课程： 3.18分数和小数比较

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选择节分数和小数比较

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分数和小数比较
Aurora just finished washing her dad's car. Her dad tells her he is going to give her a bonus on her allowance as a thank you. He tells her she has two options. She can either have a third of the money in his wallet or $6.75. Aurora looks in her dad's wallet and sees that he has $20. Aurora knows her options are $\begin{aligned} \frac{20}{3} \end{aligned}$ dollars or $6.75. How can Aurora decide which option to choose if she wants the greater amount of money?
::奥罗拉刚洗完她爸爸的车。她爸爸告诉她,他要给她津贴奖金作为感谢你。他告诉她,她有两个选择。她可以拥有钱包里三分之一的钱,也可以有6.75美元。奥罗拉看着她父亲的钱包,看到他有20美元。奥罗拉知道她的选择是203美元或6.75美元。奥罗拉怎么能决定选择哪一种选择,如果她想要更多钱的话?

In this concept, you will learn how to compare decimals and fractions.
::在这个概念中,你会学习如何比较小数数和分数。

Comparing Fractions and Decimals
::比较分数和十进数

Sometimes you will want to compare decimals and fractions. To compare a decimal to a fraction or a fraction to a decimal, you will need to convert one of the numbers so that both numbers are in the same form. It is often easier to compare numbers written in decimal form unless they are fractions with the same denominator .
::有时您会想要比较小数点和分数。要比较小数点与小数点或小数点或小数点,您需要转换其中的一个数字,以使两个数字以相同形式出现。通常比较以小数点和分数表示的数字比较容易,除非是同分数。

Once you know how a decimal and a fraction are related, you can use the following inequality symbols to describe their relationship:
::一旦您知道小数点和小数点是如何关联的,您就可以使用以下不平等符号来描述他们之间的关系:

$\begin{aligned} > \end{aligned}$ means is greater than.
::> 手段大于。

$\begin{aligned} < \end{aligned}$ means is less than.
::< 手段小于。

$\begin{aligned} = \end{aligned}$ means is equal to.
::手段等于。

Let's look at an example.
::让我们举个例子。

Compare $\begin{aligned} \frac{1}{4} \end{aligned}$ and 0.25.
::比较1 4和0.25。

First, convert $\begin{aligned} \frac{1}{4} \end{aligned}$ to a decimal. Because $\begin{aligned} \frac{1}{4} \end{aligned}$ is a common fraction, you might know that its decimal form is 0.25. Or, you can use long division.
::首先,将14转换为小数点。因为14是一个常见的分数,你可能会知道其小数点的形式是0.25。或者,你可以使用长分割法。

Now you are looking to compare 0.25 and 0.25. These two numbers are equal.
::现在你要比较0.25和0.25,这两个数字是相等的。

The answer is $\begin{aligned} \frac{1}{4} = 0.25 \end{aligned}$ .
::答案是14=0.25。

Here is another example.
::下面是另一个例子。

Compare $\begin{aligned} 1 \frac{2}{20} \end{aligned}$ and 1.3.
::比较2 20和1.3。

This time let's write both numbers as mixed numbers. First, simplify the given mixed number .
::这一次让我们把两个数字都写成混合数字。首先,简化给定的混合数字。

$\begin{aligned} 1 \frac{2}{20} = 1 \frac{1}{10} \end{aligned}$

Next, write 1.3 as a fraction. Note that 0.3 is 3 tenths so $\begin{aligned} 0.3 = \frac{3}{10} \end{aligned}$ .
::接下来,写1.3作为一个分数。请注意,0.3是十分3,0.3=3 10。

$\begin{aligned} 1.3 = 1 \frac{3}{10} \end{aligned}$

Now you are looking to compare $\begin{aligned} 1 \frac{1}{10} \end{aligned}$ and $\begin{aligned} 1 \frac{3}{10} \end{aligned}$ . Because the mixed numbers have the same denominator, you can see that $\begin{aligned} 1 \frac{1}{10} \end{aligned}$ is less than $\begin{aligned} 1 \frac{3}{10} \end{aligned}$ . This means $\begin{aligned} 1 \frac{2}{20} \end{aligned}$ is less than 1.3.
::现在,您正在比较 11 10 和 13 10 。因为混合数字具有相同的分母, 您可以看到 11 10 低于 13 10 。这意味着 12 20 低于 1. 3。

The answer is $\begin{aligned} 1 \frac{2}{20} < 1.3 \end{aligned}$ .
::答案是12 20 < 1.3。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Aurora.
::早些时候,你得到一个问题关于奥罗拉。

