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.

I seriously hope you don't underestimate just how helpful your videos are. Thank you very much and I appreciate everything you do.

Mr Mahlum brought me here

Because of this I am going to pass chemistry! Thank you so so much for posting <3

Thank u sooooo much

Thank you so much, Mr. Anderson! Honors Chemistry was kicking my butt not even 2 weeks in, but your videos on Sig Figs and the Factor Label Method have helped me so much!

Wow, this actually makes sense.

I wish you my teacher were like you and explained slow enough for me to understand!

this seriously helped me pass my chemistry test. thank you for the podcast!

Thank you so much. 🙂

I'm a student at NIU and because of my teachers accent I find lectures very hard to follow….Im so thankful for this video!!!!!

you forgot some commas in ur numbers <3

i missed the day we got the lecture over this. and the next day i came in and the teacher toled me one on one how to do it and i was ok with the simple 1 conversion but i could not do the 2 or more but now i can. and all i can say now is thank you

THANK YOU SO FREAKING MUCH!!!

Holy cow I am going to pass because of you man!

THANK YOU SO MUCH

you're the reason I passed phyics and am passing chemistry

Thank You!!! This helped me so much!

Hi

helps with homework so much. thanx man. keep up the good work!

i missed two continuous days of class and even after watching multiple videos i couldn't figure this stuff out. thank you for your video, because this is the one where everything finally clicked

This makes much more sense then the jibberish my science teacher was teaching us.

Stupid trolls disliked this.

With all the conversions from days into seconds, I couldn't help, but think of the RENT song. Thank you, Mr. Andersen!

Thanks, really informative!

Wish you were my teacher.

sig figs are so stupid and so is metric

I have a question about significant digits: Wouldn't the number of hours in a day be a constant, i.e. a real world value, and therefore have an infinite number of significant figures? I am referring to 24 hours in a day used in the video. You would need to defined the number of significant figures you are expecting in the response, correct?

is this john green

"some people refer to it as common sense" lol nice one

Who got sent from Kelleys class?!

Big help. Used this video before one of my chemistry tests, and it helped so much more!

thanks this is really helpful

Mr Anderson is the best Mr Anderson

did you have a glass of wine before making this video :^D

can you go from a smaller unit like seconds to a bigger unit like days

at 7:50 what did you multiply to get the answer? no matter what i multiply i cant do that, you also said something about dividing it. what am i doing wrong?

how did miles go to minutes?

your scientific notation was wrong you said 12 days=1036800 or 1.0*10^6 the 3,6 and 8 are significant numbers so it would be 1.0368*10^6

Teacher why are you making me watch this I know how to do basic algebra.

Could you also write the last question as 2.5 m/s x 10^1? Thank you!

HELPFUL

saw you for ap bio. Now I m using you for ap physics!

Am I the only one who still doesn’t understand this ???

It is found that most interesting channel is 'laat maar sadness ko'

My name is NEO

Class!