Mr. Andersen shows you how to use the factor label method to solve complex conversions.
Transcript Provided by YouTube:
Hi class. This is Mr. Andersen. Today I’m going to show you how to use the
factor-label method. Some science teachers refer to this as dimensional analysis. And
some people just call it common sense. And so what is the factor-label method? The factor-label
is the way that you solve a problem. And so there’s a nice method you can use to do that.
And so if I were to for example to ask you how many hours are there in a day? That thought
process you go through of remembering that it’s 24 hours in a day is actually a simple
for of the factor-label method. So what we do with that is we take a value, let’s say
55 miles per hour. And we’re going to convert that to a different unit, like meters per
second. This becomes really important in chemistry, physics, physical science, because you can
solve these very complex problems. And as long as you follow the methods that I lay
out in this podcast you should be good to go. Now an analogy or a good way to think
about how this works is what’s called six degrees of separation. So there’s a scientist
back in the 1940s I think it was who said, let’s say we have a person here who lives,
we’ll say in New York City. And then we have a person who lives way over here. Let’s say
they live in Montana. He said that we could take any two people and we could connect them
with at least six degrees of separation. In other words this guy might be friends with
this guy. And this guy might have a sister who is this person right here. Who might have
a friend who is this person. Who also has a friend who knows this person. And so the
idea is that you’re connected to anybody on the planet by no more than six degrees of
separation. There’s a funny game with movies and using Kevin Bacon. It’s called six degrees
of Kevin Bacon that uses movie trivia to kind of do the same thing. But again that’s just
kind of an analogy. So what do we do in this? Conceptually we’re taking a quantity. So let’s
say that is miles per hour. And we’re going to convert that to something like meters per
second. And so all of these questions will start with some kind of quantity. And then
we’re going to end up with a desired quantity. But you have to use your brain to figure out
what kind of conversion factor we’re going to use. In other words, what are some important
things if we’re going from hours to seconds. How are you actually going to convert that?
Or miles to meters. We’re going to have to know some kind of a conversion to make it
from that given quantity to the desired quantity. Okay. So this is my method. And there’s lots
of different methods laid out to do the factor-label method. But if you follow these steps you
can solve pretty complex problems. So let’s start with one that’s really really easy.
And let’s say we say that you’ve got one day and you want to convert that to hours. So
what is the first step? You start with the given quantity. And you always express it
as a fraction. And so even though one day doesn’t need to be written over one, let’s
just do that. Because it’s going to all you to solve the problems. Lot’s of times you’ll
actually have units over units. And so it makes it easier. Okay. Next we’re going to
convert with a conversion factor. Okay. So what does that mean? We’re here with days.
But we want to eventually make it to hours. And so what I’m going to do is I’m going to
write days underneath and I going to write hours on the top. So first we insert the conversion
factor. Then we add our numbers. Well we know that one day is 24 hours. So what’s next?
We cancel the units. This is a day on the top. So I’m going to cancel that out. And
here’s a day on the bottom. And so I’m going to cancel that out. And then the fourth step,
what I do is I actually solve the math. And so I’m going to multiple across the top. 1
times 24 hours is 24 hours. Now I’m going to multiple across the bottom. 1 times 1,
we lost the day, is 1. And so my answer equals 24 hours. Now you could have just done that
in your head. But if you followed these steps on all of the problems we work with on factor-label
method, you’ll do fine. So let’s do a couple of practice ones. So let’s say we start with
this. I’ve got 12 days over here. So I’ve got 12 days. So I write that over 1. I then
figure out my conversion factor. Well, what do I want to go to? I want to eventually make
it to seconds. And you don’t even have to know how many seconds there are in a day.
So I do know that I could go from days to hours. I also know that I could go from hours
to minutes. And I also know that I could go from minutes to seconds. Okay. So why was
I doing that? Well if I’ve got days up here, I could put days on the bottom. I know those
are going to cancel. So now I just go back. Once I have them all laid out, I now know
that 1 day has 24 hours in it. Let’s go to the next one. And that one hour has 60 minutes
in it. And I know that 1 minute has 60 seconds in it. So now the next step is to cross out
and cancel out all of the units. So I’m going to cancel out days. I’m going to cancel out
hours. I’m going to cancel out minutes. And now I’m left with seconds. And so now using
my trusty calculator I’m going to take 12 times 24 times 60 times 60. And what do I
get is, let’s write this down here, is 1,036,800 seconds. Okay. Now if you’ve watched my podcast
on significant digits you know that this is a silly answer to write because we only have
2 significant digits in this first one. This answer can only have 2 significant digits
as well. And so I would write this in scientific notation. So that’s 1, 2 , 3, 4, 5, 6. And
so this is going to be written as 1 point 0 times 10 to the 6th seconds. In other words
that’s how many seconds are in 12 days. Let’s try another one. Because that’s one had talked
about earlier. Let me erase that. Let’s say we want to go from 55 miles per hour. So I’m
going to write 55 miles. And now look what I’m going to do. I’m going to write that over
1 hour. So this is why we use fractions. Because once we start having units over units it’s
important that you’ve written it out that way. So now what do I want to start with?
Miles and I want to end us with meters. So what I could do is I could put another conversion
factor here, I know that 1 mile is exactly 1609 meters. So 1 mile is 1609 meters. I also
know, since we’re going to seconds that I could put hour up on the top. And I could
go to minute on the bottom. And I could also put the minute up on the top and I could put
seconds on the bottom. So what do we do. We’ll let’s cross them out. Oh, first I’ve got to
come back here. So 1 hour has 60 minutes in it. And then over here 1 minute has 60 seconds
in it. So now I cross out all my values. I’m going to cross out miles and miles. I’m going
to cross out, what else? Hours right here. And hours back here. And then I’m going to
cross out minutes here and minutes here. So what do I have left? Well I have meters on
the top. That didn’t get cancelled out. And then we have seconds on the bottom. And so
now I’ve made it to meters per second. So what’s that final step? I have to actually
do the math. And so I’m going to go all the way across the top. So using my trusty calculator
I’m going to take 55 times 1609. And then I’m going to take 60 times 60 which is 3600.
And I’m going to divide that out. And so the value I get is 24.5819 . . . . So it goes
out like that. So how many significant digits do we have? Well this had 2 significant digits.
And so my answer can only have 2 significant digits as well. So let me write my answer
up here. My answer is going to be 25 meters per second. That has 2 significant digits
as well. Now one thing you might be wondering is well this has two significant digits. But
doesn’t this 1 here just have one significant digit? And the right answer is no. And the
reason why is that in a conversion we think of these conversions actually having an infinite
number of significant digits. And so we don’t have to figure those in. Because we know that
1 mile is exactly 1609. And so we don’t have to worry about ones like that. Okay. So that’s
the factor-label method. And if you always follow the steps, putting fractions to start.
Then figuring out your conversion factors. Finally crossing out the units. And then doing
the math, you should make it there. Now there are a few limitations. These work really well
if we have a constant difference. In other words there’s always 1609 meters in 1 mile.
Or there’s a constant ratio between the two. But we can’t do both of those at the same
time. In other words, when you’re converting from Fahrenheit degrees to Celsius degrees,
remember you have to take that times 9 fifths and then add 32. And so since you’re doing
two things, the factor label method actually falls apart at that point. And so factor-label
method can solve a ton of things. But it does have a few limitations. But if you always
follow those four rules then you should be good to go.
This post was previously published on YouTube.
Photo credit: Screenshot from video.