The Factor-Label Method


Mr. Andersen shows you how to use the factor label method to solve complex conversions.

Transcript Provided by YouTube:

00:00
Hi class. This is Mr. Andersen. Today I’m going to show you how to use the
00:03
factor-label method. Some science teachers refer to this as dimensional analysis. And
00:08
some people just call it common sense. And so what is the factor-label method? The factor-label
00:13
is the way that you solve a problem. And so there’s a nice method you can use to do that.
00:19
And so if I were to for example to ask you how many hours are there in a day? That thought
00:25
process you go through of remembering that it’s 24 hours in a day is actually a simple
00:29
for of the factor-label method. So what we do with that is we take a value, let’s say
00:34
55 miles per hour. And we’re going to convert that to a different unit, like meters per
00:38
second. This becomes really important in chemistry, physics, physical science, because you can
00:43
solve these very complex problems. And as long as you follow the methods that I lay
00:48
out in this podcast you should be good to go. Now an analogy or a good way to think
00:54
about how this works is what’s called six degrees of separation. So there’s a scientist
00:59
back in the 1940s I think it was who said, let’s say we have a person here who lives,
01:04
we’ll say in New York City. And then we have a person who lives way over here. Let’s say
01:09
they live in Montana. He said that we could take any two people and we could connect them
01:14
with at least six degrees of separation. In other words this guy might be friends with
01:19
this guy. And this guy might have a sister who is this person right here. Who might have
01:26
a friend who is this person. Who also has a friend who knows this person. And so the
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idea is that you’re connected to anybody on the planet by no more than six degrees of
01:38
separation. There’s a funny game with movies and using Kevin Bacon. It’s called six degrees
01:43
of Kevin Bacon that uses movie trivia to kind of do the same thing. But again that’s just
01:49
kind of an analogy. So what do we do in this? Conceptually we’re taking a quantity. So let’s
01:55
say that is miles per hour. And we’re going to convert that to something like meters per
02:06
second. And so all of these questions will start with some kind of quantity. And then
02:13
we’re going to end up with a desired quantity. But you have to use your brain to figure out
02:17
what kind of conversion factor we’re going to use. In other words, what are some important
02:21
things if we’re going from hours to seconds. How are you actually going to convert that?
02:25
Or miles to meters. We’re going to have to know some kind of a conversion to make it
02:30
from that given quantity to the desired quantity. Okay. So this is my method. And there’s lots
02:36
of different methods laid out to do the factor-label method. But if you follow these steps you
02:41
can solve pretty complex problems. So let’s start with one that’s really really easy.
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And let’s say we say that you’ve got one day and you want to convert that to hours. So
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what is the first step? You start with the given quantity. And you always express it
02:58
as a fraction. And so even though one day doesn’t need to be written over one, let’s
03:03
just do that. Because it’s going to all you to solve the problems. Lot’s of times you’ll
03:07
actually have units over units. And so it makes it easier. Okay. Next we’re going to
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convert with a conversion factor. Okay. So what does that mean? We’re here with days.
03:16
But we want to eventually make it to hours. And so what I’m going to do is I’m going to
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write days underneath and I going to write hours on the top. So first we insert the conversion
03:26
factor. Then we add our numbers. Well we know that one day is 24 hours. So what’s next?
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We cancel the units. This is a day on the top. So I’m going to cancel that out. And
03:38
here’s a day on the bottom. And so I’m going to cancel that out. And then the fourth step,
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what I do is I actually solve the math. And so I’m going to multiple across the top. 1
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times 24 hours is 24 hours. Now I’m going to multiple across the bottom. 1 times 1,
03:54
we lost the day, is 1. And so my answer equals 24 hours. Now you could have just done that
04:01
in your head. But if you followed these steps on all of the problems we work with on factor-label
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method, you’ll do fine. So let’s do a couple of practice ones. So let’s say we start with
04:11
this. I’ve got 12 days over here. So I’ve got 12 days. So I write that over 1. I then
04:19
figure out my conversion factor. Well, what do I want to go to? I want to eventually make
04:24
it to seconds. And you don’t even have to know how many seconds there are in a day.
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So I do know that I could go from days to hours. I also know that I could go from hours
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to minutes. And I also know that I could go from minutes to seconds. Okay. So why was
