5.21重复小数

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  重复小数

  

  [Figure 1]

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  Jose has 10 bars of chocolate that he needs to give to 3 of his friends. How many bars of chocolate does each friend receive?
  ::Jose有10条巧克力,他需要给3个朋友。每个朋友收到多少条巧克力?

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  In this concept, you will learn to write fractions and mixed numbers as repeating decimals.
  ::在此概念中,您将学习将分数和混合数字作为重复的十进制数字来写。

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  Writing Fractions and Mixed Numbers as Repeating Decimals
  ::以重复十进制写成分数和混合数字

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  A  terminating decimal  is a decimal number that does not go on forever. The word “terminate” means to end. Most of the fractions you have been working with are terminating decimals.
  ::终止的十进制是不会永远延续的十进制数字。“终止”一词是指结束。您一直在工作的分数大多是终止十进制。

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  Here is a fraction with a terminating decimal.
  ::这是终止小数小数的分数。 NAME OF TRANSLATORS

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

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  Divide  1 by 4 to find the decimal value.
  ::除以 1 乘 4 以找到小数点值。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.25}{4\overline{)1.00}}\\ & & \underset{\_}{-8}\\ & & 20\\ & & \underset{\_}{-20}\\ & & 0\end{array}\end{array}$$

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  You use  zero  placeholders, but ultimately, the decimal will divide evenly.
  ::您使用零占位符, 但最终, 小数点会平分 。

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  A decimal that does not end and repeats the same number or numbers over and over again is called a  repeating decimal . When you divide the  numerator  by the  denominator  and keep ending up with the same number, you might have a repeating decimal.
  ::不结束并重复相同数字或数字的十进制数字,被称作重复的十进制数字。当将分子除以分母,并一直以相同数字结束时,可能会有一个重复的十进制数字。

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  Convert  $\begin{array}{r}\frac{2}{3}\end{array}$  to a decimal.
  ::将2 3转换为小数。

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  First, this does not have a base ten denominator. Divide the numerator by the denominator.
  ::首先,它没有基本十分母。将分子除以分母。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.666}{4\overline{)2.000}}\\ & & \underset{\_}{-18}\\ & & 20\\ & & \underset{\_}{-18}\\ & & 20\\ & & \underset{\_}{-18}\\ & & 2\end{array}\end{array}$$

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  The same  remainder  keeps showing up and the  quotient  becomes a series of 6’s. It does not matter if you keep adding zero placeholders. A repeating decimal is indicated by adding a line over the last digit or series of digits in the quotient that repeats itself.
  ::其余部分不断出现,商数成为6的系列。如果您继续添加零占位符并不重要。重复的十进制通过在重复的商数中最后数字或数字序列上添加一行来表示。

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  The decimal value of  $\begin{array}{r}\frac{2}{3}\end{array}$  is  $\begin{array}{r}0.\bar{6}\end{array}$  .
  ::小数点为2 3,小数点为 0. 6,小数点为 0. 6 。

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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 Jose and his chocolate bars.
  ::早些时候,你得到一个问题 关于何塞和他的巧克力棒。

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  Jose wants to give 10 chocolate bars to 3 of his friends. Divide 10 by 3 to find how many chocolate bar each friend receives.
  ::Jose想给他的3个朋友10块巧克力棒。

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  Divide 10 by 3.
  ::将10除以3除以3。

  $$\begin{array}{rl}& \stackrel{3.333}{3\overline{)10.000}}\\ & \underset{\_}{-9}\\ & 10\\ & \underset{\_}{-9}\\ & 10\\ & \underset{\_}{-9}\\ & 10\\ & -9\\ & \bar{1}\end{array}$$

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  The answer is a repeating decimal  $\begin{array}{r}3.\bar{3}\end{array}$ .
  ::答案是重复小数点3 3

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  Jose can give each friend  $\begin{array}{r}3.\bar{3}\end{array}$  bars of chocolate.
  ::Jose可以给每个朋友3块3块巧克力

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  Example 2
  ::例2

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  Is  $\begin{array}{r}\frac{4}{9}\end{array}$  a repeating decimal or a terminating decimal?
  ::4 -9是重复的十进制还是终止的十进制?

