Section outline

  • Candace uses a ruler to cut three different sized ribbons. One is 6.5 inches long. One is 6.25 inches long and the other is 6.75 inches long. She decides to  order  the ribbons from smallest to largest. Without seeing her ribbons, the only way to determine the order is to arrange the measurements from least to greatest. What is the order of the ribbons?
    ::坎迪斯用尺子剪裁三个不同大小的丝带。 一个长6.5英寸。 一个长6.25英寸,另一个长6.75英寸。 她决定把丝带从最小点到最大点。 她决定把丝带从最小点到最大点。 没有看到她的丝带, 确定顺序的唯一方法就是从最小点到最大点来排列测量。 丝带的顺序是什么?

    In this concept, you will learn how to compare decimals.

    ::在这个概念中,你会学习如何比较小数点。

    Comparing Decimals
    ::比较十进数

    When you  compare decimals , you are trying to figure out which part of a whole is greater. To do this, you need to think about the number 1.
    ::当比较小数点时,您正在试图找出整体的哪个部分更大。要做到这一点,您需要考虑数字1。

    1 is a whole. All decimals are part of 1.
    ::1 是一个整体。所有小数是 1 的一部分 。

    The closer a decimal is to 1, the larger the decimal is.
    ::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。

    Let's use  place value  to figure out which number is closer to one then compare the values.
    ::让我们使用位置值来找出哪个数字更接近一个数字,然后比较这些数值。

    0.45 ______ 0.67

    You have two decimals that both have the same number of digits in them. It is easy to compare decimals that have the same number of digits. Look at the numbers without the  decimal point  and determine which number is greater. 67 is greater. You can say that sixty-seven hundredths is closer to one than forty-five hundredths.
    ::您的两位小数位数与两位小数位数相同。 比较两位小数位数是很容易的。 看看没有小数点的数字, 并确定哪个数字更大。 67 更大。 您可以说, 六千七百位数接近四千五百位数。

    The answer is 0.45 < 0.67.
    ::答案是0.45 < 0.67。

    When comparing decimals, use the following steps:
    ::在比较小数点时,使用以下步骤:

    1. If the decimals you are comparing have the same number of digits in them, think about the value of the number without the decimal point.
      ::如果比较的十进制数字数字数与所比较的十进制数字数字数相同,请考虑数字值,不使用十进制点。
    2. The larger the number, the closer it is to one.
      ::数字越大,它就越接近一个。

    Now, let's compare decimals that don’t have the same number of digits.
    ::现在,让我们比较小数点,小数点没有相同数字。

    0.567 ______ 0.63

    Five hundred sixty-seven thousandths seems greater. However, thousandths are smaller than hundredths.
    ::5万6万7千人似乎更大 然而,千人小于千分之一

    To test this statement let’s look at a  hundreds grid  and a thousands grid.
    ::来测试这个声明, 让我们看看成百上千个网格和千个网格。

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    Now it is easier to compare. You can see that 0.63 is larger than 0.567.
    ::现在比较容易了。你可以看到0.63大于0.567。

    You can also compare without using a grid.
    ::您也可以在不使用网格的情况下比较。

    Add zeros to make sure that the digit numbers are equal. 
    ::添加零以确保数字数相等。

    0.567 ______ 0.630

    Then compare the numbers without the decimal point to determine which is greater. 640 is greater than 567.
    ::然后比较没有小数点的数字,以确定哪个更大。 640个数字大于567个。

    The answer is that 0.567 < 0.640.
    ::答案是0.567 < 0.640。

    The same technique is used when  whole numbers  are involved.
    ::当涉及全部数字时,也使用同样的技术。

    3.4 ______ 3.56

    First, add in a  zero .
    ::首先,增加零。

    3.40 ______ 3.56

    The whole number, 3 is the same, so look at the decimal. Notice that 40 is less than 56 so you can use symbols to compare.
    ::整个数字, 3是相同的, 所以请看小数点。 注意40小于56, 这样您就可以使用符号比较 。

    The answer is 3.4 < 3.56.
    ::答案是3.4 < 3.56。

    Now that you know how to compare decimals, you can  order  them.  Ordering  means that you list a series of decimals according to size. Write them from least to greatest or greatest to least.
    ::现在你知道如何比较小数, 您可以命令它们。 顺序意味着您会根据大小列出一系列小数。 把它们从最小写到最大或最大写到最小 。

    0.45, 0.32, 0.76

    To write these decimals in order  from least to greatest , start by comparing them. The greater a decimal is, the closer it is to one whole. The smaller a decimal is the farther it is from one whole. The first thing you need to look at is the digit number in each decimal. These each have two digits in them, so you can compare them right away. Next, look at each number without the decimal and write them in order from the smallest to the greatest.
    ::要按照从最小到最大的顺序写这些小数,首先比较它们。小数点越大,它就越接近于一个整体。小数点越远,它就越远于一个整体。首先你需要看的是每个小数点中的数字。每个小数点中都有两个数字,这样你就可以立即比较它们。接下来,看看每个数字没有小数点,然后写成从最小到最大。

    0.32, 0.45, 0.76

    32 is smaller than 45, 45 is greater than 32 but smaller than 76, 76 is the largest number
    ::32个小于45个,45个大于32个,但小于76个,76个最大

    The answer is 0.32, 0.45, 0.76.
    ::答案是0.32,0.45,0.76。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Candace and her ribbons.
    ::之前,你被问及Candace和她的丝带

    If the ribbons are 6.5 inches, 6.25 inches and 6.75 inches long, how can they be arranged from least to greatest?
    ::如果丝带长6.5英寸、6.25英寸和6.75英寸,那么如何将它们从最少排列到最多?

