Sometimes I just hate conversion factors so much I can hardly even describe it.
Sure I think they're easy, I think they're convenient.
If you have a problem and you're able to cancel out the right units you know you set it up
correctly.
But at the same time, I hate conversion factors and I hate them because for me, I'm all about
learning and I’m all about understanding how to solve a problem and what I don't like
about conversion factors is that it’s possible for a student to set up and solve a problem
using conversion factors and get the right answer but have no idea, absolutely no idea,
what they're doing, why they're doing it.
They’ll have absolutely no idea how the math is working.
They won't understand the problem so they won't be able to look at the final answer
and decide whether it makes sense or not.
It’s like when I first learned conversion factors, I was a unit conversion robot.
I would write out the conversion factors, I’d cancel my units, I'd multiply and divide,
get my final answer, but I had no idea what was going on.
This is a problem, I want to try to address it in this video.
In this video, I want to talk about how to understand conversion factors, okay?
I want to talk about how to understand how they work and what's really going on when
you use them.
I want to talk about how to understand the math and most importantly how to look at a
unit conversion problem and think through it so that you can then look at the answer
you get in the end and decide whether it makes sense or not.
We're going to talk about this thought process by working through this problem here.
But we're not going to use conversion factors right away.
Here, I want to find out how many inches are in 4 feet.
In order to do this, we’ll need to know the relationship the ties inches with feet.
You probably already know but there are 12 inches in 1 foot and I've drawn this out so
you can have a look at it visually.
Here's 1 foot and here are the twelve inches.
Now, how do we go from inches to feet?
Let's just think about it, okay?
If you have 1 foot, you're going to have 12 inches, okay?
If you had 2 feet, you're going to have 24 inches.
What am I doing here with the math?
What I'm doing is I’m doing multiplication, okay?
I’m doing 1 times 12 equals 12.
I'm doing 2 times 12 equals 24.
This is the number of feet, this is the number of inches.
So to figure out how many inches there are in 4 feet, I'm just going to do 4 feet times
12 inches because I know that there are 12 inches in each foot and I'm going to get 48
inches for my answer.
4 times 12.
How would I do this with conversion factors?
Okay, I'd set up a problem that looks like this.
I’d have my 4 feet here and I’d have 12 inches over 1 foot so that the feet cancel
out.
Look at the math that's going on here, though.
I'm just doing 4 times 12 and then dividing by 1 but the division by 1 doesn't change
anything here.
So the only thing that's really important is that I'm doing 4 times 12 and that is exactly
the same as what I do here when I just kind of think through the problem.
Let's look at a similar one.
Here, we're going from inches to feet.
How many feet are in 96 inches?
Let’s think about this the same way, okay?
If I had 12 inches, how many feet would that be?
It’d be 1 foot because there are 12 inches in 1 foot, okay?
If I had 24 inches I'd have 2 feet, at 36 inches I’d have 3 feet.
The math I'm doing in this case is division, okay?
I'm taking my 12 inches and I'm dividing it by 12 to get 1, 24 divided by 12 equals 2,
36 divided by 12 equals 3.
So you have inches and you want to get feet?
You divide by 12.
So I got 96 inches here and I'll divide by 12 and that will give me 8 feet.
Oh look at that I wrote 8 foot, what?
It’s like I can’t even speak English, 8 feet.
Okay, anyway, now to do this problem with a conversion factor I'd set up like this…
96 times 1 divided by 12… the inches cancel out.
I do 96 times 1 which doesn't change 96, it’s still 96 divided by 12.
So really I’m just doing 96 divided by 12 which is what I have up here.
So there are two important things to take away from this, okay?
The first is, if you have a number like 12 on the top of a conversion factor, it's the
same as just doing multiplication, okay?
I'm just doing it here because they're 12 inches in each foot, I have 4 feet so I just
do 4 times 12 and I get that.
If a number like 12 is on the bottom of a conversion factor, it's just division, okay?
For all these 96 inches, for every twelve inches there, I have 1 foot.
So I'm just doing 96 divided by 12, it gives me 8.
The other really important message here is that if you understand what's going on, your
able to look at the answer you get and decide whether it makes sense, okay?
Here we're going from feet to inches, okay?
There inches are small so there are a lot of inches in each foot.
That means when we're going from feet to inches.
If we start with a small amount of feet, we should get a bigger number of inches and that's
exactly what's going on here because there are a lot of inches in each foot.
On the other hand, when we're starting with the inches and going to feet, we should have
a lot fewer feet than we have inches.
And so here we go from a lot of inches to just a few feet and that make sense so that
I know that I set things up right and I'm on the right track.
Always keep the thought process in mind whenever you're working to a problem with unit conversions,
okay?
Here I’m going from miles to kilometers.
I've drawn out a little diagram here, obviously this is to scale.
It’s much smaller but here's one mile and this is how big a kilometer would be.
So I know that there is this many kilometers in one mile.
Kilometers are smaller than a mile so 1 mile has this many kilometers.
I want to know how many kilometers are in 2 miles.
I take this number and I multiply it by two and I get this number of kilometers.
How many kilometers are in 3 miles?
I take this number and I multiply it by 3 so we’re doing multiplication here.
So it makes sense that when we look carefully at what's going on in the conversion factor,
we’re doing 14 miles times this, the number of kilometers in 1 mile, to get the final
answer.
Now, does it make sense?
What if this were a problem on your test?
Could you figure out whether it made sense?
Well kilometers, as you can see, are smaller than miles and there are more than 1 kilometer
in 1 mile so that means that we should be getting more kilometers than miles.
Start with 14 miles and end up with 23 kilometers and that makes sense.
Here, we’re going from pounds to kilograms and there are 2.2 pounds, there they are,
that equal 1 kilogram.
So if I have 2.2 pounds, I have 1 kilogram.
I can divide that by 2.2 just to show that I get 1 kilogram, okay?
If I have 4.4 pounds, I divide that by 2.2 and I get 2 kilograms.
If I have 5.50 pounds and I divide it by 2.2, I get 2.5 kilograms.
So to go from pounds to kilograms, I want to be dividing, look at the conversion factor.
That is exactly what's going on here.
I'm starting with 53.5 pounds times 1 which doesn't change anything and I'm dividing by
2.2, just like I am here, okay?
Does the answer make sense?
Well here I have 2.2 pounds and I have 1 kilogram so there are fewer kilograms than pounds in
the same weight.
So when I'm starting with 53.5 pounds, I expect to get a smaller number of kilograms and there
I have 24.3.
So I probably set things up correctly and my final answer makes sense here.
Now a lot of times you're going to run into questions where you have to put a bunch of
conversion factors together but in a large problem like this you can still break it into
smaller sections then you can understand individually, okay?
So you can think about just this first part as being 3.5 days times 24 hours gives you
an answer in hours, okay?
That's this part and then you take this and you can pull it down and now we use 84 hours
and multiply it by this conversion factor and then get our final answer.
So even for a large thing like this, you can take it piece by piece if you want, to make
sure the each step makes sense.
So anyway, whenever you're solving these conversion factor problems, always try to make sure that
you really understand what's going on.
Ask yourself, am I multiplying here or am I dividing here?
Does it make sense that I'm doing that?
And then finally, look at the answer you end up with and ask, is it bigger or smaller than
the number that I started with and does that make sense?
And that way you won't just be a unit conversion robot, you’ll actually understand what you’re
doing and that's the most important thing to do.