Section: 公制 | 2.19公制 | The Way To Learn

Section outline

Jonathan is visiting his cousin Katie who lives in Australia. He is helping her to make pies to sell at a bake sale at her school. Katie has a 2 kilogram bag of flour. Jonathan reads the recipe for the pie dough and it says they will need 315 grams of flour for each pie. They were hoping to make 5 pies. How can Jonathan figure out if they will have enough flour to do this?
::乔纳森正在拜访住在澳洲的表弟凯蒂。他正在帮助她做派,以便在她的学校的面包销售。凯蒂有一袋2公斤的面粉。乔纳森读了派面粉的食谱,并说每个派都需要315克的面粉。他们本来想做5个馅饼。乔纳森怎么知道他们是否有足够的面粉来做这个?

In this concept, you will learn to convert between common metric units of measure.
::在这个概念中,你们将学会在通用指标计量单位之间转换。

Converting Between Common Metric Units of Measure
::通用计量单位之间的转换

The metric system is the system of measurement primarily used in science and in countries outside of the United States. The metric system includes units of length (meters), mass (grams), and capacity (liters).
::衡量系统是主要用于科学和美国以外国家的测量系统,包括长度(米)、质量(克)和能力(升)的单位。

The base unit of length is the meter . The table below shows some of the most common metric units of length and how they are related to the meter.
::基长单位为米,下表显示一些最常用的长度指标单位及其与表的关系。

Metric Units of Length
$\begin{aligned} millimeter (mm) = 0.001 meter \end{aligned}$
$\begin{aligned} centimeter (cm) = 0.01 meter \end{aligned}$
$\begin{aligned} meter (m) = 1 meter \end{aligned}$
$\begin{aligned} kilometer (km) = 1000 meters \end{aligned}$

Notice that all metric units of length include “meter”. The prefix of each unit of measurement indicates how that unit relates to the meter.
::注意所有计量单位的长度都包括“米”,每个计量单位的序号表明该单位与计量单位的关系。

“milli” means one thousandth. There are 1000 millimeters in 1 meter.
::" 毫升 " 是指千分之一。 1米内有1000毫米。

“centi” means one hundredth. There are 100 in 1 meter.
::“centi”是指第一百分之一,每1米有100分。

“kilo” means one thousand. There are 1000 in 1 kilometer .
::“Kilo”是指千人,每1公里有1000人。

The same prefixes are used throughout the metric system. The base unit of mass is the gram. The base unit of capacity is the liter. The tables below show some of the most common metric units of mass and capacity and how they are related to the gram and the liter.
::测量系统使用相同的前缀,基质量单位为克,基容量单位为公升,下表显示一些最常见的质量和容量计量单位,以及它们与克和公升的关系。

Metric Units of Mass
$\begin{aligned} milligram (mg) = 0.001 gram \end{aligned}$
$\begin{aligned} centigram (cg) = 0.01 gram \end{aligned}$
$\begin{aligned} gram (g) = 1 gram \end{aligned}$
$\begin{aligned} kilogram (kg) = 1000 grams \end{aligned}$

Metric Units of Capacity
$\begin{aligned} milliliter (mL) = 0.001 liter \end{aligned}$
$\begin{aligned} centiliter (cL) = 0.01 liter \end{aligned}$
$\begin{aligned} liter (L) = 1 liter \end{aligned}$
$\begin{aligned} kiloliter (kL) = 1000 liters \end{aligned}$

Remembering the metric prefixes can help you to remember how the different units of measurement are related.
::记住度量前缀可以帮助您记住不同计量单位是如何关联的。

Notice that the relationship between the units of measurement are all based on powers of 10. This is because 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.
::注意测量单位之间的关系都以10的功率为基础, 这是因为测量系统以10的功率为基础, 就像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, 您需要做的就是移动小数点。

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。

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。

Here is an example.
::举一个例子。

$\begin{aligned} 340 centiliters = \underline{} liters \end{aligned}$
::340厘米 = _升

First, notice that you are converting centiliters to liters. The prefix “centi” means one hundredth. That means 100 centiliters make up 1 liter.
::首先,请注意您正在将立方厘米转换为升。前缀“ centi” 表示百分之一。这意味着 100 立方厘米等于 1 升。

