Converting Units with Conversion Factors

In this video, we'll look at how to convert

units

using

conversion

factors

like this and canceling

units

. Some people call this dimensional analysis, others call it the factor label method, but at the end of this video you'll call it easy because we're going to show step by step how to solve these types of problems. So, here's the first one. We want to know what is 3.45 pounds expressed in grams? So the

conversion

we're going to do is from pounds to grams. We'll start with 3.45 pounds. Well, the next thing we need to do is go and find some kind of relationship between pounds and grams.

So how many pounds are in 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 will have a unit conversion table. It will look like this. You have a bunch of relationships between different units and you want to find the equation that talks about pounds and grams. Well? It will be this one below, 1 pound (lb) = 453.6 grams (g). This is the statement you'll want, you can get it from several places, but it's important. Now, it doesn't matter if it's pounds or grams first, you can invest as long as you have pounds and grams.

Now we have this statement that tells us how pounds relate to grams. We will now use this statement to write two conversion

factors

. A conversion factor is expressed as a fraction with a top and a bottom, so this is how we can take this and write a conversion factor. We're going to take this side of the equation, 1 pound and we're going to put it at the top of the fraction and there's a fraction line and then this part of the equation of the equation... it's going to be at the bottom, so it's going to be 453.6 grams.

And that is one of the two conversion factors. The other conversion factor that we're going to write down is... we just take this and flip it... so this 453.6 grams we now put at the top of the fraction and divide it by 1 pound. So two conversion factors that you can write from the statement here, any one of them is correct, but only one of them is the one we want to use here. Well? So we'll just use one of these. The one I'm going to use is this one because the pounds are up here and the pounds are down here.

Let me tell you what that means. So 3.45 pounds, that's not part of a fraction, is it? There is no fraction line here, so if something doesn't have the bottom of a fraction, just assume it is the top of a fraction, it's the same as being at the top of a fraction if it doesn't have a fraction. lower. , that's what I mean. Now, on the other hand, the pounds are here at the bottom of the fraction, okay? And when we use conversion factors, we want to get rid of the pounds and keep the grams. And it turns out that if the unit is above, on one side of the multiplication sign, and then it is below, on the other side of the multiplication sign, it cancels out.

So pounds are up here, pounds are down 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 the pounds were at the bottom and this way the pounds will cancel out. Now that I've written off the kilos, I'm ready to do the math. What's it gonna be? I'm going to do 3.45 times 453.6 divided by 1. Or if you have a fancy scientific calculator, you can plug this all into one expression. You can do 3.45 times... and then write this conversion factor in parentheses (453.6 divided by what?).

You really don't have to worry too much about 1 if you don't want to. I'm just putting it in there because sometimes it won't be a 1. So I just want you to get used to dividing by whatever is at the bottom of the fraction, even if in this case it turns out to be 1. So however you decide to connect this on your calculator, when you do that you will get the same number and it will be 1,560. What are the final units here? Well, I cancel out the pounds, so the final units I'll be left with will be grams.

And not worry too much about significant figures when I do these unit conversions just for this lesson because I don't want to add anything else here that will confuse you. There will be a lesson later on how to do significant figures with unit cancellation, but I don't want you to worry about sig figures now, just worry about figuring out how to do unit conversions. Anyway, 1560 grams is our final answer, let's do a couple more. How many miles is 15,100 feet? The conversion we are going to do in this problem is from units of feet to miles. We'll start with 15,100 feet.

We have to go to our unit conversion table or search for information on the Internet to find out what the relationship between miles and feet is. We have it here, so this will be the statement that we will use to write our conversion factors. Let me get this off the table. Now don't be scared because the miles are on this side and the feet are on this side. It doesn't matter which unit is on which side of the equation because you can easily reverse it, okay? You don't care which unit is on which side of the equation, all you care about is being able to have this so you can write down the conversion factor.

So, let's write down the two conversion factors that we can get from this statement. I'll take 1 mile and put it up here and I'll take the other side, 5,280 feet, and put it down. And I'll write what we might call the reciprocal of this, where we take it and flip it so that 5,280 feet is at the top and 1 mile is at the bottom. We will multiply our measurement in feet by one of these two conversion factors. Which is it going to be? We have feet that are not part of a fraction, so you assume that feet are on top of a fraction, it's the same as if they were on top of a fraction, which means we're going to want a conversion factor that has feet on the bottom of a fraction so that they cancel each other.

So it will be this one here. And now, feet up and feet down cancel out and leave me with units in miles, which is what I'm looking for here. Now how do I do the calculations? I'll do 15,100 times 1 divided by 5,280 because it's at the bottom of the fraction or if you can enter larger expressions into your scientific calculator, you can do 15,100 times and in parentheses you can do one divided by 5,280. Again, you may wonder why you have to keep doing the 1. You can skip the 1 if you want, but remember that it won't always be a 1, so it's good to get into the habit of multiplying by. whatever is at the top of the fraction and then divide by when it is at the bottom of the fraction, even if it is 1 for now.

You can do any of these expressions and you will end up with an answer of 2.86. Units are in miles. Again, I'm not paying attention to significant figures for these calculations. This is how to do this, let's do two more problems so you really understand it. This problem is about units of money. On any given day, the exchange rate between US dollars and euros is 1 US dollar equivalent to 0.78 euros. On that day, how much is 125 euros worth in US dollars? So we'll go from euros to US dollars here, starting with 125 euros and the question gives us this relationship between dollars and euros which I write here in larger letters.

In the previous two problems, I took this statement and wrote two conversion factors above and below, but flipped the top and bottom. However, what I'm going to do here is see what I'm starting with and I'll just type in the conversion factor that I need, okay? So I'm going to take 125 euros and why do I want to multiply it to cancel euros? I'm going to want the version of the conversion factor that has euros at the bottom so they cancel out. So I'm going to take this that has euros, 0.78 euros and that will be at the bottom, which means that then this US dollar will be at the top.

Look, you don't always have to write down both conversion factors, you can determine which of the two you need based on what should be at the top and what should be at the bottom. Now, the euros up here, the euros down there, they cancel out, which leaves us with dollars, which is good because that's what we're looking for and the math will be 125 times 1 divided by 0.78 or 125 times (1 divided by 0.78). ). This will give us 160 US dollars, so the dollar is doing quite well compared to the euro on this day. One more. How many liters are 23,500 milliliters? They are both metric units and many times people ask me this unit cancellation method: can I use it for metric units?

Of course, you can use it for any type of units. All you have to do is figure out what the relationship is between your two units. So we go from milliliters (mL) to liters (L) and you may already know this, but there are 1000 milliliters (mL) in 1 liter. That's what I mean, this is all you need. You can convert any two units you want as long as you know the relationship between them. We have this here for liters and milliliters. So, 23,500 ml… what 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 in the bottom.

So I'm going to put 1000 ml down here so they cancel out, that means I'm going to put 1 liter on top. Cancel, cancel, I'm left with liters so this is going to be, I'm not even going to write it because I think you're already understanding it, it's going to be 23,500 times 1 divided by 1000 which is going to be 23 .5, the final units are in liters. This is how you can convert from one unit to another by setting 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 chain multiple conversion factors because it is not always necessary to use one. Here I'm

converting

from days to seconds by setting up a bunch of conversion factors where all units cancel out. So I'm going to show you how to do it in one of the next videos and then another video that you might want to watch is about understanding unit conversion, where I talk about the rationale, the reasoning behind why you set conversion factors the way you do. that you do. , why units are canceled and how this relates to things you may be able to understand more easily.