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I doing that? Well if I’ve got days up here, I could put days on the bottom. I know those
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are going to cancel. So now I just go back. Once I have them all laid out, I now know
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that 1 day has 24 hours in it. Let’s go to the next one. And that one hour has 60 minutes
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in it. And I know that 1 minute has 60 seconds in it. So now the next step is to cross out
05:13
and cancel out all of the units. So I’m going to cancel out days. I’m going to cancel out
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hours. I’m going to cancel out minutes. And now I’m left with seconds. And so now using
05:23
my trusty calculator I’m going to take 12 times 24 times 60 times 60. And what do I
05:32
get is, let’s write this down here, is 1,036,800 seconds. Okay. Now if you’ve watched my podcast
05:46
on significant digits you know that this is a silly answer to write because we only have
05:50
2 significant digits in this first one. This answer can only have 2 significant digits
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as well. And so I would write this in scientific notation. So that’s 1, 2 , 3, 4, 5, 6. And
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so this is going to be written as 1 point 0 times 10 to the 6th seconds. In other words
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that’s how many seconds are in 12 days. Let’s try another one. Because that’s one had talked
06:16
about earlier. Let me erase that. Let’s say we want to go from 55 miles per hour. So I’m
06:23
going to write 55 miles. And now look what I’m going to do. I’m going to write that over
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1 hour. So this is why we use fractions. Because once we start having units over units it’s
06:35
important that you’ve written it out that way. So now what do I want to start with?
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Miles and I want to end us with meters. So what I could do is I could put another conversion
06:44
factor here, I know that 1 mile is exactly 1609 meters. So 1 mile is 1609 meters. I also
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know, since we’re going to seconds that I could put hour up on the top. And I could
07:02
go to minute on the bottom. And I could also put the minute up on the top and I could put
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seconds on the bottom. So what do we do. We’ll let’s cross them out. Oh, first I’ve got to
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come back here. So 1 hour has 60 minutes in it. And then over here 1 minute has 60 seconds
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in it. So now I cross out all my values. I’m going to cross out miles and miles. I’m going
07:28
to cross out, what else? Hours right here. And hours back here. And then I’m going to
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cross out minutes here and minutes here. So what do I have left? Well I have meters on
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the top. That didn’t get cancelled out. And then we have seconds on the bottom. And so
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now I’ve made it to meters per second. So what’s that final step? I have to actually
07:48
do the math. And so I’m going to go all the way across the top. So using my trusty calculator
07:53
I’m going to take 55 times 1609. And then I’m going to take 60 times 60 which is 3600.
08:02
And I’m going to divide that out. And so the value I get is 24.5819 . . . . So it goes
08:15
out like that. So how many significant digits do we have? Well this had 2 significant digits.
08:21
And so my answer can only have 2 significant digits as well. So let me write my answer
08:24
up here. My answer is going to be 25 meters per second. That has 2 significant digits
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as well. Now one thing you might be wondering is well this has two significant digits. But
08:38
doesn’t this 1 here just have one significant digit? And the right answer is no. And the
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reason why is that in a conversion we think of these conversions actually having an infinite
08:49
number of significant digits. And so we don’t have to figure those in. Because we know that
08:53
1 mile is exactly 1609. And so we don’t have to worry about ones like that. Okay. So that’s
09:00
the factor-label method. And if you always follow the steps, putting fractions to start.
09:05
Then figuring out your conversion factors. Finally crossing out the units. And then doing
09:09
the math, you should make it there. Now there are a few limitations. These work really well
09:15
if we have a constant difference. In other words there’s always 1609 meters in 1 mile.
09:21
Or there’s a constant ratio between the two. But we can’t do both of those at the same
09:26
time. In other words, when you’re converting from Fahrenheit degrees to Celsius degrees,
09:33
remember you have to take that times 9 fifths and then add 32. And so since you’re doing
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two things, the factor label method actually falls apart at that point. And so factor-label
09:42
method can solve a ton of things. But it does have a few limitations. But if you always
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follow those four rules then you should be good to go.


This post was previously published on YouTube.

Photo credit: Screenshot from video.