Next, notice you are going from a smaller unit to a larger unit. This means to determine how many liters you have, you will need to divide 340 by 100. This is the same as moving the decimal point 2 spaces to the left.
::接下来,通知您正在从一个较小的单位转到一个更大的单位。这意味着要确定您有多少升, 您需要将340除以100。这与将小数点 2 空格向左移动相同。

\begin{aligned} \frac{340}{100} = 3.4 \end{aligned}

The answer is $\begin{aligned} 340 centiliters = 3.4 liters \end{aligned}$ .
::答案是340厘米=3.4升。

Here is another example.
::下面是另一个例子。

$\begin{aligned} 5 meters = \underline{} millimeters \end{aligned}$
::5米=_毫米

First, notice that you are converting meters to millimeters. The prefix “milli” means one thousandth. That means 1000 millimeters make up 1 meter.
::首先,请注意您正在将米转换为毫米。前缀“ 毫升” 是指千分之一。这意味着 1000 毫米等于 1 公尺。

Next, notice you are going from a larger unit to a smaller unit. This means to determine how many millimeters you have, you will need to multiply 5 by 1000. This is the same as moving the decimal point 3 spaces to the right.
::下一步,通知您正在从一个更大的单位转到一个较小的单位。这意味着要确定您有多少毫米, 您需要乘以 5 乘以 1000 。这与将小数点 3 空格移到右边相同。

\begin{aligned} 5 \times 1000 = 5000 \end{aligned}

The answer is $\begin{aligned} 5 meters = 5000 millimeters \end{aligned}$ .
::答案是5米 = 5000毫米

Here is one more example.
::这里还有一个例子。

$\begin{aligned} 15 milligrams = \underline{} centigrams \end{aligned}$

::15毫克 = _ 厘米

First, notice that you are converting milligrams to centigrams. The prefix “milli” means one thousandth which means there are 1000 milligrams in one gram. The prefix “centi” means one hundredth which means there are 100 centigrams in one gram. One way to complete this problem is to first convert milligrams to grams, and then convert grams to centigrams. While doing it this way takes two steps, it allows you to practice using the prefixes.
::首先,请注意您正在将毫克转换成厘米。前缀“ mill”的意思是千分之一千,这意味着在一公克中存在1000毫克。前缀“centi”的意思是百分之一百,这意味着在一公克中存在100厘米。解决问题的方法之一是首先将毫克转换成克,然后将克转换成厘米。在这样做时,需要两步,它允许您使用前缀练习。

Convert milligrams to grams. You are going from a smaller unit to a larger unit. To determine how many grams you have, you will need to divide 15 by 1000. This is the same as moving the decimal point 3 spaces to the left.
::将毫克转换成克。您正在从一个较小的单位转换成一个更大的单位。要确定您有多少克,您需要将15克除以1000。这与将小数点3空格向左移动相同。

\begin{aligned} \begin{array}{rcl} \frac{15}{1000} & = & 0.015 \\ 15 milligrams & = & 0.015 grams \end{array} \end{aligned}

Now, convert grams to centigrams. You are going from a larger unit to a smaller unit. To determine how many centigrams you have, you will need to multiply 0.015 by 100. This is the same as moving the decimal point 2 spaces to the right.
::现在, 将克转换成厘米。您正在从一个更大的单位转换成一个较小的单位。要确定您有多少厘米, 您需要乘以 0.015 乘以 100 。这与将小数点 2 空格移到右边相同。

\begin{aligned} 0.015 \times 100 = 1.5 \end{aligned}

The answer is $\begin{aligned} 15 milligrams = 1.5 centigrams \end{aligned}$ .
::答案是15毫克=1.5厘米。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jonathan, who is helping Katie make pies.
::早些时候,你被问及乔纳森的问题他正在帮助凯蒂做派

They have a 2 kilogram bag of flour. They are hoping to make 5 pies and they need 315 grams of flour for each pie crust. Jonathan wants to see if they will have enough flour to do this.
::他们有2公斤的面粉包。他们希望做5个馅饼,每个饼壳需要315克面粉。乔纳森想知道他们是否有足够的面粉做这个。

