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concept

## Unit Conversions

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Hey, guys, remember that all of our units have to be in the S I system of units. And in order for our equations to make sense, units must be compatible with each other. Well, a lot of times in physics, you're gonna see non s I units in problems. And so deal with this. You must first convert them into s I before you start plugging them into all your physics equations. So in this video, I'm gonna teach you how to do unit conversions. It turns out there's a really simple process for doing this because you're gonna end up doing the same thing over and over again and a lot of these problems. So I've given you a list of steps here that's gonna help you get the right answer every single time. Let me just show you how it works and were to do this example together, we're gonna convert £22 into kilograms. So the way this is always gonna work is you're gonna right, you're given and your target units. Sorry. I got given on the left 22 my units are pounds. So these were my given or my starting point and eventually I want to figure out what number this converts to in kilograms, what is £22 and kilograms. So this is my target. So here's what I do have to basically convert between these units by writing these things called conversion factors by multiplying by these conversion factors, or sometimes they're called conversion ratios. And the way that we write them is ratios. And the reason I like to call them ratios is because it helps us remember they were supposed to write them as fractions. And really, these conversion factors or ratios are just relationships between different units, usually between different systems like pounds, 2 g feet, 2 m, leaders to courts, things like that, things that aren't just like multiples of 10. So we're gonna write these conversion factors as fractions. That's what's gonna go over here to get us from our given to our targets. So here's what we do. We have to identify which conversion factor is gonna help us get from, are given, which is pounds tow our target, which is kilograms. So if you look at our table here, there's actually one can factor one conversion factor that deals with changing masses from kilograms £2. So this is the conversion factor we want to use. But we want to write it as a fraction. And there's actually two ways to write this as a fraction. So one way you could do this is you could write 2.2 pounds over one kilogram. This is the conversion factor expressed as a fraction. Or you could write it the other way around. Basically flipped. You could write it as 1 kg over £2.2. Basically, they mean the same thing. It's just that one of them is flipped. Um, but essentially, it's the same. It's kind of like the same fraction. So in order to figure out which fraction we're gonna actually put inside of this bracket, we're gonna take a look at the next step. So we're always gonna right the fractions to cancel out the units on top with the units on the bottom. So what I mean by this is if we look, our pounds are on the top of this there, basically in the numerator. So what we wanna do is we want to set up the fraction that has pounds on the bottom so that it cancels. So we want pounds to appear on the bottom, so that tells us which fraction we're gonna use. We're actually gonna use this fraction over here and not this version of the conversion factor. So we're gonna use this one. So now we do is we write £2.2 on the bottom and then 1 kg on the top. Because now what happens is when you multiply by this conversion ratio, your pounds are gonna cancel, and you're just gonna be left with kilograms, which is exactly what you want. And so, basically, there's no more conversion factors that need to be done. But I just like to put, you know, at least two, just in case I need them. So we don't need this one now. The last step is we just multiply all the numbers on the top when all the numbers on the bottom, So we've got 22 on the top times, one that doesn't really do anything. And then we've got 2.2 on the bottom. So we just have to do 22 divided by 2.2, and that just gives us 10. So that means that £22 is equal to 10 kg. That's all there is to these unit conversions. So let's go ahead and get a few more examples. So we're gonna convert these following measurements. So we've got 67 a half miles an hour, 2 m per second. We're gonna follow the same list of steps, so we've got 67.5. We've got MPH. I'd like to arrange them like this so that their top and bottom so we can see how they're gonna cancel out. So now we've got these conversion factors and eventually we want end up at meters per second. So notice that we actually have two units that we have to convert. MPH will eventually turn into meters per second. So which one of these do we deal with? Well, honestly, uh, it's kind of up to you. You can deal with this like however you want basically solve for one or the other. But let's just start out with the top one. Let's start with miles. How do we get from miles? 2 m? Well, if we look at our conversion factors over here, we have a conversion factor that helps us relate. Kilometers two miles. So we can do is we can use this conversion factor. But we have to write it as a fraction. So we want miles to cancel out. So we want to write the fractions that Miles cancels out top and bottom. So if Miles is on top there when you want miles on the bottom So that 0.6 to and this is gonna be one kilometer. So now what happens is when we multiply this are miles will cancel out. So now we take a look at this unit here. Are we done well? No, because we want the kilometers. Eventually we want to get to go to meters. But this is kind of just like a metric prefix. We know that one kilometer just means 1000 m, so we could actually use metric prefixes as conversion factors. What I mean by this is that one kilometer equals one m, so we can set this up as a fraction so that we want kilometers to cancel out on the bottom so they cancel out like this and we're gonna put 1000 m here up at the top and so narrow. Now we've actually just ended up with meters, and that's exactly what I want to end up with on the top. So we're done there. So the last thing I have to do is I have to figure out how to get ours and how to eventually go two seconds. So what I want is I want a conversion factor that deals with ours on the top, and I wanna get seconds on the bottom. So there isn't actually a conversion factor here that will help us with time. But we do know that in our 60 minutes and 60 and each minute is 60 seconds. So that means that for every one hour there's 3600 seconds. And so finally we have ours that cancels out with ours. And if you take a look here, all the units have canceled out, except for the ones that we want to end up with meters and seconds. So the last thing we do is we just multiply everything across and then solve. So this just equals 67.5 and you could ignore all the ones because they don't really do anything. So 67.5 times 1000 divided by 0.6 21 times 3600. And if you work this out in your calculator and you plug it in, you're gonna get 30.2 and that's the answer in meters per second. Our guys, let's do that. One more. We're gonna convert 100 ft squared into meter squared. So the same process 100. Now we have feet squared. So now we have an exponents inside of that unit. So here's what we dio. We're gonna set up a conversion factor that helps us get to meters squared. So if you take a look at our conversion factors here, we've got one that will help us. We know that 1 ft is equal 2.35 m. We want to set it up so that the feet will cancel on the bottom. We want feet to cancel level the bottom, so that is one and this is gonna be 10.305 But what happens is if you multiply this conversion factor only once we have two units. We have two exponents. Here are two factors of feet squared, whereas this conversion factor only relates 1 ft, basically the exponents of one. So basically, what we have to dio is whenever you're converting exponents or units with exponents, you have to multiply the conversion factors as many times as the number in the exponents. So because there is too here, we actually have to do this conversion twice. So you're gonna write it again, 0.3 or 5 m and then 1 ft, because now it happens is both these feet terms will cancel out with the feet squared. And you're gonna get meters squared on that on that side. So you just multiply everything straight through ah, 100 times 1000.3 or five times 50.3 or five, and you should get 9.3 m squared. And that's the answer. Our guys. That's it for this one. Let me know if you have any questions.

2

Problem

Convert 850 ft to km.

A

259 km

B

0.259 km

C

2.79 × 10

^{6}kmD

2.79 km

3

Problem

The speed of light is approximately 3.00×10^{8} m/s. Convert this speed to yards/week (yd/wk).

A

1.84×10

^{13}yd/wkB

1.98×10

^{14}yd/wkC

1.78×10

^{15}yd/wkD

1.8×10

^{7}yd/wk4

Problem

How many gallons are in 1 cubic meter (m^{3})?

A

2639

B

3790

C

263.9

D

37.9

Additional resources for Unit Conversions

PRACTICE PROBLEMS AND ACTIVITIES (12)

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- Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile