In this video we're going to look at how to convert units using conversion factors like this and canceling units. Some people call this dimensional analysis, some people call it the factor label method, but you are going to call it easy by the end of this video because we are going to go step by step to show how to solve these kind of problems. So here is our first one.
We want to know what is 3.45 pounds expressed per second. grams. So the conversion that we're going to be doing is we're going to be doing pounds to grams and we're going to be starting with 3.45 pounds.
Okay, the next thing we got to do is we got to go and we got to find some kind of relationship between pounds and grams. So, how many pounds are there and how many grams? You can find this information on the internet, you can find it in a textbook, you can probably find it like in the back of a notebook where they'll have a conversion table for the units. something like this. You've got a bunch of these relationships between different units and you want to find the equation that talks about pounds and grams.
So it's going to be this one down here, one pound equals 453.6 grams. So this is the statement that you're going to want. You can get it from a variety of places but it's important. Now it doesn't matter whether pounds or grams is first.
It can be be flipped just as long as it has both pounds and grams in it. So now we have this statement that tells us how pounds relate to grams. We're going to use this statement now to write two conversion factors. A conversion factor is expressed as a fraction with a top and a bottom.
So here's how we can take this and write a conversion factor. We're going to take this side of the equation, one pound, and put it on the top of the fraction and there's a fraction line. And then this part of the equation is going to be on the bottom. So it's going to be 453.6 grams.
Now that's one of the two conversion factors. The other conversion factor that we're going to write is we just take this and we flip it. So this, 453.6 grams, we put that now on the top of the fraction and divide it by 1 pound.
So, two conversion factors that you can write. right from this statement here. Either one of them is correct, but only one of them is what we want to be using here. So we're just going to use one of these.
The one that I'm going to use is this one because pounds is up here and pounds is down here. Let me tell you what that means. So 3.45 pounds, that's not part of a fraction.
There's no fraction line here. And so if something does not have the bottom of a fraction, you just assume that it it is the top of a fraction. It's the same as it being on the top of a fraction if it doesn't have a bottom.
That's what I mean. Now, on the other hand, pounds is down here on the bottom of the fraction. Okay?
And when we're using conversion factors, we want to get rid of pounds, and we want to be left with grams. And it turns out that if a unit is on the top, on one side of the multiplication sign, and then it's on the bottom, on the other side of the multiplication sign, it cancels out. So pounds...
So pounds is on top here, pounds is on bottom there, so they both cancel out and that leaves me with units of grams. So just to review, I wanted to use this version of the conversion factor because pounds was on the bottom and this way pounds will cancel out. Now I've cancelled out pounds, I'm ready to do the math.
What's it going to be? I'm going to do 3.45 times 400. 453.6 divided by 1. Or, if you have a fancy scientific calculator, you can plug this whole thing in one expression. You can do 3.45 times, and then write this conversion factor in parentheses.
453.6 divided by 1. Now, you don't really have to worry about the 1 too much if you don't want to. I'm just putting it there because sometimes this won't... won't be a 1. So I just want you to get used to dividing by whatever is on the bottom of the fraction even if it happens to be 1 in this case. So however you decide to plug this into your calculator, when you crank through it you're going to get the same number and that's going to be 1560. What are the final units here?
Well I cancelled out pounds so the final units that I'm going to be left with are the ones that I'm going to be using with our grams. I'm not worrying too much about significant figures when I'm doing these unit conversions just for this lesson because I don't want to add another thing in here to confuse you. There'll be a lesson later about how to do significant figures with unit cancellation, but I don't want you to worry about sig figs now.
Just worry about figuring out how to do the unit conversions. So anyway, 1,560 grams is our final answer. Let's do a couple more. How many miles is 15,100? So the conversion we're going to be doing in this problem is from units of feet into miles and we'll be starting with 15,100 feet.
We got to go to our unit conversion table. table or find the information on the internet to figure out what the relationship is between miles and feet. We got it right here.
So this is going to be the statement that we're going to use to write our conversion factors. Let me pull this off the table here. Now don't freak out that miles is on this side and feet is on this side. It doesn't matter what unit is on what side of the equation because you could just easily flip it.
You don't care what unit is on what side of the equation, all you care about is the is being able to have this so then you can write the conversion factor. So let's write the two conversion factors that we can get from this statement. I'll take one mile and I'll put it on top here.
