5.3小数比率的比较

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 小数比率的比较

  Collapse Expand

  小数比率的比较

  

  播放段落

  Erinda went with her dad to the toy store. She was looking for stuffed animals to give to children in need during the holidays. Luckily for Erinda, the store was having a big sale, and all the stuffed animals were marked down one third. Some of the toys that Erinda would like to buy were originally priced at 99 cents. How can she convert  $\begin{array}{r}\frac{1}{3}\end{array}$  to a decimal to calculate how much money she can save on each stuffed animal?
  ::Erinda和她父亲一起去玩具店。她正在寻找填充的动物,以便在假期里喂给有需要的儿童。幸运的是,Erinda说,商店有一笔大买卖,所有的填充的动物都记下了三分之一。Erinda想要买的一些玩具最初的价格是99美分。她如何将13到小数转换为13到1小数,以计算每只填充的动物能储蓄多少钱?

  播放段落

  In this concept, you will learn how to convert and compare ratios in decimal form.
  ::在此概念中,您将学习如何转换和比较小数位数中的比率。

  播放段落

  Comparing Ratios in Decimal Form
  ::以十进制表格比较比率

  播放段落

  A  ratio  is a relationship between two numbers by division.
  ::A比率是按司划分的两个数字之间的关系。

  播放段落

  Fractions are ratios.
  ::分数是比率。

  播放段落

  Decimals are ratios.
  ::十进制是比率。

  播放段落

  Remember that decimals are based on multiples of 10, so if possible, convert fractions to one of these multiples.
  ::记住小数点以 10 的倍数为基础, 所以如果可能的话, 将分数转换成这些倍数之一 。

  播放段落

  To convert a ratio to its decimal form:
  ::转换与其小数点表数的比率:

  播放段落

  First, write the ratio as a fraction.
  ::首先,将比率写成一个分数。

  播放段落

  Next,  divide  the  numerator  by the  denominator . "Denominator" and "down" both start with the letter "d." 
  ::下一步,将分子除以分母。 “ 主宰者” 和“ 下降” 都以字母“ d” 开头。

  播放段落

  Look at this example.
  ::看看这个例子。

  播放段落

  Rewrite the ratio 1 to 4 in decimal form.
  ::以小数格式重写 1 至 4 的比 。

  播放段落

  First, write the ratio as a fraction.
  ::首先,将比率写成一个分数。

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

  播放段落

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

  $\begin{array}{r}\frac{1}{4}=4\overline{)1}\end{array}$

  播放段落

  Since 1 cannot be evenly divided by 4, rewrite 1 as a decimal with a  zero  after the  decimal point . Any number of zeroes can be annexed because  $\begin{array}{r}1=1.0=1.00=1.000\end{array}$ , etc.
  ::由于 1 无法平均除以 4 , 将 1 改写为小数, 小数点后为零。 任何零数都可以附上, 因为 1 = 1. 0 = 1. 00 = 1. 000 等。

  播放段落

  Before you divide, remember to put a decimal point in the  quotient  directly above the decimal point in the  dividend .
  ::在除法前,请记住在股息小数点上方直接加上小数点中的小数点。

  播放段落

  Then, divide.
  ::然后,分裂。

  $$\begin{array}{rl}& \stackrel{0.2}{4\overline{)1.0}}\\ & \underset{\_}{-8}\\ & 2\end{array}$$

  播放段落

  Continue adding zeroes after the decimal point and dividing until the quotient has no  remainder .
  ::在小数点后继续增加零,并进行除法,直到商数没有剩余部分。

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

  播放段落

  The answer is 0.25. The decimal form of the ratio  $\begin{array}{r}\frac{1}{4}\end{array}$  is 0.25.
  ::答案是0.25。 14比小数位为0.25。

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about Erinda and the one-third-off sale at the toy store.
  ::早些时候,你得到一个问题 关于Erinda 和三分之一的销售 在玩具店。

  播放段落

  She found some stuffed animals that were originally 99 cents.How much will she save on each toy?
  ::她发现一些填充的动物 原本是99美分。 她能为每只玩具节省多少?

  播放段落

  First, write the ratio as a fraction.
  ::首先,将比率写成一个分数。

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

  播放段落

  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。

  $$\begin{array}{rl}& \stackrel{0.333}{3\overline{)1.000}}\\ & \underset{\_}{-9}\\ & 10\\ & \underset{\_}{-9}\\ & 1\end{array}$$

  播放段落

  Then, recognize that .333 is a  repeating decimal  and  round  to two places.
  ::然后,承认333是重复小数点,然后四舍五入到两个位。

  $\begin{array}{r}.333\approx .33\end{array}$

  播放段落

  The answer is  $\begin{array}{r}\frac{1}{3}\end{array}$ off the price of each toy is 33 cents. Erinda will save 33 cents on each toy. 
  ::答案是每只玩具价格13美元,每只玩具价格33美分。埃琳达将节省每只玩具33美分。

  播放段落

  Example 2
  ::例2

  播放段落

  Rewrite the ratio 9:5 in decimal form.
  ::以小数格式重写 9: 5 的比 。

  播放段落

  First, rewrite the ratio as a fraction.
  ::首先,将比率重写为分数。

    $\begin{array}{r}\frac{9}{5}\end{array}$

  播放段落

  Next, divide the numerator by the denominator, remembering to annex zeroes and continue until there is no remainder.
  ::其次,将分子除以分母,记住附件零,并持续到没有剩余部分为止。

  $$\begin{array}{rl}& \stackrel{1.8}{5\overline{)9.0}}\\ & \underset{\_}{-5}\\ & 40\\ & \underset{\_}{-40}\\ & 0\end{array}$$

  播放段落

  The answer is 1.8 The decimal form of 9:5 is 1.8
  ::答案是 1. 8 ,小数点为 9: 5, 小数为 1. 8

  播放段落

  Example 3
  ::例3

  播放段落

  Compare the two ratios by converting them to decimals. Are they equivalent?
  ::通过将其换算为小数点来比较这两个比率。 它们是否等值?

