米 <--> 千米

(Video) Converting Measurements

by tecmath

This video by tecmath goes over distance measurements in the metric system. Specifically, we learn how to convert between centimeters and meters.

$\large{\text{Summary}}$

The main metric unit of length is the meter $(\text{m})$. In other words, the meter is the $\textbf{base unit}$ of length. That means a meter is defined as the distance which a beam of light travels in a single second. There are also a few other major units of length we see all the time. The ones we'll talk about here are kilometers $(\text{km})$, centimeters $(\text{cm})$, and millimeters $(\text{mm})$.

$$\begin{array}{|c|} \hline 1{,}000\text{ meters}=1\text{ kilometer}\\ 1\text{ meter}=100\text{ centimeter}\\ 1\text{ meter}=1{,}000\text{ millimeter}\\ \hline \end{array}$$

Among other things, we can conclude:

-A kilometer is bigger than a meter.

-A meter is bigger than a centimeter.

-A meter is bigger than a millimeter.

$\large{\text{An Example}}$

Suppose we want to convert $5\text{ km}$ to $\text{m}$. We can use these conversions by setting up a conversion chart. Start by writing down what we are given: $5\text{ km}$. $$\begin{array}{c|c} 5\text{ km}&\\ \hline & \end{array}$$

We now want to place a conversion to the right of it. We want a conversion factor where $\text{km}$s are on the bottom. That way we can cancel the $\text{km}$ units out, and all that will remain are $\text{cm}$. We know $1\text{ km}$ equals $1000\text{ m}$. $$\begin{array}{c|c|c} 5\text{ km}&1{,}000\text{ m}&\\ \hline &1\text{ km}& \end{array}$$

Next, cancel units. $$\begin{array}{c|c|c} 5\cancel{\text{ km}}&1{,}000\text{ m}&\\ \hline &1\cancel{\text{ km}}& \end{array}$$

$$=\frac{5\times1{,}000}{1}\text{ m}$$ $$=\boxed{5{,}000\text{ m}}$$

If you're interested we can also convert between grams and kilograms, between kilometers and miles, or between feet and meters. The strategy of converting between units remains the same. However, the exact numbers we use will change.

Converting Between Centimeters and Meters

To convert from centimeters to meters, simply divide the number of centimeters by $100$ and change the units to m. The m is an abbreviation for meters.

To convert from meters to centimeters, simply multiply the number of meters by $100$ and change the units to cm. The cm is an abbreviation for centimeters.

As you might expect, these conversions are reversible. If we start with meters, convert to centimeters, and then convert back, we'll get the number we started with. As a result, converting back is a way of checking your work.

Here's another way to think about this. Converting from meters to centimeters means we multiply by $100$. To go back, we divide by $100$. But this is the same thing as multiplying by $\frac{1}{100}$. Why is the fraction $\frac{1}{100}$ so remarkable? Well, it's the multiplicative inverse of $100$.

Step One: Divide the Number of Centimeters by $100$

We want to convert $560\text{ cm}$ to meters. This is done via division by $100$.

$$\dfrac{560}{100} = 5.6$$

Step Two: Change the Units to $\text{m}$

$$560\text{ cm} \rightarrow 5.6 \text{ m}$$

Now, here's another question for some additional practice.

Step One: Multiply the Number of Meters by $100$

We want to convert $2\text{ m}$ to centimeters. This boils down to multiplying $2 \cdot 100$:

$$2 \cdot 100 = 200$$

Step Two: Change the Units to $\text{cm}$

$$2\text{ m} \rightarrow 200\text{ cm}$$

Thus our final answer is $\boxed{200 \text{ cm}}$.

Convert Meters to Kilometers

Meters and kilometers are units used to measure length. There are many other types of units, but these are two of the most common. The other one you'll see a lot is centimeters.

$$1\text{ kilometer (km)} = 1{,}000\text{ meters (m)}\\ 1{,}000\text{ meters (m)}=1\text{ kilometers (km)}$$ $$1{,}000 \text{ m}\times\frac{1 \text{km}}{1{,}000\text{m}}=1\text{ km}$$

Let’s take a look at an example.

Convert $2{,}000\text{ meters}$ to $\text{kilometers}$.