Her dad is offering her either a third of the money in his wallet $\begin{aligned} (\frac{20}{3} dollars) \end{aligned}$ or $6.75 as a thank you for washing his car. Aurora is trying to decide which option to choose.
::她父亲向她提供钱包里三分之一的钱(203美元)或6.75美元,作为感谢你洗他的车。 Aurora正试图决定选择哪一种选择。

First, Aurora should convert $\begin{aligned} \frac{20}{3} \end{aligned}$ to a mixed number.
::首先,奥罗拉应该把203转换成混合数字

$\begin{aligned} \frac{20}{3} = 6 \frac{2}{3} \end{aligned}$

Next, Aurora should write $\begin{aligned} 6 \frac{2}{3} \end{aligned}$ as a decimal. She can use long division to convert $\begin{aligned} \frac{2}{3} \end{aligned}$ to a decimal.
::下一步, Aurora 应该在小数点后写 6 2 3 。她可以使用长分割法将 2 3 转换为小数点。

$\begin{aligned} \begin{array}{rcl} \overset{0.66 \dots}{3 \bar{) 2.00}} \\ \underline{- 18} \\ 20 \\ \underline{- 18} \\ 20 \end{array} \end{aligned}$

She should notice that this is a repeating decimal .
::她应该注意到,这是重复的十进制。

$\begin{aligned} 6 \frac{2}{3} = 6. \bar{6} \end{aligned}$

Now Aurora is looking to compare $\begin{aligned} 6. \bar{6} \end{aligned}$ and 6.75. She can round $\begin{aligned} 6. \bar{6} \end{aligned}$ to the nearest hundredth since it is an amount of money.
::现在奥罗拉正在比较6.6和6.75。她可以大约6.6到最近的100,因为它是一笔钱。

$\begin{aligned} 6. \bar{6} \end{aligned}$ rounds to 6.67.
::6. 6轮到6.67

6.67 is less than 6.75. This means $\begin{aligned} \frac{20}{3} \end{aligned}$ is less than 6.75.
::6.67小于6.75,这意味着20 3小于6.75。

The answer is if Aurora wants the greater amount of money, she should choose the $6.75.
::答案是如果Aurora想要更多钱她应该选择6.75美元

Example 2
::例2

Compare 0.45 and $\begin{aligned} \frac{6}{10} \end{aligned}$ .
::比较0.45和6 10。

First, convert $\begin{aligned} \frac{6}{10} \end{aligned}$ to a decimal. Notice that $\begin{aligned} \frac{6}{10} \end{aligned}$ is read “6 tenths”. This means $\begin{aligned} \frac{6}{10} \end{aligned}$ is equivalent to 0.6.
::第一,将6 10改为小数点后,注意6 10改为“6 10”,这意味着6 10等于0.6。

Now you are looking to compare 0.45 and 0.6. Note that 0.6 is the same as 0.60. 0.45 is less than 0.60. This means 0.45 is less than $\begin{aligned} \frac{6}{10} \end{aligned}$ .
::现在,您要比较0.45和0.6。请注意,0.6与0.60相同。0.45小于0.60。这意味着0.45小于6 10。

The answer is $\begin{aligned} 0.45 < \frac{6}{10} \end{aligned}$ .
::答案是0.45 < 6 10。

Example 3
::例3

Compare 0.5 and $\begin{aligned} \frac{1}{4} \end{aligned}$ .
::比较0.5和14。

First, convert $\begin{aligned} \frac{1}{4} \end{aligned}$ to a decimal. Because $\begin{aligned} \frac{1}{4} \end{aligned}$ is a common fraction, you might know that its decimal form is 0.25. Or, you can use long division.
::首先,将14转换为小数点。因为14是一个常见的分数,你可能会知道其小数点的形式是0.25。或者,你可以使用长分割法。

Now you are looking to compare 0.5 and 0.25. Note that 0.5 is the same as 0.50. 0.50 is greater than 0.25. This means 0.5 is greater than $\begin{aligned} \frac{1}{4} \end{aligned}$ .
::现在,您要比较0.5和0.25。请注意,0.5与0.50.0.50相同。0.50大于0.25。这意味着0.5大于14。

