2.21长度、质量、容量的公制单位换算

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  长度、质量、容量的公制单位换算

  

  [Figure 1]

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  Charlotte is going on vacation with her parents and her 3 month old baby brother for a week. Her baby brother drinks 750 milliliters of formula each day. Charlotte’s mom has 6 liters of formula that she is bringing on the trip. How can Charlotte help her mom to figure out if she has enough formula for the trip?
  ::夏洛特和她的父母和三个月大的弟弟去度假一周。 她的弟弟每天喝750毫升的配方。 夏洛特的妈妈有6升她要带的配方。 夏洛特如何帮助她妈妈弄清楚她是否有足够的配方来旅行?

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  In this concept, you will learn how to convert among metric units of measure using powers of 10.
  ::在这个概念中,你们将学会如何使用10的功率在计量计量单位之间转换。

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  Converting Metric Units of Measure
  ::转换计量单位

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  Recall that the  metric system  is the system of measurement primarily used in science and in countries outside of the United States.
  ::回顾衡量系统是主要用于科学和美国以外国家的计量系统。

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  In the metric system, the base unit of  length  is the  meter  (m). The base unit of mass is the gram (g). The base unit of  capacity  is the liter (L). The same prefixes are used throughout the metric system. The prefix of each unit of measurement indicates how that unit relates to the base unit.
  ::在公制系统中,基长单位为米(m)。 基重单位为克(g)。 基容量单位为公升(L)。在整个公制系统中使用相同的前缀。每个计量单位的前缀表明该单位与基准单位的关系。

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  • “milli” means one thousandth. For example, there are 1000 millimeters in 1 meter.
    ::“毫升”是指千分之一。例如,一米内有1000毫米。
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  • “centi” means one hundredth. For example, there are 100   in 1 meter.
    ::“centi”是指第100倍,例如,每1米有100个。
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  • “kilo” means one thousand. For example, there are 1000   in 1  kilometer .
    ::“千公里”是指千公里,例如,每1公里就有1000公里。

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  The metric system is based on powers of 10 just like our number system. To move between different units of length, mass, and capacity all you need to do is move the decimal point.
  ::公制系统以10的功率为基础, 和我们的数字系统一样。 要在长度、 质量和能力的不同单位之间移动, 您只需要移动小数点 。

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  • Any time you are going from a smaller unit of measure to a larger unit of measure you will need to divide or move the decimal point to the left.
    ::当您从一个较小的计量单位向一个更大的计量单位前进时,您需要将小数点向左分隔或移动。
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  • Any time you are going from a larger unit of measure to a smaller unit of measure you will need to multiply or move the decimal point to the right.
    ::每当您从较大的度量单位向较小的度量单位前进时,您需要乘以小数点或将小数点向右移动。

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  The table below shows the most common metric conversions.
  ::下表显示最常用的计量换算方法。

  Common Metric Length Conversions

  Kilometers (km) to Meters (m)	$\begin{array}{r}\times 1000\end{array}$	Move decimal point 3 to the right
  Meters (m) to Centimeters (cm)	$\begin{array}{r}\times 100\end{array}$	Move decimal point 2 to the right
  Meters (m) to Millimeters (mm)	$\begin{array}{r}\times 1000\end{array}$	Move decimal point 3 to the right
  Centimeters (cm) to Millimeters (mm)	$\begin{array}{r}\times 10\end{array}$	Move decimal point 1 to the right
  Millimeters (mm) to Centimeters (cm)	$\begin{array}{r}÷10\end{array}$	Move decimal point 1 to the left
  Millimeters (mm) to Meters (m)	$\begin{array}{r}÷1000\end{array}$	Move decimal point 3 to the left
  Centimeters (cm) to Meters (m)	$\begin{array}{r}÷100\end{array}$	Move decimal point 2 to the left
  Meters (m) to Kilometers (km)	$\begin{array}{r}÷1000\end{array}$	Move decimal point 3 to the left

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  The same conversions will work for grams and liters. Just use the prefixes to find the correct conversion.
  ::相同的转换对克和升有效。 只要使用前缀查找正确的转换即可 。

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  Here is an example.
  ::举一个例子。

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  Convert 525 meters to centimeters.
  ::转换525米到厘米

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  First, notice that you are going from a larger unit to a smaller unit. This means you will need to multiply and move the decimal point to the right.
  ::首先,请注意您正在从一个较大的单位转到一个较小的单位。这意味着您需要乘以小数点,然后将小数点移到右边。

