# Lesson Video: Converting Lengths: Meters and Centimeters Mathematics

In this video, we will learn how to measure length using mixed units, convert between lengths using partitioning, and compare lengths given in meters and centimeters.

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### Video Transcript

Converting Lengths: Meters and Centimeters

In this video, we’re going to learn how to measure length using mixed units, to convert between lengths using partitioning, and also to compare lengths given in meters and centimeters. Which of these two snakes is longer, the one that measures 100 centimeters or the one that measures one meter? Well, this is a trick question to test whether you’re awake. They’re both the same length. One meter is exactly the same length as 100 centimeters, and it’s important that we remember this fact because we’re going to be using it again and again in this video.

This is because we’re going to be learning how to convert measurements so we can write them in three different ways: in centimeters and then, depending on the measurement, either meters or meters and centimeters. We’ll see when we need to use this in a moment. But for now, because we know that one meter is the same as 100 centimeters, we can start to use this to help us convert between the two. This snake is two meters long. How many centimeters long is it? We know that one meter is worth 100 centimeters, and so two meters would be two lots of 100 centimeters or 200 centimeters. It’s quite easy to convert between the two when we’re thinking of whole numbers of meters.

Three meters is 300 centimeters. Four meters is 400 centimeters and so on. And we can even work the other way, changing centimeters into meters. This snake is 600 centimeters long. And what’s the fact that we need to use to help us here? We know 100 centimeters are the same as one meter. So we need to ask ourselves, how many lots of 100 are there in 600? There are six lots of 100 in 600. And if each of these is worth one meter, then we know the snake is six meters long. 600 centimeters equals six meters. They’re just different ways of saying the same length.

So far, we’ve been looking at measurements that are whole numbers of meters. But what about this snake? It’s 228 centimeters long. Because 228 isn’t a multiple of 100, we’re going to need to give the measurement in meters and some centimeters. And to do this, we need to start with 228 and partition it so we take the 100s out. There are two 100s in 228, so we can partition this number into 200 and then the 28 that’s left over. Now because we’ve split up this number or partitioned it so that we could see the 100s, we can convert them. We know that 200 centimeters are exactly the same as two meters, so at least we’ve changed part of our measurement into meters. We can’t change it all though; we’ve still got those 28 centimeters left over. This snake’s length is two meters and 28 centimeters.

You know, we can also convert in the opposite direction. We can start with a measurement in meters and centimeters and then convert it so that we write it just in centimeters. This snake is one meter and 15 centimeters long. Now we can partition this length into a part worth one meter and another part worth 15 centimeters. A part of the length is already in centimeters, so we don’t need to worry about this for now. Let’s just concentrate on the part that isn’t in centimeters. How many centimeters are the same as one meter? 100 centimeters. And we know if we put our two parts back together again — 100 plus another 15 is 115 centimeters. One meter 15 centimeters is the same as 115 centimeters.

Let’s have a go at answering some questions now where we have to convert between meters and centimeters.

Look at the ruler. One meter equals 100 centimeters. How many centimeters are in three meters? Three meters equals what centimeters.

To begin within this question, we’re told to look at the picture of the ruler. So, we better start by doing that. What can we see? Looks a little bit like a number line, doesn’t it? It starts at zero. And we can see each multiple of 10 is labeled: 10, 20, 30, and so on all the way up to 100. Now if we look at the start of the ruler, we can see the letters cm. This shows us the unit of measurement that our ruler shows. cm stands for centimeters. And so when we’re counting 10, 20, 30, and so on, we’re counting in centimeters. This ruler goes from zero to 100 centimeters.

But there’s something else interesting about our ruler. Can you spot it? At the other end of the ruler, there’s an arrow labeled one m. So if we count all the way up to 100 centimeters, it’s the same as one m. Do you know what one m stands for? Of course, we’re told in the fact above the ruler, aren’t we? One meter. One meter is the same as 100 centimeters, and our ruler helps to show this. Now, if one meter is the same as 100 centimeters, we can use this to help answer our question “How many centimeters are in three meters?” Let’s use a bar model to help us.