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  Convert the fraction to a decimal. Divide 4 by 9.
  ::将分数转换为小数点。除以 4 乘 9 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.4444}{9\overline{)4.0000}}\\ & & \underset{\_}{-36}\\ & & 40\\ & & \underset{\_}{-36}\\ & & 40\\ & & \underset{\_}{-36}\\ & & 40\\ & & \underset{\_}{-36}\\ & & 4\end{array}\end{array}$$

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  The same remainder keeps showing up and the quotient will go on and on as a series of 4s.
  ::其余部分不断出现 商数会继续持续 以4的系列进行

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  The decimal value of  $\begin{array}{r}\frac{4}{9}\end{array}$  is a repeating decimal,  $\begin{array}{r}0.\bar{4}\end{array}$ .
  ::小数点为 4 9 是重复的小数点, 0. 4 。

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  Example 3
  ::例3

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  Determine if the fraction is a repeating or terminating decimal.
  ::确定分数是重复还是终止小数。

  $$\begin{array}{r}\frac{1}{3}\end{array}$$

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  Convert the fraction to a decimal. Divide 1 by 3.
  ::将分数转换为小数点。除以 1 3。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.3333}{3\overline{)1.0000}}\\ & & \underset{\_}{-9}\\ & & 10\\ & & \underset{\_}{-9}\\ & & 10\\ & & \underset{\_}{-9}\\ & & 10\\ & & \underset{\_}{-9}\\ & & 1\end{array}\end{array}$$

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  The decimal value of  $\begin{array}{r}\frac{1}{3}\end{array}$  is a repeating decimal,  $\begin{array}{r}0.\bar{3}\end{array}$ .
  ::小数点为13是重复的小数点, 0。 3 。

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  Example 4
  ::例4

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  Determine if the fraction is a repeating or terminating decimal.
  ::确定分数是重复还是终止小数。

  $$\begin{array}{r}\frac{1}{8}\end{array}$$

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  Convert the fraction to a decimal. Divide 1 by 8.
  ::将分数转换为小数点。除以 1 乘 8 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.125}{8\overline{)1.000}}\\ & & \underset{\_}{-8}\\ & & 20\\ & & \underset{\_}{-16}\\ & & 40\\ & & \underset{\_}{-40}\\ & & 0\end{array}\end{array}$$

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  The decimal value of  $\begin{array}{r}\frac{1}{8}\end{array}$  is a terminating decimal, 0.125.
  ::小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后,小数点后为0.125。

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  Example 5
  ::例5

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  Determine if the fraction is a repeating or terminating decimal.
  ::确定分数是重复还是终止小数。

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

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  First, convert the fraction part to a decimal.
  ::首先,将分数部分转换为小数点。

  $$\begin{array}{r}\frac{1}{2}=0.5\end{array}$$

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  Then, place the whole number to the left of the  decimal point .
  ::然后将整个数字放在小数点左边。

  $$\begin{array}{r}5\frac{1}{2}=5.5\end{array}$$

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  The decimal value of  $\begin{array}{r}5\frac{1}{2}\end{array}$  is a terminating decimal, 5.5.
  ::小数点为5,12,小数点为终止小数点5.5。

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  Review
  ::回顾

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  Determine if the fractions are repeating or terminating decimals.
  ::确定分数是重复还是终止小数。

  1. $\begin{array}{r}\frac{14}{3}\end{array}$
  2. $\begin{array}{r}\frac{34}{9}\end{array}$
  3. $\begin{array}{r}\frac{23}{3}\end{array}$
  4. $\begin{array}{r}\frac{17}{4}\end{array}$
  5. $\begin{array}{r}\frac{19}{6}\end{array}$
  6. $\begin{array}{r}\frac{12}{5}\end{array}$
  7. $\begin{array}{r}3\frac{1}{3}\end{array}$
  8. $\begin{array}{r}8\frac{1}{2}\end{array}$
  9. $\begin{array}{r}9\frac{2}{3}\end{array}$
  10. $\begin{array}{r}11\frac{4}{5}\end{array}$
  11. $\begin{array}{r}16\frac{1}{4}\end{array}$
  12. $\begin{array}{r}\frac{44}{3}\end{array}$
  13. $\begin{array}{r}\frac{66}{7}\end{array}$
  14. $\begin{array}{r}\frac{18}{4}\end{array}$
  15. $\begin{array}{r}\frac{74}{7}\end{array}$

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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