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  Next, remember that there are 100 centimeters in a meter. This means you will need to multiply by 100 or move the decimal point 2 to the right. Insert zeros into the blank spaces.
  ::下一步, 请记住一个计数计有100厘米。 这意味着您需要乘以100, 或者将小数点 2 移到右边。 在空白空格中插入零 。

  $$\begin{array}{r}525\times 100=52,500\end{array}$$

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  The answer is  $\begin{array}{r}525\text{ meters}=52,500\text{ centimeters}.\end{array}$
  ::答案是525米=52,500厘米

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  Here is another example.
  ::下面是另一个例子。

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  Convert 95,231 milligrams to kilograms.
  ::将95,231毫克转化为公斤。

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  First, notice that you are going from a smaller unit to a larger unit. This means you will need to divide and move the decimal point to the left.
  ::首先,请注意您正在从一个较小的单位转到一个较大的单位。这意味着您需要将小数点除以并移动到左边。

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  Next, remember that there are 1000 milligrams in a gram and 1000 grams in a kilogram. This means there are 1,000,000  $\begin{array}{r}(1000\times 1000)\end{array}$  milligrams in a kilogram. You will need to divide by 1,000,000 or move the decimal point 6 to the left.
  ::下一步, 请记住每公斤有1000毫克, 每公斤有1000毫克。 这意味着每公斤有1,000万毫克。 您需要将小数点 6 除以 1 000 000 毫克, 或者将小数点 6 移到左边 。

  $$\begin{array}{r}\frac{95231}{1000000}=0.095231\end{array}$$

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  The answer is  $\begin{array}{r}95,231\text{ milligrams}=0.095231\text{ kilograms}.\end{array}$
  ::答案是95,231毫克=0.0952331公斤。

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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 Charlotte and her family trip with her baby brother.
  ::早些时候,你得到一个问题 关于夏洛特 和她的家庭旅行 与她的弟弟。

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  Her brother drinks 750 milliliters of formula a day and her mom has 6 liters of formula packed for the 7 day trip. Charlotte wants to make sure they have enough formula.
  ::她的哥哥每天喝750毫升的配方,她妈妈七天的行程里有6升配方,夏洛特想确保他们有足够的配方。

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  First, Charlotte should figure out how many milliliters of formula her brother will need for the 7 days. He drinks 750 milliliters a day, so multiply 750 times 7.
  ::首先,夏洛特应该找出她哥哥7天需要多少毫升配方。他每天喝750毫升,乘750乘以7。

  $$\begin{array}{r}750\times 7=5250\end{array}$$

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  Her brother will need 5250 milliliters of formula for the trip.
  ::她哥哥需要5250毫升的配方

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  Next, convert 5250 milliliters to liters. Charlotte should notice that she is going from a smaller unit to a larger unit. This means she will need to divide and move the decimal point to the left.
  ::下一步, 将 5250 毫升转换为升。 夏洛特应该注意到她正在从一个较小的单位转到一个更大的单位。 这意味着她需要将小数点除以并移动到左边 。

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  Now, Charlotte needs to remember that there are 1000 milliliters in a liter. This means she will need to divide by 1000 or move the decimal point 3 to the left.
  ::现在,夏洛特需要记住一公升里有1000毫升。 这意味着她需要除以1000, 或者将小数点3移到左边。

  $$\begin{array}{r}\begin{array}{rcl}5250÷1000& =& 5.250\\ 5250\text{ milliliters}& =& 5.25\text{ liters}\end{array}\end{array}$$

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  The answer is that because Charlotte’s mom has 6 liters of formula and Charlotte’s brother will need 5.25 liters of formula, Charlotte’s mom has enough formula for the trip.
  ::因为夏洛特的母亲有6升配方, 夏洛特的兄弟需要5.25升配方, 夏洛特的母亲有足够的配方。

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  Example 2
  ::例2

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  Convert 150 grams to centigrams.
  ::将150克转换为厘米。

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  First, notice that you are going from a larger unit to a smaller unit. This means you will need to multiply and move the decimal point to the right.
  ::首先,请注意您正在从一个较大的单位转到一个较小的单位。这意味着您需要乘以小数点,然后将小数点移到右边。

