Section: 公制度量的比较 | 2.22公制度量的比较

Section outline

Sarah and Laura both just joined the track team at school. So far they are really enjoying it! They are training for a meet next weekend where they will both be competing in long distance running events. Their coach told Sarah that she will be running in the 5000 m event. Laura will be running the 10k. At first, Sarah and Laura aren’t sure what this means. How can they figure out who will be running the longer distance?
::Sarah 和 Laura 都刚刚加入了学校的轨道团队。目前他们真的非常享受! 他们正在训练下周末的会面, 他们将在长途赛事中竞争。他们的教练告诉Sarah她将在5000米的活动中竞选。 Laura将运行10公里。起初, Sarah 和 Laura 不知道这意味着什么。他们怎么才能知道谁将跑得更远呢?

In this concept, you will learn how to compare given metric units of measure.
::在这个概念中,你将学会如何比较特定计量单位。

Comparing Metric Measurements
::比较计量

Sometimes you will want to compare different metric measurements. Knowing how to convert between metric units of measure and how to compare decimal numbers makes this possible.
::有时候,你会想要比较不同的计量尺度。知道如何在计量单位之间转换和如何比较小数数字,就能够做到这一点。

You can compare two metric measurements in the same way that you compare decimal numbers. You just have to make sure that your measurements are in the same unit first.
::您可以以比较小数数字的同样方式比较两个衡量尺度。您只需要先确保您的测量尺度在同一单位内。

Here are the steps for comparing metric measurements.
::以下是比较衡量尺度的步骤。

If necessary, convert one of the measurements so that both measurements are in the same unit.
::如有必要,转换一个测量数据,使两个测量数据都在同一单位内。

Working from left to right, compare digits that have the same place value. Starting with the digit on the left and moving right, whichever number first has a larger digit is the larger number overall.
::从左到右工作,比较具有相同位数的位数。从左边的数字开始,向右移动,以数字首位的位数较大者为总数字较大者。

You can use an inequality symbol to show how two metric measurements are related.
::您可以使用不平等符号来显示两种衡量尺度之间的关系。

Here is an example.
::举一个例子。

$\begin{aligned} 4.56 g \underline{} 456 m g \end{aligned}$
::4.56克 _ 456克

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 4.56 g to mg.
::首先,您希望两种测量都在同一单位中。您转换哪个单位并不重要。让我们将4.56克转换为毫克。

Now, 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. Because there are 1000 milligrams in a gram, you will need to move the decimal point 3 to the right.
::现在请注意, 您正在从一个更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, 并将小数点移到右边。因为一克中有1000毫克, 您需要将小数点 3 移到右边。

$\begin{aligned} \begin{array}{rcl} 4.56 \times 1000 & = & 4560 \\ 4.56 g & = & 4560 m g \end{array} \end{aligned}$

Next, rewrite your problem with both measurements in the same unit.
::接下来,重写你的问题在同一单位的两次测量。

$\begin{aligned} 4560 m g \underline{} 456 m g \end{aligned}$

Now, compare the two numbers. 4560 has a digit in the thousands place while 456 does not. 4560 is the bigger number. This means 4560 milligrams is more than 456 milligrams, so 4.56 grams is more than 456 milligrams.
::现在,比较这两个数字。 4560在千个地方有一个数字, 而456没有。 4560是最大的数字。这意味着 4560毫克的4560毫克超过456毫克, 所以4.56克超过456毫克。

The answer is $\begin{aligned} 4.56 g > 456 m g \end{aligned}$ .
::答案是4.56克 > 456克。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Sarah and Laura's upcoming track meet.
::早些时候,你遇到了一个问题关于莎拉和劳拉的即将到来的赛道见面。

Sarah will be running the 5000 m while Laura will be running the 10K. They are wondering who will have to run the longer distance.
::莎拉将运行5000米而劳拉将运行10K。他们想知道谁将不得不运行更长的距离。

First, Sarah and Laura need to know that 10K means 10 kilometers. With running races, the letter “K” is often used to mean kilometer . So they are comparing 5000 with 10 kilometers.
::首先,Sarah和Laura需要知道,10K代表10公里。在赛跑中,字母“K”通常用千米来表示。所以他们把5000和10公里作比较。

$\begin{aligned} 5000 m \underline{} 10 k m \end{aligned}$
::5000米 _ 10千米

Now, the girls will need both measurements to be in the same unit. They can convert 5000 meters to kilometers. Because there are 1000 meters in a kilometer, they will need to divide and move the decimal point 3 to the left.
::现在,女孩需要两种测量结果才能在同一单位内。她们可以转换5000米到千米。因为每公里有1000米,她们需要将小数点3分到左边。

