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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
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