4.20长度、质量、容量的公制单位换算

章节大纲

• 选择节常规

  折叠 展开

  常规

  全部折叠 展开全部

  • 选择活动新闻通告

    

    新闻通告 讨论区
• 选择节长度、质量、容量的公制单位换算

  折叠 展开

  长度、质量、容量的公制单位换算

  

  [Figure 1]

  播放段落

  Caleb is playing a math game on the computer. He has to compare metric units by filling in the blank with the correct sign. His choices are greater than (>), less than (<), or equal to (=). This is the problem Caleb is working on.
  ::Caleb正在计算机上玩数学游戏。 他必须用正确符号填空来比较测量单位。 他的选择大于( > ) 、 小于( < ) 或等于( = ) 。 这就是 Caleb正在处理的问题 。

  $$\begin{array}{r}5.5g\underset{\_}{}4,500mg\end{array}$$

  播放段落

  What should Caleb choose?
  ::Caleb应该选择什么?

  播放段落

  In this concept, you will learn to convert  metric units of length , mass, or  capacity .
  ::在此概念中,您将学会转换长度、质量或容量的计量单位。

  播放段落

  Converting Length and Mass in Metric Units
  ::转换计量单位的长度和质量

  播放段落

  This concept combines a couple of different skills. Here you will combine converting metric units of length, mass, and capacity and multiplying decimals using powers of ten.
  ::这个概念结合了几种不同的技能。 在这里, 您将结合转换长度、 质量和容量的计量单位, 并使用十倍的功率乘以小数。

  播放段落

  Converting metric units using powers of ten involves moving the decimal point.
  ::使用十分功率转换计量单位时,需要移动小数点。

  播放段落

  Use this chart as a guide.
  ::使用此图表作为向导 。

  Metri Unit	kilo-	hecto-	deka-	(base unit) meter/gram/liter	deci-	centi-	milli-
  Symbol	k	h	da	m/g/L	d	c	m
  Number	1,000	100	10	1	0.1	0.01	0.001

  

  [Figure 2]

  播放段落

  Here is a conversion problem.
  ::这是一个转换问题。

  $$\begin{array}{r}150cm=\underset{\_}{}mm\end{array}$$

  播放段落

  When you convert a larger unit to a smaller unit, multiply the number by a power of ten. 1  centimeter  is equal to 10  millimeter . You multiply by a power of ten once or  $\begin{array}{r}{10}^1\end{array}$ . Therefore, multiply 150 cm by 10.
  ::当将较大单位转换为较小单位时,乘以10的功率。1厘米等于10毫米。乘以10或10.1的功率。因此,乘以150厘米乘以10。

  $$\begin{array}{r}150cm\times 10=\underset{\_}{}mm\end{array}$$

   

  播放段落

  Move the decimal point one place to the right when multiplying by 10. The decimal point in a whole number is after the number. Add a zero placeholder to 150.
  ::乘以 10 时将小数点 1 移到右侧。整个数字中的小数点在数字之后。将一个零占位符加到 150 。

  $$\begin{array}{r}150cm=1,500mm\end{array}$$

  播放段落

  Let’s look at this one involving capacity.
  ::让我们来看看这个涉及能力的问题。

  $$\begin{array}{r}1,250mL=\underset{\_}{}L\end{array}$$

  播放段落

  When you convert a smaller unit to a larger unit, divide the number by a power of ten. 1,000 milliliters is equal to 1 liter. You divide by a power of ten 3 times or  $\begin{array}{r}{10}^3\end{array}$ . Divide 1250 milliliters by 1,000.
  ::当将较小单位转换为较大单位时,数字除以10的功率。1000毫升等于1升。除以10 3倍或10 3的功率。除以1 250毫升除以1 000。

  $$\begin{array}{r}1,250mL÷1,000=\underset{\_}{}L\end{array}$$

  播放段落

  Move the decimal point three places to the left when dividing by 1,000.
  ::当除以 1 000 时, 将小数点 3 位移到左边 。

  $$\begin{array}{r}1,250milliliters=1.25Liters\end{array}$$

  播放段落

  You can convert any unit of measure as long as you know the conversion equivalents and remember how to use powers of ten to move the decimal point to the left or to the right.
  ::您可以转换任何计量单位,只要知道转换等值,并记住如何使用十分的功率将小数点向左或向右移动。