Since we know that $1{,}000\text{ meters}=1\text{ kilometer}$, we can use this information to set up a conversion chart. Start by writing down $2{,}000\text{ meters}$. $$\begin{array}{c|c} 2{,}000\text{ m}&\\ \hline & \end{array}$$ Now we want to convert $\text{meters}$ to $\text{kilometers}$. $$\begin{array}{c|c|c} 2{,}000\text{ m}&1\text{ km}&\\ \hline &1{,}000\text{ m}& \end{array}$$ Next, cancel out the common units. Kilometers appears in both the top row and the bottom row, so we can cancel them out. $$\begin{array}{c|c|c} 2{,}000\cancel{\text{ m}}&1\text{ km}\\ \hline &1{,}000\cancel{\text{ m}} \end{array}$$ $$\begin{array}{c|c|c} 2{,}000&1\text{ km}\\ \hline &1{,}000 \end{array}= \frac{2{,}000\times1}{1{,}000}\text{ km}$$ $$=2 \text{ km}$$ We can also express this conversion chart in the following way: $$\begin{align} 2{,}000 \text{ m} \times \frac{1 \text{ km}}{1{,}000 \text{ m}} &= 2{,}000 \cancel{\text{ m}} \times \frac{1 \text{ km}}{1{,}000 \cancel{\text{ m}}} \\ &= \frac{2{,}000}{1{,}000} \text{ km} \\ &= 2 \text{ km} \\ \end{align}$$

These two methods are nearly the same. There is only one major difference. The first method represents the calculation with a table. On the other hand, the second method uses a bunch of $=$ signs to connect steps.

We are now going to take a look at some of the types of problems you might encounter about converting between meters and kilometers. A typical such problem will involve one or more of these conversions. At times there will be extra steps as well, especially for word problems.

We can solve this problem by setting up a conversion chart. $$\begin{array}{c|c} 15\text{ km}&1{,}000\text{ m}\\ \hline &1\text{ km} \end{array}$$ $$\begin{array}{c|c} 15\cancel{\text{ km}}&1{,}000\text{ m}\\ \hline &1\cancel{\text{ km}} \end{array}=\boxed{15{,}000\text{ m}}$$

Set up a conversion chart for each distance. In order to add distances, they must all be in the same units. While we can use any unit of distance to add the distances together, let's be careful. We're told we want the final answer in meters. That means any distances not in meters, we must convert to meters. Three of the four distances we're given are actually in kilometers:

-Nick's house to campus

-Campus to Nick's friend's house

-Nick's friend's house to Nick's house

Our strategy is as follows: we'll convert all of the distances to meters. Then we will add all of the distances together. That way, our final answer is in the units we want.

$$\begin{array}{c|c} 0.6\text{ km}&1{,}000\text{ m}\\ \hline &1\text{ km} \end{array}$$ $$\begin{array}{c|c} 0.6\cancel{\text{ km}}&1{,}000\text{ m}\\ \hline &1\cancel{\text{ km}} \end{array}=600\text{ m}$$ $$\begin{array}{c|c} 0.2\text{ km}&1{,}000\text{ m}\\ \hline &1\text{ km} \end{array}$$ $$\begin{array}{c|c} 0.2\cancel{\text{ km}}&1{,}000\text{ m}\\ \hline &1\cancel{\text{ km}} \end{array}=200\text{ m}$$ $$\begin{array}{c|c} 0.9\text{ km}&1{,}000\text{ m}\\ \hline &1\text{ km} \end{array}$$ $$\begin{array}{c|c} 0.9\cancel{\text{ km}}&1{,}000\text{ m}\\ \hline &1\cancel{\text{ km}} \end{array}=900\text{ m}$$

Now, add all the distances traveled together. $$600\text{ m} + 1{,}400\text{ m} + 200\text{ m} + 900\text{ m} = \boxed{3{,}100\text{ meters}}$$

NOTE: There is another way to do this problem. We could convert the distance Nick walks around campus to kilometers, and then add all of the distances together. The units of all these distances would still be the same, but they'd be kilometers. That would introduce an extra step at the end: converting back to meters.

No mater which technique you use, you should get the same answer. In fact, it's good to do it both ways. That way you can check your work! With a lot of numbers floating around, that is always a good thing.

Converting Between Meters and Kilometers

To convert from meters to kilometers, simply divide the number of meters by $1{,}000$ and change the units to km.

To convert from kilometers to meters, simply multiply the number of kilometers by $1{,}000$ and change the units to m.

From this we can get a few extra pieces of information. First of all, a meter is smaller than a kilometer. We can fit many meters into the same distance that a kilometer covers.

Next, we have a way of checking our work in these conversion problems. If we divide a quantity in meters by $1000$, we get the same distance in kilometers. Then if we multiply this number by $1000$, we should get the number we started with. If not, you made a mistake somewhere. In some cases it may also be easier to do this by rewriting your numbers in scientific notation.

Step One: Divide the Number of Meters by $1000$

We want to convert $300\text{ m}$ to $\text{kilometers}$. $$\dfrac{300}{1{,}000} = 0.3$$

Step Two: Change the Units to $\text{km}$

$$300\text{ m} \rightarrow 0.3 \text{ km}$$

Step One: Multiply the Number of Kilometers by $1000$

We want to convert $24\text{ km}$ to $\text{meters}$. $$24 \cdot 1{,}000 = 24{,}000$$

Step Two: Change the Units to $\text{m}$

$$24\text{ km} \rightarrow 24{,}000 \text{ m}$$