Unit Conversions: Study with Video Lessons, Practice Problems & Examples

Unit conversions are essential in physics, requiring compatibility with the SI system. To convert units, identify given and target units, then use conversion factors as fractions to cancel out units. For example, to convert 22 pounds to kilograms, use the factor 1 kg/2.2 lbs. Multiply the values accordingly to find the result. This method applies to various conversions, such as speed (miles per hour to meters per second) and area (square feet to square meters), ensuring accurate calculations in scientific contexts.

Unit Conversions

Hey, guys. So remember that all of our units have to be in the SI system of units. And in order for our equations to make sense, units must be compatible with each other. A lot of times in physics, you're going to see non-SI units in problems, and to deal with this, you must first convert them into SI before you start plugging them into all your physics equations. So, in this video, I'm going to teach you how to do unit conversions. It turns out there's a really simple process for doing this because you're going to end up doing the same thing over and over again in many of these problems. So I'm giving you a list of steps here that's going to help you get the right answer every single time. Let me just show you how it works, and we're going to do this example together. We're going to convert 22 pounds into kilograms. So the way this is always going to work is you're going to write your given and your target units. So I have my given on the left, 22, and my units are pounds. These are my given or my starting point. And eventually, I want to figure out what number this converts to in kilograms. What is 22 pounds in kilograms? So this is my target. So here's what I do. I 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 as ratios and the reason I like to call them ratios is because it helps us remember that we're 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 to grams, feet to meters, liters to quarts, things like that. Things that aren't just like multiples of 10. So we're going to write these conversion factors as fractions. That's what's going to 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 going to help us get from our given, which is pounds, to our target, which is kilograms. So if you look at our table here, there's actually 1 conversion factor, one conversion factor that deals with changing masses from kilograms to pounds. So this is the conversion factor we want to use, but we want to write it as a fraction. And there are actually 2 ways to write this as a fraction. So one way you can do this is you could write 2.2 pounds over 1 kilogram. This is the conversion factor expressed as a fraction, or you can write it the other way around, basically flipped. You could write it as 1 kilogram over 2.2 pounds. Basically, they mean the same thing. It's just that one of them is flipped. But essentially, it's the same it's kind of like the same fraction. So in order to figure out which fraction we're going to actually put inside of this bracket, we're going to take a look at the next step. So we're always going to write 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. They're basically in the numerator. So what we want to 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 going to use. We're actually going to use this fraction over here and not this version of that conversion factor. So we're going to use this one. So now what we do is we write 2.2 pounds on the bottom and then 1 kilogram on the top. Because now what happens is when you multiply by this conversion ratio, your pounds are going to cancel, and you're just going to 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 2 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 and all the numbers on the bottom. So we've got 22 on the top times 1, 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 pounds is equal to 10 kilograms. That's all there is to these unit conversions. So let's go ahead and get a few more examples. So we're going to convert these following measurements. So we got 67.5 miles an hour to meters per second. So we're going to follow the same list of steps. So we've got 67.5. We've got miles per hour. I like to arrange them like this so that they're top and bottom, so we can see how they're going to cancel out. So now we've got these conversion factors, and eventually, we won't end up at meters. So notice that we actually have 2 units that we have to convert. Miles per hour will eventually turn into meters per second. So which one of these do we deal with? Well, honestly, it's kind of up to you. You can deal with this, like, however you want. Basically, solve for 1 or the other, but let's just start off with the top one. Let's start with miles. How do we get from miles to meters? Well, if we look at our conversion factors over here, we have a conversion factor that helps us relate kilometers to miles. So what 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. We want to write the fractions that miles cancel out top and bottom. So if miles are on top, then we want miles on the bottom. So this is 0.621, and this is going to be 1 kilometer. So now what happens is when we multiply this, our 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 go to meters. But this is kind of just like a metric prefix. We know that 1 kilometer just means 1000 meters. So we can actually use metric prefixes as conversion factors. What I mean by this is that 1 kilometer equals 1000 meters. 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 going to put 1000 meters here up at the top. And so 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 hours and how to eventually go to seconds. So what I want is I want a conversion factor that deals with hours on the top, and I want to get seconds on the bottom. So there is a conversion factor here that'll help us with time, but we do know that an hour is 60 minutes and 60, and each minute is 60 seconds. So that means that for every 1 hour, there are 3600 seconds. And so finally, we have hours that cancel out with hours. 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 can ignore all the ones because they don't really do anything. So 67.5 times 1000 divided by 0.621 times 3600. And if you work this out on your calculator and you plug it in, you're going to get 30.2, and that's the answer in meters per second. Alright, guys. Let's do one more. We're going to convert 100 feet squared into meters squared. So same process, 100. Now we have feet squared. So now we have an exponent inside of that unit. So here's what we do. We're going to 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'll help us. We know that 1 foot is equal to 0.305 meters. We want to set it up so that the feet will cancel out at the bottom. So we want feet to cancel out at the bottom, so that is 1 and this is going to be 0.305. But what happens is, if you multiply this conversion factor only once, we have 2 units. We have 2 exponents here or 2 factors of feet squared, whereas this conversion factor only relates 1 foot or basically the exponent of 1. So basically, what we have to do 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 exponent. So because there is 2 here, we actually have to do this conversion twice. So you're going to write it again. 0.305 meters and then 1 foot. Because now what happens is both these feet terms will cancel out with the feet squared, and you're going to get meters squared on that on that side. So now you just multiply everything straight through. A 100 times 0.305 times 0.305, and you should get 9.3 meters squared. And that's the answer. Alright, guys. That's it for this one. Let me know if you have any questions.

