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

Everyone. Welcome back. So in this practice problem here, we're gonna take a look at how many gallons are in 1 cubic meter. So what that means is we're actually trying to take a cubic meter. So I'm gonna have 1 meters cubed over here, and I'm trying to figure out actually how many gallons are in that. Right? So there's gonna be some number there for gallons. So notice how these are actually all units of volume. So we're gonna be using these conversion factors over here to do that. Let's go ahead and get started. Alright? So, basically, what I'm gonna do is I know what my target I know what my starting variable is. I've got 1 meter cubed, and then I'm gonna have a bunch of conversion factors. I don't exactly know how many, but I wanna end up with gallons. Alright? So if you look actually over here at these conversion factors, let's see what we can use. So we know that 1 gallon is equal to 3.79 liters. This is actually our target variable, our target unit over here, but then this is relates it to liters. And now if you look over here at the second conversion factor, we've got 1 milliliter is equal to 1 centimeter cubed. This last one over here deals with liters. Right? This is like the other unit that we had over here, but it also relates it to quartz. And we actually have nothing about quartz over here. So instead, we're not gonna use that conversion factor. If you actually take a look what's going on here, we're gonna go from meters cubed to get to centimeters cubed. Right? Because that's just a metric prefix. After that, we can convert this to milliliters. And then from milliliters, we can convert this to liters because that's just another metric prefix. And then from there, we can relate this to gallons by using this conversion factor. Alright? So we basically got all the sort of, like, steps of the train track already laid out. So the first thing we're gonna have to do over here is we're gonna have to multiply by some conversion factor. And remember, what I want here is I wanna cancel out meters cubed on the bottom, but I wanna replace it with something else that gets me closer to gallons. Alright? So what I'm gonna do here is remember, I wanna get this to centimeters cubed so I can use this conversion factor. That's just a metric prefix. Right? One meter is equal to 100 centimeters. So, basically, all these things are just powers of 10. So what I can do here is I'm just gonna do 100. This is gonna be centimeters divided by 1 meter. But remember that we have an exponent here, which is meters cubed. So whatever this conversion factor is, I have to apply it as many times as there are exponents in this term. In other words, I have to do a 3rd exponent up here. You have to do this, otherwise, you're gonna get the wrong answer. Alright? So that's the first one. So now what I'm gonna do here is I have another conversion factor. And now what I'm gonna do is now that I have this thing in centimeters cubed, I wanna convert this to milliliters. Alright? And if you look here, what's gonna happen is this is just gonna be 1 centimeter cubed. I'm sorry. Actually, I want 1 centimeter to be on the bottom. So this is gonna be 1 centimeter cubed, and this is exactly equal to 1 milliliter. Right? Because that's what this tells us over here. Alright? So now what happens is that is gonna cancel out with that, and this is gonna cancel out with this. Okay? So now what happens is there's another conversion factor where I'm gonna have to go from milliliters, and I'm gonna have to have to convert it to liters. That's just another, you know, metric prefix. This is just gonna be that 1, 1 liter is equal to 1,000 milliliters. Alright? I want milliliters to be on the bottom. So this is gonna be, 1,000 milliliters on the bottom, and I'm gonna have 1 liter at the top. Alright? So now what you're gonna see is that milliliters will cancel. And now the very last conversion factor is I'm gonna have that 1 liter is equal to or sorry. 3.79 liters is equal to 1 gallon. Alright? So with the what's gonna happen here is that we're gonna have 3.79 liters is gonna be 1 gallon. And then what we're gonna be left with is just finally gallons. Notice how every others every other unit has canceled out. Alright. So now all we're really left with is once we set all these things up and all of the units canceled, all all we have to do is just multiply everything on the top and then divide it by everything on the bottom that's multiplied. And what you end up with, by the way, is because all of these things at the top are really just ones except for this unit over here, what you're gonna end up with is just 100 cubed. And then on the bottom, you're gonna have these things that are ones, so 1 times 1, but then you're gonna have a 1,000 times 3.79 on the bottom. So this is gonna be 1,000 times, 3.79. Alright? And if you actually go ahead and work sorry. I could do multiplication here. If you actually go ahead and work this out, which you're gonna end up with is 2263 0.9 gallons. Alright? So that is our answer. 1 meter cubed is equal to 263.9 gallons. That's your final answer. Let me know if this makes sense, and let me know if you have any questions. Thanks for watching.