  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 Caleb’s math problem.
  ::Caleb的数学问题。

  播放段落

  Caleb has to compare  $\begin{array}{r}5.5g\underset{\_}{}4,500mg\end{array}$  complete the math problem.
  ::Caleb必须比较5.5克_4,500米克 才能解决数学问题

  播放段落

  First, convert 5.5 g to mg. You are converting a larger unit to a smaller unit so you will multiply.
  ::首先,将5.5克转换为毫克。您正在将一个更大的单位转换为一个较小的单位,这样您就可以乘以乘法。

  $$\begin{array}{r}5.5g=\underset{\_}{}mg\end{array}$$

  播放段落

  Then, multiply 5.5 by a power of  $\begin{array}{r}{10}^3\end{array}$  or 1,000. Move the decimal point three places to the right.
  ::然后,乘以5.5乘以10 3 或 1 000 的功率。将小数点三移到右边。

  $$\begin{array}{r}\begin{array}{rcl}5.5g\times 1,000& =& \underset{\_}{}mg\\ 5.5g& =& 5,500mg\end{array}\end{array}$$

  播放段落

  Next, substitute 5,500 mg for 5.5 g in the original problem and compare.
  ::其次,以5,500毫克替代原问题5.5克,并进行比较。

  $$\begin{array}{r}5,500mg\underset{\_}{}4,500mg\end{array}$$

   

  $$\begin{array}{r}5,500mg>4,500mg\end{array}$$

  播放段落

  Caleb should answer that 5.5 g is greater than (>) 4,500 mg.
  ::Caleb应回答说,5.5克大于( >)4,500毫克。

  播放段落

  Example 2
  ::例2

  播放段落

  Convert the units of measurement.
  ::转换计量单位。

  $$\begin{array}{r}12,350mL=\underset{\_}{}L\end{array}$$

  播放段落

  First, identify the unit conversion. You are converting a smaller unit to a larger unit so you will divide. You know that a milliliter is one-thousandth of a liter.
  ::首先,识别单位转换。您正在将一个较小的单位转换成一个更大的单位, 这样您就可以分裂。 您知道一毫升是一升的千分之一。

  播放段落

  Then, divide 12,350 by a power of  $\begin{array}{r}{10}^3\end{array}$  or 1,000. Move the decimal point three places to the left.
  ::然后将12 350除以 10 3 或 1 000 的功率。 将小数点 3 移到左边 。

  $$\begin{array}{r}\begin{array}{rcl}12,350mL÷1,000& =& \underset{\_}{}L\\ 12,350mL& =& 12.35L\end{array}\end{array}$$

  播放段落

  12,350 milliliters is equal to 12.35 liters.
  ::12,350毫升等于12.35升。

  播放段落

  Example 3
  ::例3

  播放段落

  Convert the units of measurement.
  ::转换计量单位。

  $$\begin{array}{r}1,340mL=\underset{\_}{}L\end{array}$$

  播放段落

  First, identify the unit conversion. You are converting a smaller unit to a larger unit so you will divide.
  ::首先,指定单位转换。您正在将一个较小的单位转换成一个更大的单位,这样您就可以分割。

  播放段落

  Then, divide 1,340 mL by a power of  $\begin{array}{r}{10}^3\end{array}$  or 1,000. Move the decimal point three places to the left.
  ::然后将1,340毫升除以10,3或1,000的功率。将小数点三移到左边。

  $$\begin{array}{r}\begin{array}{rcl}1,340mL÷1,000& =& \underset{\_}{}L\\ 1,340mL& =& 1.34L\end{array}\end{array}$$

