25. The denominator of the fraction will be 100.
  ::接下来,请大声读读小数点右侧的数字部分。0.25是“第25百位”。分数的分子数将是25。分数的分母将是100。分数的分母将是100。

  $$\begin{array}{r}\frac{25}{100}\end{array}$$

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  Now, simplify your fraction. Both the numerator and the denominator are divisible by 25.
  ::现在,简化你的分数。 分子和分母的分母 都可除以 25 。

  $$\begin{array}{r}\frac{25÷25}{100÷25}=\frac{1}{4}\end{array}$$

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  Finally, add the 5 from the original mixed number.
  ::最后,加上原来的混合数字中的5。

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

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  The answer is  $\begin{array}{r}5.25=5\frac{1}{4}\end{array}$ .
  ::答案是5.25=5 1 4。

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  Example 3
  ::例3

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  Convert 0.5 to a fraction.
  ::将0.5转换成分数。

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  First, read the decimal out loud. 0.5 is “5 tenths”. The numerator of the fraction will be 5. The denominator of the fraction will be 10.
  ::首先,大声读出小数小数。0.5是“十分之五”。分数的分子数将是5。分数的分母将是10。分数的分母将是10。

  $$\begin{array}{r}\frac{5}{10}\end{array}$$

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  Next, simplify your answer. Both the numerator and the denominator are divisible by 5.
  ::接下来,简化您的回答。 分子和分母的分母 均在 5 分辨 。

  $$\begin{array}{r}\frac{5÷5}{10÷5}=\frac{1}{2}\end{array}$$

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  The answer is  $\begin{array}{r}0.5=\frac{1}{2}\end{array}$ .
  ::答案是0.5=12

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  Example 4
  ::例4

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  Convert 0.67 to a fraction.
  ::将0.67转换成一个分数。

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  First, read the decimal out loud. 0.67 is “67 hundredths”. The numerator of the fraction will be 67. The denominator of the fraction will be 100.
  ::首先,大声读出小数小数。0.67是“67万”,分数的分子数将是67,分数的分母将是100。

  $$\begin{array}{r}\frac{67}{100}\end{array}$$

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  This fraction is already in  simplest form .
  ::此分数已经以最简单的形式出现 。

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  The answer is  $\begin{array}{r}0.67=\frac{67}{100}\end{array}$ .
  ::答案是0.67=67 100

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  Example 5
  ::例5

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  Convert 3.21 to a mixed number.
  ::3.21转换成混合数字。

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  First, set aside the 3.
  ::首先,把三号放下

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  Next, read the portion of the number to the right of the decimal point out loud. 0.21 is “21 hundredths”. The numerator of the fraction will be 21. The denominator of the fraction will be 100.
  ::接下来,请大声读读小数点右侧的数字部分。 0.21是“ 2100 ” 。 分数的分子数将是 21 分数的分母将是 100。 分数的分母将是 100 分数 。

  $$\begin{array}{r}\frac{21}{100}\end{array}$$

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  This fraction is already in simplest form. Now, add the 3 from the original mixed number.
  ::此分数已经以最简单的形式出现。 现在, 从原始混合数中添加 3 。

  $$\begin{array}{r}3\frac{21}{100}\end{array}$$

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  The answer is  $\begin{array}{r}3.21=3\frac{21}{100}\end{array}$ .
  ::答案是3.21=3 21 100。

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  Review
  ::回顾

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  Write each decimal as a fraction or mixed number in simplest form.
  ::以最简单的形式将每个小数点以分数或混合数形式写成。

  1. 0.3
  2. 0.4
  3. 0.2
  4. 0.53
  5. 0.55
  6. 0.08
  7. 0.25
  8. 0.23
  9. 0.876
  10. 0.512
  11. 74.34
  12. 3.88
  13. 5.6
  14. 12.8
  15. 23.06
  16. 0.987

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  Reviews (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