The answer is $\begin{aligned} 0.5 > \frac{1}{4} \end{aligned}$ .
::答案是0.5 > 14。

Example 4
::例4

Compare $\begin{aligned} 3 \frac{3}{5} \end{aligned}$ and 3.56.
::比较3 5和3.56。

First, convert $\begin{aligned} 3 \frac{3}{5} \end{aligned}$ to a decimal. You can use long division to convert $\begin{aligned} \frac{3}{5} \end{aligned}$ to a decimal.
::首先,将 3 3 5 转换为小数点。您可以使用长分割法将 3 5 转换为小数点。

$\begin{aligned} \begin{array}{rcl} \overset{0.6}{5 \bar{) 3.0}} \\ \underline{- 30} \\ 0 \end{array} \end{aligned}$

$\begin{aligned} 3 \frac{3}{5} = 3.6 \end{aligned}$

Now you are looking to compare 3.6 and 3.56. Note that 3.6 is the same as 3.60. 3.60 is greater than 3.56. This means $\begin{aligned} 3 \frac{3}{5} \end{aligned}$ is greater than 3.56.
::现在,您要比较3.6和3.56。请注意,3.6与3.60相同。3.60大于3.56。这意味着,3,3,3,5大于3.56。

The answer is $\begin{aligned} 3 \frac{3}{5} > 3.56 \end{aligned}$ .
::答案是3 3 5 > 3.56。

Example 5
::例5

Compare $\begin{aligned} \frac{2}{8} \end{aligned}$ and 0.25.
::比较2,8和0.25。

Let's write both numbers as fractions. First, simplify the given fraction.
::让我们将两个数字都写成分数。首先,简化给定的分数。

$\begin{aligned} \frac{2}{8} = \frac{1}{4} \end{aligned}$

Next, write 0.25 as a fraction. You might recognize 0.25 as a common decimal that is equivalent to $\begin{aligned} \frac{1}{4} \end{aligned}$ .
::下一步,将 0.25 写成一个分数。您可以识别0. 25 是一个共同的十进制小数, 相当于 14 。

$\begin{aligned} 0.25 = \frac{1}{4} \end{aligned}$

Now you are looking to compare to $\begin{aligned} \frac{1}{4} \end{aligned}$ and $\begin{aligned} \frac{1}{4} \end{aligned}$ . These fractions are equal. This means $\begin{aligned} \frac{2}{8} \end{aligned}$ is equal to 0.25.
::现在您正在寻找比较 14 和 14。这些分数是相等的。这意味着 2 8 等于 0.25 。

The answer is $\begin{aligned} \frac{2}{8} = 0.25 \end{aligned}$ .
::答案是2 8=0.25。

Review
::回顾

Compare the following decimals and fractions using an inequality symbol.
::使用不平等符号比较以下小数点和分数。

$\begin{aligned} \frac{1}{3} and 0.5 \end{aligned}$
::1、3和0.5

$\begin{aligned} \frac{6}{10} and 0.9 \end{aligned}$
::6 10和0.9

$\begin{aligned} 0.25 and \frac{1}{10} \end{aligned}$
::0.25和1 10

$\begin{aligned} 0.16 and \frac{33}{100} \end{aligned}$
::0.16和33 100

$\begin{aligned} \frac{3}{5} and 0.6 \end{aligned}$
::5和0.6

$\begin{aligned} \frac{3}{15} and 0.15 \end{aligned}$
::15和0.15

$\begin{aligned} \frac{6}{7} and 0.99 \end{aligned}$
::6、7和0.99

$\begin{aligned} \frac{3}{4} and 0.75 \end{aligned}$
::3 和 0.75

$\begin{aligned} \frac{1}{9} and 0.33 \end{aligned}$
::9和0.33

$\begin{aligned} \frac{7}{10} and 0.8 \end{aligned}$
::7、10和0.8

Write the following values in order from least to greatest.
::写下以下值, 以从最小到最大顺序排列。

$\begin{aligned} 0.25, \frac{1}{3}, 0.54 \end{aligned}$

$\begin{aligned} 0.55, \frac{3}{4}, 0.613 \end{aligned}$

$\begin{aligned} 0.252, \frac{1}{9}, 0.31 \end{aligned}$

$\begin{aligned} 0.05, \frac{7}{8}, 0.546 \end{aligned}$

$\begin{aligned} 0.09, \frac{1}{10}, 0.88 \end{aligned}$

Review (Answers)
::回顾(答复)

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。

Resources
::资源

章节大纲

常规

分数和小数比较

Comparing Fractions and Decimals ::比较分数和十进数

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Comparing Fractions and Decimals
::比较分数和十进数

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源