    First, add zeros to make the digit numbers equal.
    ::首先,添加零,使数字数相等。

    6.50, 6.25, 6.75

    Next, compare the numbers without a decimal to determine which is greater.
    ::接下来,比较没有小数点的数字,以确定哪个更大。

    675 is greater than 650 and 650 is greater than 625
    ::675人超过650人,650人超过625人

    Then, list the numbers in order from least to greatest.
    ::然后,按照从最少到最大的顺序列出数字。

    6.25, 6.5, 6.75

    The answer is 6.25, 6.5, 6.75.
    ::答案是6.25、6.5、6.75。

    Candace's ribbons are arranged with the 6.25 inch ribbon first then the 6.5 inch ribbon and the 6.75 inch ribbon.
    ::坎迪斯的丝带先用6.25英寸的丝带安排,然后是6.5英寸的丝带和6.75英寸的丝带安排。

    Example 2
    ::例2

    Compare the two decimals.
    ::比较小数点后两个小数点。

    0.256 _____ 0.17

    First, add zeros to make the digit numbers equal.
    ::首先,添加零,使数字数相等。

    0.256 ______ 0.170

    Next, compare the numbers without a decimal to determine which is greater.
    ::接下来,比较没有小数点的数字,以确定哪个更大。

    256 is greater than 170
    ::256个大于170个

    Then, make the comparison between the decimals.
    ::然后对小数点进行比较。

    0.256 > 0.17

    The answer is that 0.256 is greater than 0.17.
    ::答案是0.256大于0.17。

    Example 3
    ::例3

    Compare the two decimals.
    ::比较小数点后两个小数点。

    0.0987 ______ 0.987

    First, add zeros to make the digit numbers equal.
    ::首先,添加零,使数字数相等。

    0.0987 ______ 0.9870

    Next, compare the numbers without a decimal to determine which is greater.
    ::接下来,比较没有小数点的数字,以确定哪个更大。

    9870 is greater than 987
    ::9870大于987

    Then, make the comparison between the decimals.
    ::然后对小数点进行比较。

    0.0987 < 0.987

    The answer is that 0.0987 is less than 0.987.

    ::答案是0.0987还不到0.987。

    Example 4
    ::例4

    Compare the two decimals.
    ::比较小数点后两个小数点。

    0.453 ______ 0.045

    First, notice that the decimals have the same number of digits. This means that you can go directly to comparing the numbers without a decimal to determine which is greater.
    ::首先,请注意小数点的位数相同。这意味着您可以直接比较数字,而不用小数点即可确定哪个数字更大。

    453 is greater than 45
    ::453大于45

    Then, make the comparison between the decimals.
    ::然后对小数点进行比较。

    0.453 > 0.045

    The answer is that 0.453 is greater than 0.045.
    ::答案是0.453大于0.045。

    Example 5
    ::例5

    Order the decimals from least to greatest.
    ::将小数点从最小排列到最大。

    0.34, 0.745, 0.281

    First, add zeros to make the digit numbers equal.
    ::首先,添加零,使数字数相等。

    0.340, 0.745, 0.281

    Next, compare the numbers without a decimal to determine which is greater.
    ::接下来,比较没有小数点的数字,以确定哪个更大。

    0.745 is greater than 0.34 and 0.34 is greater than 0.281
    ::0.745大于0.34,0.34大于0.281

    Then, list the numbers in order from least to greatest.
    ::然后,按照从最少到最大的顺序列出数字。

    0.281, 0.34, 0.745

    The answer is 0.281, 0.34, 0.745.
    ::答案是0.281,0.34,0.745。

    Review
    ::回顾

    Compare the following decimals using <, >, or =
    ::使用 <, > 或 = 比较以下小数

    1. 0.4 ______ 0.2
    2. 0.67 ______ 0.75
    3. 0.90 ______ 0.9
    4. 0.234 ______ 0.54
    5. 0.123 ______ 0.87
    6. 0.954 ______ 0.876
    7. 0.32 ______ 0.032
    8. 0.8310 ______ 0.0009
    9. 0.9876 ______ 0.0129
    10. .08761 ______ 0.9992

    Order the following decimals from least to greatest.
    ::将以下小数点从最小顺序排列到最大顺序。

    1. 0.8, 0.9, 0.2, 0.4
    2. 0.02, 0.03, 0.07, 0.05, 0.04
    3. 0.34, 0.21, 0.05, 0.55
    4. 0.07, 0.7, 0.007, 0.0007
    5. 0.87, 1.0, 0.43, 0.032, 0.5
    6. 0.067, 0.055, 0.023, 0.011, 0.042
    7. 0.55, 0.22, 0.022, 0.033, 0.055
    8. 0.327, 0.222, 0.0222, 0.321, 0.4
    9. 0.65, 0.6, 0.67, 0.678, 0.69
    10. 0.45, 0.045, 4.5, 0.0045, 0.00045

    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