Converting Units

Video Transcription

Hi, this is Anthony Varela. And today, we're going to convert units. So we'll talk about conversion factors. And then we'll use conversion factors to convert units of length and time, and then convert units of area and volume.

So first let's talk about what it means to convert a unit. So a ruler is a good example of unit conversion because, on one side of our ruler, we have inches. And on the other side of our ruler, we have centimeters. And so we can measure some distance. And we could express that in inches and then convert that into centimeters.

So we get a different number. But it's also a different unit, talking about the same actual distance. Another example of converting units might be from pounds to ounces, talking with the same actual weight, just in different units.

And so to convert units, we use conversion factors. And so what a conversion factor is, it's a fraction equal to 1 that is multiplied by a quantity to convert it into an equivalent quantity, but in different units. So the big idea with conversion factors is that it changes our units, but keeps the actual quantity the same.

So we can think of this as going from three feet to 36 inches. How do we do that? Well, we have to multiply it by some conversion factor. And the important thing here is that that conversion factor equals one because three feet and 36 inches are the same. It's just that we have different units. So we have different numbers in front of those units.

So let's think more about how we convert three feet into 36 inches. Well, I know a relationship between feet and inches. In one foot, there are 12 inches. So this is how I like to convert. I like to take what we're starting with and put that over 1 because I know I'm going to be multiplying by a fraction. So I might as well start with a fraction.

We're going to multiply it by a conversion factor. And the biggest thing here is to decide what goes in the top and what goes in the bottom of the fraction. Well, I'd like to convert into inches. So I'm going to put feet on the bottom because I know that that's going to cancel then when I multiply.

And then I have to put a what's equal to one foot in my numerator. That would be 12 inches. So when I multiply then 3 feet over 1 by 12 inches over 1 foot, my units of feet will cancel. So I'm left with just 36 inches. 3 times 12 is 36. The units of feet cancel. And the only unit left is inches.

Well, let's convert some units of time. So I'd like to convert 80 seconds into minutes. So I'm going to start with the relationship between seconds and minutes. There are 60 seconds in one minute.

So I'm starting with 80 seconds. And I'm putting that over 1. I need to multiply it by a conversion factor. I'm going to multiply it by 1 minute over 60 seconds. And I'm choosing to do it this way so that my units of seconds cancel. And I'm left with just minutes.

So now I have 80/60 minutes. And I can round this to the nearest hundredth and express it as a decimal, 1.33 minutes.

Well, we can use multiple conversion factors to go from one unit to another. So let's convert 2.5 feet into centimeters. Now, I don't know offhand how many centimeters are in one foot. But I do know that one inch is 2.54 centimeters. And one foot is 12 inches. So we're going to be using these to make our conversion factors.

Let's start with our 2.5 feet. And I know our relationship between feet and inches. So I'm going to have a conversion factor with 12 inches on the top and one foot on the bottom so my units of feet cancel. This would be good if I wanted my final answer to be in inches. But I want this to be in centimeters.

So let's use another conversion factor. Here with 2.54 centimeters on the top and 1 inch on the bottom so that my units of inches cancel, as well. So multiplying across now, we have 76.2 and our units of feet and inches canceled. So I know that my 76.2 is talking about centimeters. That's how many centimeters are in 2 and 1/2 feet.

Let's convert time using multiple conversion factors. Now, how many minutes are in one week? Well, I know that one week is seven days. I know that one day is 24 hours. And I know that one hour is 60 minutes. So I'm going to be using these to make my conversion factors.

Starting out with one week, I know that one week is seven days. So I'll use a conversion factor with days on top and weeks in the bottom, so many weeks cancel. I know that in one day there are 24 hours. So another conversion factor with hours on top and days on the bottom so that our units of days cancel.

And one more conversion factor, one hour and 60 minutes. So I'm putting 60 minutes on top and 1 hour on the bottom. So my units of hours cancel. My denominator just multiplies 1 times 1 times 1 times 1. So I just can multiply across my numerator now. That's 10,080. And everything but the minutes cancelled. So I know that 10,080 is talking about minutes.

So now let's talk about converting units of area. This is interesting. How many square inches are in three square feet? Well, I know that there are 12 inches in a foot. So you might guess then that there are 12 squared inches in one square foot. Well, take a look at this.

Here's what a square foot looks like. Dimensions are one foot by one foot. So multiply the dimensions together, we get 1 square foot. Well, I know that the dimensions of this are also 12 inches by 12 inches. When I multiply the two dimensions, I get 144 square inches, a big difference.

So I'm going to use 144 square inches in 1 square foot to make my conversion factor. So let's start with our 3 square feet. I need to multiply this by a conversion factor. Putting 144 square inches on the top and 1 square foot on a bottom, so my units of squared feet cancel. And I have 432 square inches. So remember, when you're converting area, make sure that you square those units to ensure that you have the correct conversion factor.

In a similar idea with converting units of volume, how many cubic meters are in 35,000 cubic centimeters? Well, we can start with the relationship between linear meters and linear centimeters. So 1 meter equals 100 centimeters. And now I'd like cubic meters and cubic centimeters. So I'm going to cube these two quantities.

1 meter cubed is 1 cubic meter. But 100 centimeters cubed is 1 million cubic centimeters. So it sounds crazy, but it's true. In one cubic meter there are 1 million cubic centimeters. So we're going to use this to make our conversion factor.

So let's start out with 35,000 cubic centimeters. That's what we'd like to convert into cubic meters. So to convert into cubic meters, I'm going to have 1 cubic meter on top and 1 million cubic centimeters on the bottom so my units of cubic centimeters cancel.

Well, now I just have 35,000 divided by 1 million. That's 0.035 and my units are cubic meters. So remember, when you're converting volume, make sure that you cube those units to make sure that you're using the right conversion factor.

So let's review. With converting units, we talked about a conversion factor. It changes the units but keeps the actual quantity the same. When you're converting area, make sure that you square the units to ensure you have the correct conversion factor. And with volume, cube the units so you have the correct conversion factor. It makes a big difference.

All right. Thanks for watching this video on converting units. See you next time.