Convert 850 ft to km.

• A. 259 km
• B. 0.259 km
• C. 2.79 × 10⁶ km
• D. 2.79 km

The speed of light is approximately 3.00×10⁸ m/s. Convert this speed to yards/week (yd/wk).

• A. 1.84×10¹³ yd/wk
• B. 1.98×10¹⁴ yd/wk
• C. 1.78×10¹⁵ yd/wk
• D. 1.8×10⁷ yd/wk

How many gallons are in 1 cubic meter (m³)?

• A. 2639
• B. 3790
• C. 263.9
• D. 37.9

Here’s what students ask on this topic:

How do you convert pounds to kilograms?

To convert pounds to kilograms, you use the conversion factor 1 kg/2.2 lbs. Start by writing your given value in pounds and your target unit in kilograms. For example, to convert 22 pounds to kilograms, set up the conversion factor so that pounds cancel out:

$\frac{1}{2.2}kg/lbs$

Multiply 22 by the conversion factor:

$22\; imes\frac{1}{2.2}=\; 10\; kg$

So, 22 pounds is equal to 10 kilograms.

What is the process for converting miles per hour to meters per second?

To convert miles per hour (mph) to meters per second (m/s), follow these steps:

1. Convert miles to meters using the conversion factor: 1 mile = 1609.34 meters.

2. Convert hours to seconds using the conversion factor: 1 hour = 3600 seconds.

For example, to convert 67.5 mph to m/s:

$67.5\; imes\frac{1609.34}{1}imes\frac{1}{3600}=\; 30.2\; m/s$

So, 67.5 mph is equal to 30.2 m/s.

How do you convert square feet to square meters?

To convert square feet to square meters, use the conversion factor: 1 foot = 0.305 meters. Since you are dealing with square units, you need to apply the conversion factor twice:

For example, to convert 100 square feet to square meters:

$100\; imes\frac{0.305}{1}^2\; =\; 9.3\; m^2$

So, 100 square feet is equal to 9.3 square meters.

Why is it important to convert units to the SI system in physics?

Converting units to the SI system in physics is crucial because it ensures consistency and compatibility in calculations. The SI system is universally accepted and used in scientific contexts, allowing for clear communication and comparison of results. Using SI units helps avoid errors that can arise from unit mismatches and simplifies the application of equations and formulas, which are typically derived using SI units. This standardization is essential for accurate and reliable scientific measurements and analyses.

What are conversion factors and how are they used in unit conversions?

Conversion factors are ratios that express the relationship between different units of measurement. They are used to convert a quantity from one unit to another by multiplying the given value by the appropriate conversion factor. For example, to convert 22 pounds to kilograms, you use the conversion factor 1 kg/2.2 lbs. By setting up the conversion factor so that the units cancel out, you can accurately convert the measurement:

$22\; imes\frac{1}{2.2}=\; 10\; kg$

Conversion factors ensure that the units are compatible and the calculations are correct.