$\begin{aligned} \begin{array}{rcl} \frac{5000}{1000} & = & 5 \\ 5000 m & = & 5 k m \end{array} \end{aligned}$

Next, they can rewrite the problem with both measurements in the same unit.
::其次,他们可以重写两个测量器在同一单元中的问题。

$\begin{aligned} 5 k m \underline{} 10 k m \end{aligned}$

Now, they can compare the two numbers. 5 is less than 10. This means 10 kilometers is more than 5 kilometers, so 10 kilometers is more than 5000 meters.
::现在,他们可以比较这两个数字。 5小于10, 这意味着10公里超过5公里, 10公里超过5000米。

The answer is the 10K that Laura will be running is longer than the 5000 m that Sarah will be running.
::答案是劳拉将运行的10K 比莎拉运行的5000米还要长

Example 2
::例2

$\begin{aligned} 743 k m \underline{} 74, 300, 000 m m \end{aligned}$
::74,300,000米 743公里-74,300,000米

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 74,300,000 mm to km.
::首先,您希望两种测量都在同一单位内。您转换哪个单位并不重要。让我们将74,300,000毫米转换为千米。

Now, 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. Because there are 1,000,000 millimeters in a kilometer (1,000 millimeters in a meter and 1,000 meters in a kilometer means $\begin{aligned} 1, 000 \times 1, 000 = 1, 000, 000 millimeters \end{aligned}$ in a kilometer), you will need to move the decimal point 6 to the left.
::现在请注意, 您正在从一个较小的单位向一个更大的单位前进。这意味着您需要将小数点分隔, 并将小数点向左移动。因为每公里有1,000,000毫米( 每公里有1,000毫米, 每公里有1,000米, 每公里有1,000米) 意味着每公里 1,000 × 1, 000 = 1, 000, 000 毫米), 您需要将小数点 6 向左移动。

$\begin{aligned} \begin{array}{rcl} \frac{74, 300, 000}{1, 000, 000} & = & 74.3 \\ 74, 300, 000 m m & = & 74.3 k m \end{array} \end{aligned}$

Next, rewrite your problem with both measurements in the same unit.
::接下来,重写你的问题在同一单位的两次测量。

$\begin{aligned} 743 k m \underline{} 74.3 k m \end{aligned}$

Now, compare the two numbers. 743 km has a digit in the hundreds place while 74.3 does not. 743 is the bigger number. This means 743 kilometers is more than 74.3 kilometers, so 743 kilometers is more than 74,300,000 millimeters.
::现在,比较这两个数字。743公里在数百个地方有一个数字,而74.3公里没有。743公里是最大的数字。这意味着743公里超过74.3公里,因此743公里超过74 300 000毫米。

The answer is $\begin{aligned} 743 k m > 74, 300, 000 m m \end{aligned}$ .
::答案是743公里 > 74, 300, 000米。

Example 3
::例3

$\begin{aligned} 45 c m \underline{} 500 m m \end{aligned}$
::45厘米-500米

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 500 mm to cm.
::首先,您希望两种测量都在同一单位内。您转换哪个单位并不重要。让我们将500毫米转换为 cm 。

Now, 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. Because there are 10 millimeters in a centimeter , you will need to move the decimal point 1 to the left.
::现在请注意, 您正在从一个较小的单位转到一个更大的单位。这意味着您需要将小数点向左分隔和移动。因为一厘米内有 10 毫米, 您需要将小数点 1 向左移动。

$\begin{aligned} \begin{array}{rcl} \frac{500}{10} & = & 50 \\ 500 m m & = & 50 c m \end{array} \end{aligned}$

Next, rewrite your problem with both measurements in the same unit.
::接下来,重写你的问题在同一单位的两次测量。

$\begin{aligned} 45 c m \underline{} 50 c m \end{aligned}$

Now, compare the two numbers. Both numbers start with a digit in the tens place. 5 is greater than 4. This means 45 is less than 50 centimeters, so 45 centimeters is less than 500 millimeters.
::现在,比较这两个数字。两个数字以十位数开始,五位数大于四位数,这意味着45厘米小于50厘米,45厘米小于500毫米。

The answer is $\begin{aligned} 45 c m < 500 m m \end{aligned}$ .
::答案是45厘米 < 500米。

Example 4
::例4

$\begin{aligned} 2 k m \underline{} 400 m \end{aligned}$
::2千米 _ 400米

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 400 m to km.
::首先,您希望两种测量都在同一单位内。您转换哪个单位并不重要。让我们将400米转换为千米。

Now, 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. Because there are 1000 meters in a kilometer, you will need to move the decimal point 3 to the left.
::现在请注意, 您正在从一个较小的单位转到一个更大的单位。这意味着您需要将小数点向左分隔和移动。因为一公里内有1000米, 您需要将小数点 3 向左移动。