And then I'll take the other side, 5,280 feet. Now put that on the bottom and now I'll write what we could call the reciprocal of this where we take it and we flip it up so that 5,280 feet is on the top and 1 mile is on the bottom. We're going to be multiplying our measurement in feet by one of these two conversion factors. Which one is it going to be? We have feet not as part of a fraction so you assume that feet is on the top of a fraction.
It's the same as if it's on the bottom. on the top of the fraction which means that we are going to want a conversion factor that has feet on the bottom of the fraction so they cancel out. So it is going to be this one here and now feet on the top and feet on the bottom cancel out and they leave me units in miles which is what I'm looking for here.
Now how do I do the math? I'll do 15,100 times 1 divided by 5,280 because it's on the bottom of the fraction or if you can plug in the fraction. plug larger expressions into your scientific calculator. You can do 15,100 times, and then in brackets, I mean in parentheses, you can do 1 divided by 5,280. Again, you might wonder why you have to keep doing the 1. You can leave the 1 out if you want, but remember, this isn't always going to be a 1. So it's a good thing to get in the habit of multiplying by whatever's on the top of the fraction, and then dividing by whatever's on the bottom of the fraction, even if it's 1 for right now.
You can do either one of these. these expressions and you're going to end up with an answer of 2.86 units are in miles. Again, I'm not really paying attention to significant figures for these calculations. That's how you do this.
Let's do two more problems so you'll really get the hang of it. This problem is about units of money. On a certain day, the exchange rate between US dollars and euros is 1 US dollar equals 0.78 euros.
On that day, the exchange rate How much is 125 euros worth in U.S. dollars? So, we will be going from euros to U.S. dollars here, starting with 125 euros. And the question gives us this relationship between dollars and euros, which I'll just write in bigger letters here.
In the two previous problems, I took this statement. and I wrote two conversion factors, top and the bottom, then I flipped the top and the bottom. What I'm going to do here, though, is I'm going to look at what I'm starting with and I'm just going to write the one conversion factor that I need.
So I'm going to take 125 euros and what do I want to multiply that by to cancel out euros? I'm going to want the version of the conversion factor that has euros on the bottom, so they'll cancel out. So I'm going to take... Take this thing that has euros, 0.78 euros, and that will be on the bottom, which means then this one US dollar will be on the top.
So you don't always have to write out both of the conversion factors. You can figure out which of the two you need based on what should be on the top and what should be on the bottom. Now euros up here, euros down there, they cancel out. That leaves us with dollars, which is good because that's what we're looking for.
and the math is gonna be 100. 125 times 1 divided by 0.78 or 125 times 1 divided by 0.78. going to give us 160 US dollars. So the dollar is doing pretty well compared to the Euro on this day. One more. How many liters is 23,000 liters?
500 milliliters. These are both metric units. And you know, a lot of times people ask me, this unit canceling method, can I use it for metric units? Of course, you can use it for any type of units.
All you got to do is figure out what the relationship between your two units is. So we are going from milliliters, ml, to liters, l. And you may already know this, but there is a...
thousand milliliters in one liter. That's what I mean. This is all you need. You can convert any two units that you want just as long as you know the relationship between them. So we have this here for liters and milliliters.
So 23,500 ml. Which conversion factor am I going to want to use here? Since I want to get rid of milliliters, I want to use a version of this that puts milliliters on the bottom. So...
I'll put 1,000 milliliters down here, so they'll cancel out. And that means that I'll put 1 liter on the top. Cancel, cancel. I'm left with liters.
And so this is going to be, I'm not even going to write it out because I think you're getting the hang of it. It's going to be 23,500 times 1 divided by 1,000, which is going to be 23.5. Final units are in liters. So that's it. And that's how you can convert from one unit to another by setting up your conversion factors and canceling your units.
So where do you go from here? There are two more videos that may be of interest to you. The first is to show how to string multiple conversion factors together because you don't just always have to use one. Here I'm converting from days all the way to seconds by setting up a bunch of conversion factors where all the units cancel. So I'll show you how to do that in one of the next videos.
And then another video that you might want to watch. to watch is about understanding unit conversion where I talk about the rationale, the reasoning behind why you set up conversion factors the way you do, why the units cancel, and how this relates to things that you might be able to more easily understand.