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  Next, remember that there are 100 centigrams in a gram. This means you will need to multiply by 100 or move the decimal point 2 to the right. Insert zeros into the blank spaces.
  ::下一步, 请记住, 一公克中有 100 厘米。 这意味着您需要乘以 100 或将小数点 2 向右移动。 在空白空格中插入 零 。

  $$\begin{array}{r}150\times 100=15,000\end{array}$$

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  The answer is  $\begin{array}{r}150\text{ grams}=15,000\text{ centigrams}.\end{array}$
  ::答案是150克=15 000厘米

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  Example 3
  ::例3

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  Convert 500 meters to centimeters.
  ::将500米转换到厘米

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  First, notice that you are going from a larger unit to a smaller unit. This means you will need to multiply and move the decimal point to the right.
  ::首先,请注意您正在从一个较大的单位转到一个较小的单位。这意味着您需要乘以小数点,然后将小数点移到右边。

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  Next, remember that there are 100 centimeters in a meter. This means you will need to multiply by 100 or move the decimal point 2 to the right. Insert zeros into the blank spaces.
  ::下一步, 请记住一个计数计有100厘米。 这意味着您需要乘以100, 或者将小数点 2 移到右边。 在空白空格中插入零 。

  $$\begin{array}{r}500\times 100=50,000\end{array}$$

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  The answer is  $\begin{array}{r}500\text{ meters}=50,000\text{ centimeters}.\end{array}$
  ::答案是500米 = 50,000厘米

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  Example 4
  ::例4

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  Convert 120 meters to kilometers.
  ::将120米转换为公里

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  First, notice that you are going from a smaller unit to a larger unit. This means you will need to divide and move the decimal point to the left.
  ::首先,请注意您正在从一个较小的单位转到一个较大的单位。这意味着您需要将小数点除以并移动到左边。

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  Next, remember that there are 1000 meters in a kilometer. This means you will need to divide by 1000 or move the decimal point 3 to the left.
  ::下一步, 请记住每公里有1000米。 这意味着您需要除以 1000 或将小数点 3 向左移动 。

  $$\begin{array}{r}120÷1000=0.120\text{or}0.12\end{array}$$

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  The answer is  $\begin{array}{r}120\text{ meters}=0.12\text{ kilometers}.\end{array}$
  ::答案是120米=0.12公里

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  Example 5
  ::例5

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  Convert 50 centiliters to liters.
  ::将50厘米转换为升。

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  First, notice that you are going from a smaller unit to a larger unit. This means you will need to divide and move the decimal point to the left.
  ::首先,请注意您正在从一个较小的单位转到一个较大的单位。这意味着您需要将小数点除以并移动到左边。

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  Next, remember that there are 100 centiliters in a liter. This means you will need to divide by 100 or move the decimal point 2 to the left.
  ::下一步, 请记住一升内有 100 厘米。 这意味着您需要除以 100 或将小数点 2 向左移动 。

  $$\begin{array}{r}50÷100=0.5\end{array}$$

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  The answer is  $\begin{array}{r}50\text{ centiliters}=0.5\text{ liters}.\end{array}$
  ::答案是50厘米=0.5升。

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  Review
  ::回顾

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  Convert the following metric units of length.
  ::转换以下计量长度单位。

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  1. 10 cm to millimeters
     ::10厘米至毫米
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  2. 100 kilometers to meters
     ::100公里至100米
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  3. 453 meters to kilometers
     ::453米至453公里
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  4. 1,567 kilometers to meters
     ::1 567公里至1 567公里
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  5. 6,700 centimeters to meters
     ::6,700厘米到米6,700厘米
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  6. 7.8 meters to centimeters
     ::7.8米至厘米

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  Convert the following measurements into milliliters.
  ::将以下测量值转换为毫升。

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  7. 65.57 liters
     ::65.57升
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  8. 28.203 centiliters
     ::28.203 立方厘米
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  9. 0.009761 kiloliters
     ::0.009761千升

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  Convert the following measurements into centigrams.
  ::将以下测量数据转换成厘米。

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  10. 29.467 grams
      ::29.467克
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  11. 0.0562 milligrams
      ::0.0562毫克
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  12. 0.0450584 kilograms
      ::0.0450584公斤

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  Convert the following measurements into kiloliters.
  ::将以下测量转换成千升。

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  13. 89.96 liters
      ::89.96升
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  14. 45,217 milliliters
      ::45 217毫升
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  15. 3,120,700 centiliters
      ::3 120 700 厘米

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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