$\begin{aligned} \begin{array}{rcl} \frac{400}{1000} & = & 0.4 \\ 400 m & = & 0.4 k m \end{array} \end{aligned}$

Next, rewrite your problem with both measurements in the same unit.
::接下来,重写你的问题在同一单位的两次测量。

$\begin{aligned} 2 k m \underline{} 0.4 k m \end{aligned}$

Now, compare the two numbers. 2 is greater than 0.4. This means 2 kilometers is greater than 0.4 kilometers, so 2 kilometers is greater than 400 meters.
::现在,比较这两个数字。 2 大于 0. 4。这意味着 2 公里大于 0. 4 公里, 2 公里大于 400 米。

The answer is $\begin{aligned} 2 k m > 400 m \end{aligned}$ .
::答案是2千米 > 400米。

Example 5
::例5

$\begin{aligned} 6 L \underline{} 60, 000 m L \end{aligned}$
::6 L_ 60,000 毫升

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 60,000 mL to L.
::首先,您希望两种测量都在同一单位内。您转换哪个单位并不重要。让我们将 6万毫升转换为 L 。

Now, 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. Because there are 1000 milliliters in a liter, you will need to move the decimal point 3 to the left.
::现在请注意, 您正在从一个较小的单位转到一个更大的单位。这意味着您需要将小数点除以并移动到左边。因为一升中有1000毫升, 您需要将小数点 3 移到左边。

$\begin{aligned} \begin{array}{rcl} \frac{60, 000}{1000} & = & 60 \\ 60, 000 m L & = & 60 L \end{array} \end{aligned}$

Next, rewrite your problem with both measurements in the same unit.
::接下来,重写你的问题在同一单位的两次测量。

$\begin{aligned} 6 L \underline{} 60 L \end{aligned}$

Now, compare the two numbers. 60 is greater than 6. This means 6 liters is less than 60 liters, so 6 liters is less than 60,000 milliliters.
::现在,比较这两个数字。 60 大于 6, 这意味着 6 升不到 60 升, 所以 6 升不到 60 毫升。

The answer is $\begin{aligned} 6 L < 60, 000 m L \end{aligned}$ .
::答案是6 L < 60,000 m L。

Review
::回顾

Compare or order the following measurements. Write <, >, or = for each blank.
::比较或排序以下测量。为每个空白写入 < 、 > 或 = 。

$\begin{aligned} 14 k m \underline{} 56 m \end{aligned}$
::14千米_ 56米

$\begin{aligned} 1.23 m \underline{} 123 k m \end{aligned}$
::1.23米 _ 123公里

$\begin{aligned} 3.4 k m \underline{} 340 m \end{aligned}$
::3.4千米 _ 340米

$\begin{aligned} 18 g \underline{} 0.18 k g \end{aligned}$
::18克 _0.18千克克克

$\begin{aligned} 27 m \underline{} 2700 k m \end{aligned}$
::27米-2700公里

$\begin{aligned} 14 l \underline{} 2100 m l \end{aligned}$
::14 l_2100米l

$\begin{aligned} 5 g \underline{} 0.0005 k g \end{aligned}$
::5克_0.0005千克克

$\begin{aligned} 18 m m \underline{} 0.18 c m \end{aligned}$
::18米_0.18厘米

$\begin{aligned} 2.3 k m \underline{} 2700 m \end{aligned}$
::2.3公里千米-2700米

$\begin{aligned} 3.48 c l \underline{} 0.348 l \end{aligned}$
::3.48 c l _ 0.348 l

$\begin{aligned} 57.21 k g \underline{} 572, 100 c g \end{aligned}$
::57.21千克_ 572克,100克

$\begin{aligned} 91.17 m m \underline{} 0.09117 m \end{aligned}$
::91.17米 _ 0.09117米

$\begin{aligned} 4.4 c l \underline{} 0.44 m l \end{aligned}$
::4.4 c l _ 044毫升

Order the following measurements from least to greatest: 79,282 kg, 7,838,200 cg, 7,938,200 mg, 79,382 g.
::将以下测量从最小到最大顺序排列:79 282公斤、7 838 200克、7 938 200毫克、79 382克。

Order the following measurements from least to greatest: 2,261,000 cl, 21,061 l, 21.06 kl, 21,161,000 ml.
::将以下测量从最小到最大顺序排列:2,261,000 克,21,061升,21,06 kl,21,161,000 ml。

Review (Answers)
::回顾(答复)

Section outline

Comparing Metric Measurements ::比较计量

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)

Comparing Metric Measurements
::比较计量

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)