Dimensional Analysis Explained!
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Robin Reaction dot com. In this video I’m going to explain how to do dimensional analysis Which is just converting units from one to another so it’s the same thing as unit conversions It’s also called the factor label method or the unit factor method no matter what you call it It’s just converting from one unit to another in this video I’m going to go into a good amount of detail with how to do these math steps But if I’m skipping too many steps and you still find yourself confused I have a video on unit conversion which goes over every single possible step pretty slowly So you can completely completely get it. So I’ll link to that video So if you watch this video, I’m going a little bit too fast for you Go ahead and watch that video and then come back here. So first let’s go ahead and do this first problem So we’re going to convert 3.2 miles into feet All right. So the first thing we’re going to do for these problems is we’re going to have this grid system That’s usually how dimensional analysis is shown Sometimes it’s just going to be parentheses sometimes it might look a little bit different but in general we’re going to set up something that looks like this we can plug our numbers into it and all it means is that we are going to be multiplying or dividing These numbers it’s just a way that we’re going to do our algebra or our multiplication so even though it’s a grid what it really is doing is it’s multiplying we go ahead and we put 3.2 miles on the top. We always put whatever number we’re given in this case 3.2 miles on the top and I like to have a 1 on the denominator just to remind myself I’m really just doing fraction math here. Even though I’m drawing it like a grid So next we have to go ahead and get our conversion factor So that is down here at the bottom in the box so a conversion factor just tells you how many units equals how many of your other units we’re always going to have at least two units in these problems and It’s going to depend on your class if you have to memorize them or not I’d say it’s about 50/50 between teachers that make you memorize conversion factors or teachers that give them to you So please feel comfortable asking your teacher Hey to give them to us or do we have to memorize them and if so Which ones do we have to memorize that’s something that they just really need to tell you so we can see in this problem Our two units are miles and feet So we go ahead and we can find that we have this conversion factor right here That’s going to relate miles to feet and our next goal is we want to cancel out miles because the goal is to cancel out Miles and end up in feet, so to do that. We’re going to just write miles on the denominator Because writing it down here is going to allow us to cancel out the miles that’s on top That’s just how we cancel in algebra. We have one on the top one on the bottom It’s all being multiplied and divided we can cancel Next we’re going to add our other unit, which is feet in just the spot that remains in this case it was on top so we can just add it to the top and now we plug in the numbers that are Associated with each unit so we can see that next to mile We have the number one So that gets written in next a mile and then for feet we have five thousand two hundred and eighty and that’s gonna get written in next two feet now that we have our number that we were given in the problem and our conversion factor all Correctly plugged in to our dimensional analysis We can go ahead and cancel out miles and then we’ll end up in feet so now the only thing left to do is to go ahead and do your math so both 3.2 and 5,280 are on the same side. They’re both on the top which means they get multiplied together the denominator is only one so you can ignore it or divide by one the same thing and we get 16,000 896 feed so now going ahead and doing sig figs and Only worry about this if your teacher has said that you need to do problems using significant figures Otherwise, you can ignore this part we can go ahead and see that 3.2 you has two sig figs So that’s how many our answer is allowed to keep which means that we’re going to round up to 17,000 and our final answer is going to be 17,000 feet no decimal point other. Otherwise that would add more sig figs. All right, so next let’s do an example It’s a little bit more complicated Convert eighteen point five grams per second into kilograms per minute. All right so first We set up our grid And we go ahead and put our given number into our grid So the number always goes on top eighteen point five and now for this problem We have to look a little bit more carefully at the units. We see that it says grams per second So we need to know that per is just the math word for division. That’s all that means So if we’re going to rewrite eighteen point five grams per second, it’s going to look like this. That’s all that means so that means that grams is going to go on the top next to eighteen point five and that Seconds goes on the bottoms because the per is indicating. Hey, that seconds is divided So if we rewrite that number if you just saw it on its own it would look like this eighteen point five grams per second So now we have two things We have to convert we have to take grams to kilograms and seconds into minutes And so it doesn’t matter what order we do this in but we do have to do both conversions before we can plug in and solve So let’s go ahead and look at our conversion factors and we see that a thousand grams equals one kilogram So let’s just start with this one. So we’re going to turn grams into kilograms So again, we just need to cancel out grams. This is the goal with this step and so because grams is on the top We’re going to cancel it out by putting it on the bottom So we write in grams on the bottom or the denominator and then we’re going to write the other unit kilograms on Top so now we have grams and kilograms and now we just have to match up the numbers So we have a thousand next to grams. So we write a thousand in and we have one next to kilograms so we write that in and Now just do the same thing for the other conversion. So in this case, we have 60 seconds equals one minute And so we need to cancel out seconds. So going ahead and going from second into minute Now we look for our conversion factor that has those two things. It’s 60 seconds equals one minute So now I have to go ahead and plug in seconds. And in this case since seconds is originally on the bottom in the dough It