If we know one meter is the same as 100 centimeters, then two meters must be the same as two lots of 100 centimeters or 200 centimeters. And so to answer our question, three meters will be the same as three lots of 100 centimeters or 300 centimeters. The number of centimeters that are in three meters is 300. Three meters equals 300 centimeters.

Write in centimeters: eight meters and five centimeters.

In this question, we’re given a measurement. Now we might think at first glance that this looks like two measurements because not only can we see a number of meters, but also some centimeters too. But this is one single measurement. It just means slightly more than eight meters, eight meters and five centimeters. Now at the moment, this measurement has been written, as we’ve said already, in meters and also centimeters. But we can convert this measurement so that we write it just in centimeters, which is exactly what this question asks us to do. To help us, we can split up or partition eight meters five centimeters. And we can split it into eight meters and five centimeters.

Now our question asks us to write the whole measurement in centimeters. And at the moment, part of it already is in centimeters, so we can ignore this for a moment. Let’s concentrate on the part that isn’t in centimeters. How can we convert eight meters into centimeters? Is there a fact we can use to help us? We know that one meter is the same as 100 centimeters, and so eight meters must be the same as eight lots of 100 centimeters or 800 centimeters. Now that we’ve converted our number of meters into centimeters, both parts are written in centimeters. So we just need to add the two parts back together again. 800 centimeters plus another five centimeters equals 805 centimeters. We can write eight meters and five centimeters in centimeters as 805 centimeters.

Complete: What centimeters equals four meters and 70 centimeters.

To help us answer this question, we’re shown a part–whole model. Now, normally, if we wanted to find the missing number here, that’s the missing whole, with a part–whole model, we just add the two parts together. But in this particular question, we can’t just add four and 70 to find the answer. Can you see why? In this question, the numbers four and 70 represent two measurements: four meters and 70 centimeters. We can’t just add four and 70 together because they’re different units. If we look at the missing number in our part–whole model, we can see that we’re looking for a number of centimeters. And we can see this in the question, too.

For us to write this whole measurement in centimeters, we’re going to need to change those four meters into centimeters, aren’t we? Is there a fact We know that can help us? We know that one meter is the same as 100 centimeters, and so four meters is the same as four lots of 100 centimeters or 400 centimeters. Should we write this on our part–whole model to help us? Instead of four meters, let’s write 400 centimeters instead. They’re exactly the same. Now we can add our two parts together. 400 plus another 70 equals 470. And so we know that four meters and 70 centimeters is exactly the same distance as 470 centimeters. Our missing number is 470.

A red car is 411 centimeters long, a blue car is 500 centimeters long, and a black car is three meters long. Which car is the longest?

In this question, we need to compare the lengths of three cars. Let’s have a look at the measurements: 411 centimeters, 500 centimeters, three meters. What do you notice about these measurements? They’re not all measured in the same unit, are they? We’ve got two measurements in centimeters and one in meters. This means that we can’t just compare the numbers and look at them and see which one is largest.

Instead, we’re going to have to convert the measurements so that they’re all in the same unit of measurement. Should we change them all into meters or centimeters? It doesn’t matter which we choose, but with questions like this, we need to use a bit of common sense. Two of our measurements are already in centimeters, so the quickest thing to do would be to change the one that’s in meters into centimeters, and then they’re all in centimeters. We know that one meter is the same as 100 centimeters, and so three meters is the same as three lots of 100 centimeters or 300 centimeters.

Now that all our measurements are in centimeters, we could show them all on a number line. A red car is 411 centimeters. That’s about here on the number line. A blue car is 500 centimeters long. And although we said a black car was three meters, we worked out this was exactly the same as 300 centimeters. We made sure all our measurements were in the same unit so that we could then compare them. The longest of the three cars is the blue car.

So what have we learned in this video? We’ve learned how to measure length using mixed units, convert between lengths using partitioning, and compare lengths given in meters and centimeters.