Measuring lengths in different units

So I have the same green rectangle up here and down here, and what I want to do is measure its width. But we're going to measure its width in two different ways. Up here, we're going to measure its width in terms of how many of these paper clips wide the rectangle is, and down here, we're going to measure its width in terms of how many centimeters wide this rectangle is.

So let's start on top. Pause the video. How many paper clips wide is this rectangle?

All right, now let's do this together. We can see that the rectangle starts right over here and it ends right over here on the right if we're thinking about its width. And so we have one, two, three, four, five, six, seven, eight, nine, ten paper clips. So this rectangle is, we could say, ten paper clips wide.

Now, if we want to measure it in terms of centimeters, we would do the same thing, but we would use this ruler. Let me do this in a different color. So the left edge is there, the right edge is right over there, and it looks like this rectangle is also one, two, three, four, five centimeters wide, five centimeters wide.

So notice: the same rectangle has the same width. It's ten paper clips wide and it's five centimeters wide. So its width is more paper clips than centimeters, is one way to think about it.

Now, based on that, what is a larger unit of measurement: the paper clip, at least these paper clips, or the centimeter? Pause the video. Think about that.

Well, you might just see it naturally where, if you just look at a centimeter right over here, it looks wider than a paper clip. But you could also tell that by looking at the measurement. We needed more paper clips to cover the width of this rectangle than we needed centimeters. And so, because we needed more paper clips, that means that this is a smaller unit of measure.

Because we needed more of them, so this is a smaller unit of measure. Or maybe actually I should make the arrow point right over here. The paper clip is the smaller unit of measure, and then the centimeter is the larger unit of measure. We needed fewer centimeters to make up the width of the rectangle than paper clips. So the centimeter is larger, and you can see that visual if you just look at that width compared to that width. It's clear that a centimeter is wider than this paper clip.