means to cancel it out. We’re going to have to put it on the numerator or on top So this is our first example where we’re going to actually plug in seconds We’re going to plug in a unit first that goes on top and that means the only other space left Four minutes is on the bottom. So that’s where that goes And now that we have our units we’re going to go ahead and plug in our numbers So 6d goes next to seconds and 1 goes next to minutes. And so now we are ready to solve So first we can go ahead and cancel out all the units that cancelled out grams is completely gone Seconds is completely gone and we can see we’re going to end up in kilograms and minutes Which is what we want it. We want two kilograms per minute. So now we can go ahead and do the math So remember that this is just multiplication and division everything on top is multiplication So I’m going to go ahead and multiply 18 point five times 60 and then I’m gonna go ahead and divide that number by a thousand All right so we have one point 1 1 and then we can see our units are kilograms per Minute kilograms divided by minute and this is using three sig figs from 18.5 and so This is also something you should probably check with your teacher with but in general by and large Your sig figs only come from the problem that you are given and in this case The only number we have is 18 point five. So you’re never going to use things like one kilogram as a sig fig or a Thousand grams the sig fig it’s usually just going to be whatever number you had There are some conversion factors where that’s not true and your teacher may have some exceptions It’s just going to depend on their personal policy. So now we’re ready to do this last problem This is really going to give you kind of a taste of a longer dimensional analysis problem And also just one that’s more complicated in general So we’re going to have to use a ton of different cancelling out to get to our eventually answer So we’re asked if you’re going 78 miles per hour. What’s your speed in nanometers per Second, so we start as we’ve done all these problems before by writing our number down with the correct units in the correct place so 78 miles goes on top We still have miles per hour It’s still the word for division hour goes on the bottom And then we know we’re trying to end up at nanometers per second so if we look right now at our conversion factors We don’t have anything that takes you from miles directly to nanometers or hours directly to second So we’re gonna have to do is stack up a bunch of different conversion factors until we can eventually get to the unit’s we want So the only thing we have with miles, is that one mile equals 5,280 feet so let’s go ahead and convert into feet so we need to cancel out miles so that goes on the denominator and then we need to put feet on the numerator and then we put one and 5,280 in their appropriate places So next let’s go ahead and just keep on going with our length So the only other thing we have that has feet is that 12 inches equals one foot? So let’s go ahead and we’ll write in foot It’s going to be now in the denominator and then we’re going to write inches in the other location and we plug in the appropriate numbers 1 and 12 and So keep on going we’re trying to get to nanometers. The next thing we have is going to relate centimeters and inches So inches goes on the bottom. We need to cancel out that inches centimeters goes on top It’s 2.5 centimeters in one inch and now continuing to just keep on going We’re trying to get to nanometers. The only thing we have with nano meters equals meters So now we have to go from centimeters to meters. So we go ahead using 100 cm equals one meter we are going to write in cm in the bottom meters in the top and we’re going to Write in a hundred next to centimeters and one next to meter and then cancel out Next we’re finally getting to nanometers and meters. That’s one of our units. That is our goal And so we’re going to write in meters in the denominator nanometers on the top One on the bottom and then one meter equals 10 to the power 2 10 to the 9 nanometers, so that goes on top So now we’re in nanometers, but we’re still in hours and we have to get two seconds So to do that we’re going to first have to convert from hour to minute So we go ahead and now looking all the way back hours on the bottom. We need it on the top So we go ahead and write our on top minute on the bottom 60 minutes one hour we can cancel out our and now our very Last conversion is we have to go from minute to seconds So we go ahead using one minute equals 60 seconds We put minutes on the top seconds on the bottom and then we have one minute and 60 seconds So now we can see that all other units have been crossed out and we’re ending up in nanometers per second That’s our goal. So now remember the math for all of this is that the top is completely Multiplied so we need to go ahead we need to multiply 78 times 5,280 times 12 times 2.5 4 times 1 times 10 to the power of 9 times 1 times 1 That’s the math we need for the top. And so that turns out to be before sig figs 1.25 5 times 10 to the 16 nanometers and Now we need to go to the denominator. So again, it’s all multiplied so it’s going to be all the ones in the beginning time 100 times 1 times 60 times 60 and So getting that number we end up with 360,000 seconds And so now we just need to do our final step of actually Dividing and we need to also include sig figs. In this case. We have two sig figs coming from 78 miles per hour And so doing our division we end up with 3.5 times 10 to the power of 10 Nanometers per second. All right Hope this video helped you understand what dimensional analysis is again? If this was overwhelming watch my video on unit conversions and then come back here These are pretty complicated unit conversions. Good luck Hey, I hope you liked that video. Please feel free to like comment or scribe and if you go to my website I have a ton of free practice problems. You can check out if you need even more help You can hire me for one-on-one private tutoring sessions that are online. All right. Thanks. That’s it. Happy studying

8 thoughts on “Dimensional Analysis Explained!

  1. Awesome stuff! Clear explanation. However, if I could offer one comment for improvement; you sound bored! You obviously enjoy math, so why not put a bit of energy into it! 🙂

  2. Amazing video! I'm a 30 year old software developer and I just understood unit conversion for the first time XD. Thank you so much!

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