First, Jonathan should figure out how much flour they need total. They need 315 grams of flour for each pie and they want to make 5 pies. To figure out the total amount of flour they need he should multiply.
::首先,乔纳森应该弄清楚他们需要多少面粉。他们需要315克面粉来做每个馅饼,他们想做5个馅饼。要想弄清楚他们需要的面粉总量,他应该增加。

\begin{aligned} 315 \times 5 = 1575 \end{aligned}

They need 1575 grams of flour to make 5 pies.
::他们需要1,575克面粉做5个派

Now, Jonathan should convert 1575 grams to kilograms. The prefix “kilo” means one thousand. That means 1000 grams make up 1 kilogram.
::现在,乔纳森应该把1,575克转换成公斤。前缀“kilo”的意思是千。这意味着1000克等于1公斤。

Next, Jonathan should notice he is going from a smaller unit to a larger unit. This means to determine how many kilograms he has, he will need to divide 1575 by 1000. This is the same as moving the decimal point 3 spaces to the left.
::接下来,乔纳森应该注意到他正在从一个较小的单位到一个更大的单位。这意味着要确定他有多少公斤, 他需要将1575除以1000。这与将小数点3空格向左移动相同。

\begin{aligned} \frac{1575}{1000} = 1.575 \end{aligned}

They need 1.575 kilograms of flour to make 5 pies.
::他们需要1,575公斤面粉才能做5个馅饼。

The answer is because they need 1.575 kilograms of flour and they have 2 kilograms of flour, they have enough flour to make their pies.
::答案是因为他们需要1,575公斤面粉,他们有两公斤面粉,有足够的面粉做派。

Example 2
::例2

Convert 25,000 centimeters to kilometers.
::转换25000厘米到公里

First, notice that you are converting centimeters to kilometers. The prefix “centi” means one hundredth which means there are 100 centimeters in one meter. The prefix “kilo” means one thousand which means there are 1000 meters in one kilometer.
::首先,请注意您正在将厘米转换为公里。前缀“ centi” 表示百分之一, 这意味着一米内有100厘米。前缀“ kilo” 表示千分之一公里内有1000米。

To complete this problem, you will first convert centimeters to meters, and then convert meters to kilometers.
::为了解决这个问题,你首先将厘米转换成米,然后将米转换成公里。

Convert centimeters to meters. You are going from a smaller unit to a larger unit. To determine how many meters you have, you will need to divide 25,000 by 100. This is the same as moving the decimal point 2 spaces to the left.
::将厘米转换为米。您正在从一个较小的单位转换为更大的单位。要确定您有多少米, 您需要将 25,000 乘以 100 。这与将小数点 2 空格向左移动相同。

\begin{aligned} \begin{array}{rcl} \frac{25000}{100} & = & 250 \\ 25, 000 centimeters & = & 250 meters \end{array} \end{aligned}

Now, convert meters to kilometers. You are going from a smaller unit to a larger unit. To determine how many kilometers you have, you will need to divide 250 by 1000. This is the same as moving the decimal point 3 spaces to the left.
::现在, 将米转换为公里。您正在从一个较小的单位转换为一个更大的单位。要确定您有多少公里, 您需要将250 乘 1 000 。这与将小数点3 空格向左移动相同。

\begin{aligned} \begin{array}{rcl} \frac{250}{1000} & = & 0.25 \\ 250 meters & = & 0.25 kilometers \end{array} \end{aligned}

The answer is $\begin{aligned} 25, 000 centimeters = 0.25 kilometers \end{aligned}$ .
::答案是25,000厘米 =0.25公里

Example 3
::例3

$\begin{aligned} 87 centigrams = \underline{} grams \end{aligned}$
::87厘米 = _克

First, notice that you are converting centigrams to grams. The prefix “centi” means one hundredth. That means 100 centigrams make up 1 gram.
::首先,请注意您正在将厘米克转换为克。前缀“ centi” 表示百分之一。这意味着 100 厘米等于 1 公克。

