Question Video: Arranging Areas in Descending Order by Converting Their Units Mathematics

Order the areas from greatest to least: 10 dm², 2500 mm², 150 cm².


Video Transcript

Order the areas from greatest to least: 10 square decimeters, 2500 square millimeters, and 150 square centimeters.

So we’re working with areas. And we know this because the units are squared. And unfortunately, each of these units are different. We have square decimeters, square millimeters, and square centimeters. So if we want to arrange these areas, we need to convert them to be all in the same square unit. We can choose which unit we would like to convert to.

Let’s go ahead and choose square millimeters. So let’s begin first with converting 10 square decimeters to square millimeters. In one square decimeter, there are 10000 square millimeters. So we need to take our 10 from the square decimeters and multiply it by 10000. This means there are 100000 square millimeters in 10 square decimeters.

So after we’re done with converting, we will rewrite each of these areas again in terms of our square millimeters. But first, let’s finish converting all of these areas.

Now, our second area is 2500 square millimeters. We don’t need to convert this because it’s already in square millimeters. Now, our third area is 150 square centimeters. In one square centimeter, there are 100 square millimeters. So we need to take our 150 square centimeters and multiply it by 100. This means there are 15000 square millimeters in 150 square centimeters.

So now, we are truly able to compare these numbers because each area is in terms of square millimeters. And we’re supposed to order these areas from greatest to least. So we’re looking at 100000, 2500, and 15000.

The largest would be the 100000 and then the next largest would be 15000 and then the smallest would be 2500. However, when we go to list these, we need to put them back in their original form.

So our largest area was 100000 square millimeters and that was originally 10 square decimeters. Next would be the 15000 Square millimeters and that was originally 150 square centimeters. And lastly, our smallest, which we did not have to convert, was 2500 square millimeters.

So the areas from greatest to least would be 10 square decimeters, 150 square centimeters, and 2500 square millimeters.

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