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Converting Units

Converting Units

Author: Colleen Atakpu

This lesson demonstrates how to use conversion factors to convert units, including square and cubic units.

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Today we're going to talk about converting units. Unit conversion allows us to express the same measurement using different units. So for example, I could have 8 ounces, or I could say half a pound. You could have 30 minutes or half of an hour. We can use unit conversion for any type of measurement including length, time, area, volume, weight, or rates. So let's look at two examples that require one conversion factor. And we're going to start with an example that we already know the answer to. We already know that 30 minutes is equal to 0.5, or half of an hour. But let's use conversion factors to see why that is.

So when you set up unit conversion, you're going to use the multiplication of fractions. So I'm going to start with my 30 minutes. And as a fraction, I can write that as 30 minutes over 1. Now I'm going to multiply that by a conversion factor so that I no longer am having minutes as my unit, but hours. So I want to have one hour on the top of my conversion factor, and 60 minutes on the bottom. Now we know that one hour is 60 minutes, so this fraction is equal to 1. And the reason that I want minutes on the bottom and hours on the top is because I want my minutes on the top and on the bottom to cancel, so I'll be left with just hours from my units.

So I know that my units are going to be hours. And now I just need to simplify-- 30 times 1 in the numerators of my fraction is going to give me 30, and 1 times 60 in the denominator of my fraction is going to give me 60. So I can simplify 30 over 60 to be 1/2 of an hour. All right. So let's see what that looks like for something that we don't already know. Let's say I want to convert 5 kilometers to some distance in miles.

So again, I'm going to be multiplying fractions together. So I'll start with what I have, 5 kilometers. And I'll make it as a fraction with 1 in the denominator. I'm going to multiply that by my conversion factor. And that is that 1 kilometer is equal to 0.621 miles. Again, I want kilometers in the bottom of my conversion factor so that the kilometers here and here will cancel, and I'll be left with miles, which is what I want to convert to.

So now that I have the unit that I want to convert to, I can simply simplify in the numerator and the denominator of my fractions. So 5 times 0.621 is going to give me 3.105, and 1 times 1 is just 1. So 5 kilometers is equal to 3.105 miles.

All right. Let's look at a couple of examples where we have to use more than one conversion factor. So first, let's see 365 days is the same as how many minutes? So I'm going to start by writing 365 days as a fraction over 1, and I'm going to multiply that by a conversion factor where days is in the bottom. So I'm going to use one day is equal to 24 hours. But I know that, even though I know that these days are going to cancel, I don't want to know my conversion and hours, I want to know minutes. So I need to use another conversion factor.

So I'm going to multiply by something with hours in the bottom. Again, so that the hours will cancel, and I know that I want to end up with minutes. So I'm going to say that 1 hour is equal to 60 minutes. So now my hours will cancel out, and I'm left with minutes for my unit. So now that I have the unit that I want, I'm going to go ahead and simplify my fraction. So in the numerators, I've got 365 times 24 times 60. And that's going to give me 525,600 over 1. So now I found that there are 525,600 minutes in 365 days.

So for our second example, we want to convert one mile into inches. So again, I'm going to start with one mile over 1. I'm going to multiply by a conversion factor that has miles at the bottom. So I'm going to say 1 mile is equal to 5,280 feet. So now my miles will cancel out. And I want to be inches, not feet. So I need another conversion factor.

Again, we want feet on the bottom so they cancel, and we want inches on the top, because that's what we're looking for. So in 1 foot, there are 12 inches. So now my feet units cancel on the top and on the bottom, and I know that I have inches as my unit, so I just need to simplify my fractions. So 1 times 5,280 times 12 in my numerators will give me 63,360. And I just have 1 times 1 times 1 in the bottom. So I now know that there are 63,360 inches in one mile.

So first I want to convert 6,360 square yards into square inches. And this is the approximate area of a football field. So I'm going to start with a fraction-- 6,360 square yards over 1. And I'm going to multiply that by something that has square yards in the bottom. And I'm going to use 1 square yard and convert that to feet squared. Now, we know that 1 yard is equal to 3 feet. But if we're looking at a square yard, that means that we need to square the 3. And so 1 square yard is actually equal to 9 square feet.

Similarly, I need another conversion factor, because I want inches and not feet. So I'm going to have feet squared at the bottom, 1 foot squared. And I'm going to convert that to inches squared. So again, we know that there are 12 inches in a foot. But in 1 square foot, we need to multiply 12 times 12. So there are 144 inches squared in 1 foot squared.

So now I see that my yards cancel. My feet cancel. And I'm left with inches squared. So I can simplify my fraction. So 6,360 times 9 times 144 is going to give me 8,242,560 inches squared in one football field.

So for our last example, we're going to do a conversion with measurements of volume. We've got 3,500 feet cubed, which is about the volume of a semitruck, and we're going to convert that to meters cubed. So I'm going to start the same way, 3,500 feet cubed over 1. I'm going to multiply that by a conversion factor that has feet cubed in the bottom, in the denominator of my fraction. And I know that 1 foot is approximately 0.304 meters. However, I need to cube the 0.304, because I'm talking about volume. I'm talking about cubic units.

So 1 foot cubed is actually 0.028 meters cubed. So now, I can see that my feet cubed will cancel, and I'm left with meters cubed, which is what I want. So now, I just need to simplify my fraction-- 3,500 times 0.028 is going to give me approximately 98.3, and that's going to be meters cubed.

So let's go over our key points from today. As always, make sure you get these down into your notes so you can refer to them later. So we started by talking about the fact that unit conversion allows us to express measurements with different units. The same measurement, but with different units. And we can use unit conversion for any type of measurement such as length, time, area, volume, or rate, such as miles per hour.

And then we saw, with our last two examples, that when you're converting with square units, it requires you to square the linear conversion. And when you're converting with cubic units, it requires you to cube the linear conversion. So I hope that these notes in these examples that we did today helped you understand a little bit more about unit conversion.

Keep using your notes and keep on practicing, and soon you'll be a pro. Thanks for watching.

Terms to Know
Conversion Factor

A fraction equal to one that is multiplied by a quantity to convert it into an equivalent quantity in different units.