  播放段落

  $\begin{array}{r}\frac{7}{14}\end{array}$ and  $\begin{array}{r}\frac{11}{20}\end{array}$
  ::7、14和11 20

  播放段落

   First, rewrite  $\begin{array}{r}\frac{7}{14}\end{array}$  in decimal form by dividing the numerator by the denominator.
  ::首先,将分子除以分母,以小数格式重写7-14。

  $$\begin{array}{rl}& \stackrel{0.5}{14\overline{)7.0}}\\ & \underset{\_}{-70}\\ & 0\\ & \underset{\_}{-0}\\ & 0\end{array}$$

   

  播放段落

  Next, rewrite  $\begin{array}{r}\frac{11}{20}\end{array}$  in decimal form.
  ::下一位,重写小数点的1120

  $$\begin{array}{rl}& \stackrel{0.55}{20\overline{)11.00}}\\ & \underset{\_}{-100}\\ & 100\\ & \underset{\_}{-100}\\ & 0\end{array}$$

  播放段落

  Then, compare the two values by writing each one to the same number of decimal places.
  ::然后,将这两个值进行比较,将每个值写成小数位数与小数位数比较。

  $\begin{array}{r}\frac{7}{14}=0.50\end{array}$

  
  $\begin{array}{r}\frac{11}{20}=0.55\end{array}$

  
  $\begin{array}{r}0.50<0.55\end{array}$    

  播放段落

  The answer is that the ratios are not equivalent.  $\begin{array}{r}\frac{7}{14}<\frac{11}{20}\end{array}$
  ::答案是,这些比率并不相等。 7 14 < 11 20

  播放段落

  Example 4
  ::例4

  播放段落

  Compare 5 to 10 and   $\begin{array}{r}\frac{2}{5}\end{array}$  and tell if they are equivalent.
  ::与5比10比10,5比2,5比5,并表明它们是否相等。

  播放段落

  First, write 5 to 10 as a fraction.
  ::首先,写5到10作为一个分数。

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

  播放段落

  Next, write each fraction as a decimal. 
  ::接下来,将每一分数写为小数点。

    $\begin{array}{r}\frac{5}{10}=0.5\end{array}$

  播放段落

  Then, remember that decimals are based on multiples of 10, and convert  $\begin{array}{r}\frac{2}{5}\end{array}$  to tenths by multiplying both the numerator and denominator times 2.
  ::然后,记住小数点以10的倍数为基础,然后将25乘以乘以分子和分母乘以2,将25乘以10转换为10。

    $\begin{array}{r}\frac{2\times 2}{5\times 2}=\frac{4}{10}\end{array}$ = 0.4

  播放段落

  Next, compare the decimals. 
  ::接下来,比较小数点。

  $\begin{array}{r}0.5>0.4\end{array}$  

  播放段落

  The answer is that the ratios are not equivalent.
  ::答案是比率不相等。

  播放段落

  Example 5
  ::例5

  播放段落

  Compare 6 to 10 and 1:4
  ::比较6至10和1:4

  播放段落

  First, write the ratios as fractions.
  ::首先,将比率写成分数。

  播放段落

  $\begin{array}{r}\frac{6}{10}\end{array}$ and  $\begin{array}{r}\frac{1}{4}\end{array}$
  ::6、10和1 4

  播放段落

  Next, convert the fractions to decimals.
  ::下一步,将分数转换为小数。

    $\begin{array}{r}\frac{6}{10}=0.60\end{array}$

    $\begin{array}{r}\frac{1}{4}=0.25\end{array}$

  播放段落

  Then, compare the decimals.
  ::然后,比较小数点。

    $\begin{array}{r}0.60>0.25\end{array}$

  播放段落

  The answer is that the ratios are not equivalent.
  ::答案是比率不相等。

  播放段落

  Review
  ::回顾

  播放段落

  Write each ratio as a decimal. Round to the nearest hundredth when necessary.
  ::必要时将每一比率写为小数点。 圆到最接近的百分百位数 。

  播放段落
  1. 1 to 4
     ::1至4
  播放段落
  2. 3 to 6
     ::3至6 3至6
  3. 3:4
  播放段落
  4. 8 to 5
     ::8至5
  播放段落
  5. 7 to 28
     ::7 至 28
  播放段落
  6. 8 to 10
     ::8 至 10
  播放段落
  7. 9 to 100
     ::9 至 100
  8. 15:20
  9. 18:50
  播放段落
  10. 3 to 10
      ::3至10
  播放段落
  11. 6 to 8
      ::6至8项
  播放段落
  12. 15 to 35
      ::15至35岁

  播放段落

  Compare the following ratios using <, >, or =.
  ::使用 < 、 > 或 = 比较以下比率。

  播放段落
  13. .55 ____1 to 2
      ::.55 1 至 2
  播放段落
  14. 3:8 _____ 4 to 9
      ::3:8 4至9
  播放段落
  15. 1 to 2 _____ 4:8
      ::1至2 4:8

  播放段落

  Review (Answers)
  ::回顾(答复)

  播放段落

  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 。

  播放段落

  Resources
  ::资源