Next, notice you are going from a smaller unit to a larger unit. This means to determine how many grams you have, you will need to divide 87 by 100. This is the same as moving the decimal point 2 spaces to the left.
::接下来,通知您正在从一个较小的单位转到一个更大的单位。这意味着要确定您有多少克, 您需要将87除以100。这与将小数点 2 空格向左移动相同。

\begin{aligned} \frac{87}{100} = 0.87 \end{aligned}

The answer is $\begin{aligned} 87 centigrams = 0.87 grams \end{aligned}$ .
::答案是87厘米=0.87克。

Example 4
::例4

$\begin{aligned} 2.4 meters = \underline{} millimeters \end{aligned}$
::2.4米=_毫米

Next, notice you are going from a larger unit to a smaller unit. This means to determine how many millimeters you have, you will need to multiply 2.4 by 1000. This is the same as moving the decimal point 3 spaces to the right.
::下一步,通知您正在从一个更大的单位转到一个较小的单位。这意味着要确定您有多少毫米, 您需要乘以2.4乘以1000。这与将小数点3空格向右移动相同。

\begin{aligned} 2.4 \times 1000 = 2400 \end{aligned}

The answer is $\begin{aligned} 2.4 meters = 2400 millimeters \end{aligned}$ .
::答案是2.4米=24毫米。

Example 5
::例5

$\begin{aligned} 15 kilometers = \underline{} meters \end{aligned}$
::15公里=_米

First, notice that you are converting kilometers to meters. The prefix “kilo” means one thousand. That means 1000 meters make up 1 kilometer.
::首先,请注意您正在将公里转换为米。前缀“ kilo” 是指千。这意味着1000米等于1公里。

Next, notice you are going from a larger unit to a smaller unit. This means to determine how many meters you have, you will need to multiply 15 by 1000. This is the same as moving the decimal point 3 spaces to the right.
::下一步,通知您正在从一个更大的单位转到一个较小的单位。这意味着要确定您有多少米, 您需要乘以 15 乘以 1000 。这与将小数点 3 空格移到右边相同。

\begin{aligned} 15 \times 1000 = 15, 000 \end{aligned}

The answer is $\begin{aligned} 15 kilometers = 15, 000 meters \end{aligned}$ .
::答案是15公里=15,000米

Review
::回顾

Fill in the blanks with the equivalent measurement.
::填空时填充等量测量。

$\begin{aligned} 1, 000 centimeters = \underline{} meters \end{aligned}$
::1 000厘米=_米

$\begin{aligned} 10 kiloliters = \underline{} centiliters \end{aligned}$
::10千立升=_厘米

$\begin{aligned} 1, 000 milligrams = \underline{} centigrams \end{aligned}$
::1,000毫克 = _ 厘米

$\begin{aligned} 100 milliliters = \underline{} centiliters \end{aligned}$
::100毫升= _ 厘米

$\begin{aligned} 200 milligrams = \underline{} kilograms \end{aligned}$
::200毫克=_千克

$\begin{aligned} 20 centimeters = \underline{} meters \end{aligned}$
::20厘米=_米

$\begin{aligned} 2 liters = \underline{} kiloliters \end{aligned}$
::2升=_千升

$\begin{aligned} 2, 000 centigrams = \underline{} kilograms \end{aligned}$
::2 000厘米=_公斤

Fill in the blanks with the equivalent measurements for 180.76 centimeters.
::填满空白,对180.76厘米进行等量测量。

$\begin{aligned} \underline{} meters \end{aligned}$
::_米

$\begin{aligned} \underline{} millimeters \end{aligned}$
::_毫米

$\begin{aligned} \underline{} kilometers \end{aligned}$
::_公里

Fill in the blanks with the equivalent measurements for 0.4909 kiloliters.
::填充空格,对0.4909千立升进行等量测量。

$\begin{aligned} \underline{} liters \end{aligned}$
::升数(_升)

$\begin{aligned} \underline{} centiliters \end{aligned}$
::_ 厘米

$\begin{aligned} \underline{} milliliters \end{aligned}$
::_ 毫升

How many liters in one kiloliter?
::一个千升里程有多少升?

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。

Section outline

Converting Between Common Metric Units of Measure ::通用计量单位之间的转换

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