  播放段落

  1,340 milliliters is equal to 1.34 liters.
  ::1,340毫升等于1.34毫升。

  播放段落

  Example 4
  ::例4

  播放段落

  Convert the units of measurement.
  ::转换计量单位。

  $$\begin{array}{r}66g=\underset{\_}{}mg\end{array}$$

  播放段落

  First, identify the unit conversion. You are converting a larger unit to a smaller unit so you will multiply.
  ::首先,识别单位转换。您正在将更大的单位转换成较小的单位,这样您就可以乘以。

  播放段落

  Then, multiply 66 g by a power of  $\begin{array}{r}{10}^3\end{array}$  or 1,000. Move the decimal point three places to the right.
  ::然后,将66克乘以10 3 或 1 000 的功率。将小数点三移到右边。

  $$\begin{array}{r}\begin{array}{rcl}66g\times 1,000& =& \underset{\_}{}mg\\ 66g& =& 66,000mg\end{array}\end{array}$$

  播放段落

  66 grams is equal to 66,000 milligrams.
  ::66克等于66 000毫克。

  播放段落

  Example 5
  ::例5

  播放段落

  Convert the units of measurement.
  ::转换计量单位。

  $$\begin{array}{r}1,123m=\underset{\_}{}km\end{array}$$

  播放段落

  First, identify the unit conversion. You are converting a smaller unit to a larger unit so you will divide.
  ::首先,指定单位转换。您正在将一个较小的单位转换成一个更大的单位,这样您就可以分割。

  播放段落

  Then, divide 1,123 m by a power of  $\begin{array}{r}{10}^3\end{array}$  or 1,000. Move the decimal point three places to the left.
  ::然后将1,123米除以10,3或1,000的功率。将小数点三移到左边。

  $$\begin{array}{r}\begin{array}{rcl}1,123m÷1,000& =& \underset{\_}{}km\\ 1,123m& =& 1.123km\end{array}\end{array}$$

  播放段落

  1,123   is equal to 1.123 kilometers.
  ::1,123公里等于1,123公里。

  播放段落

  Review
  ::回顾

  播放段落

  Convert the units of measurement using powers of ten.
  ::使用10的功率转换测量单位。

  播放段落
  1. 5.6 km = ______ m
     ::5.6公里=_____米
  播放段落
  2. 8900 m = ______ km
     ::8900米 = 千公里
  播放段落
  3. 9230 m = ______ km
     ::9230米 = 千米
  播放段落
  4. 40 cm = ______ mm
     ::40厘米=_____毫米
  播放段落
  5. 5000 mm = ______ cm
     ::5000毫米 = 厘米
  播放段落
  6. 500 cm = ______ m
     ::500厘米=_____米
  播放段落
  7. 7.9 m = ______ cm
     ::7.9米=_____厘米
  播放段落
  8. 99 m = ______ cm
     ::99米=_____厘米
  播放段落
  9. 460 m = ______ cm
     ::460米=____厘米
  播放段落
  10. 34 cm = ______ m
      ::34厘米=_____米
  播放段落
  11. 4.3 km = ______ m
      ::4.3公里=_____米
  播放段落
  12. 760 m = ______ km
      ::760米=公里
  播放段落
  13. 4300 m = ______ km
      ::4300米=_____公里
  播放段落
  14. 5000 g = ______ kg
      ::500 000 g = _____公斤
  播放段落
  15. 560 mL = ______ L
      ::560 毫升= °L
  播放段落
  16. 6210 mL = ______ L
      ::6210毫升=°°L
  播放段落
  17. 8900 mL = ______ L
      ::8900毫升= °L
  播放段落
  18. 7.5 L = ______ mL
      ::7.5 L = mL
  播放段落
  19. 0.5 L = ______ mL
      ::0.5 L = mL

  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