# Converting Units with Conversion Factors

In this video, we’re going to look at how

to convert units using conversion factors like this and canceling units. Some people

call this dimensional analysis, some people call this the factor label method but you

are going to call it easy by the end of this video because we’re going to go step by step

to show how to solve these kind of problems. So, here is our first one. We want to know,

what is 3.45 pounds expressed in grams? So the conversion that we’re going to be doing

is we’re going to be doing pounds to grams. We’re going to be starting with 3.45 pounds.

Okay, the next thing we got to do is we got to go and we got to find some kind of relationship

between pounds and grams. So how many pounds are there in how many grams? You can find

this information on the internet, you can find it in a textbook, you can probably find

it like in the back of a notebook where they’ll have a conversion table for the units. It’s

going to look something like this. You got a bunch of relationships between different

units and you want to find the equation that talks about pounds and grams. Okay? It’s going

to be this one down here, 1 pound (lb)=453.6 grams (g). So this is the statement that you’re

going to want, you can get it from a variety of places but it’s important. Now, it doesn’t

matter whether pounds or grams is first, it can be flipped just as long as it has both

pounds and grams. So now, we have this statement that tells us how pounds relate to grams.

We’re going to use this statement now to write two conversion factors. A conversion factor

is expressed as a fraction with a top and a bottom so here’s how we can take this and

write a conversion factor. We’re going to take this side of the equation, 1 pound and

put it on the top of the fraction and there’s a fraction line and then this part equation

of the equation… it’s going to be on the bottom so it’s going to be 453.6 grams. And

now that’s one of the two conversion factors. The other conversion factor that we’re going

to write is… we just take this and we flip it… so this 453.6 grams we put that now

on the top of the fraction and divide it by 1 pound. So two conversion factors that you

can write from the statement here, either one of them is correct but only one of them

is what we want to be using here. Okay? So we’re just going to use one of these. The

one that I’m going to use is this one because pounds is up here and pounds is down here.

Let me tell you what that means. So 3.45 pounds, that’s not a part of a fraction, right? There’s

no fraction line here and so if something does not have the bottom of a fraction you,

just assume that it is the top of a fraction it is the same as it being on the top of a

fraction if it doesn’t have a bottom, that’s what I mean. Now on the other hand, pounds

is down here on the bottom of the fraction, okay? And when we’re using conversion factors,

we want to get rid of pounds and want to be left with grams. And it turns out if the unit

is on top, on one side of the multiplication sign, and then it’s on the bottom, on the

other side of a multiplication sign, it cancels out. So pounds is on top here, pounds is on

bottom there, so they both cancel out and that leaves me with units of grams. So just

to review, I wanted to use this version of the conversion factor because pounds was on

the bottom and this way pounds will cancel out. Now I’ve cancelled out pounds, I’m

ready to do the math. What’s it going to be? I’m going to do 3.45 times 453.6 divided 1.

Or if you have a fancy scientific calculator, you can plug this whole thing in one expression.

You can do 3.45 times… and then write this conversion factor in parentheses (453.6 divided

by what?). You don’t really have to worry about 1 too much if you don’t want to. I’m

just putting it in there because sometimes this won’t be a 1. So I just want you to get

used to dividing by whatever is on the bottom of the fraction even if it happens to be 1

in this case. So however you decide to plug this in your calculator, when you crank through

it you’re going to get the same number and that’s going to be 1,560. What are the final

units here? Well I cancel out pounds so the final units I’m going to be left with are

grams. And not worrying too much about significant figures when I’m doing these unit conversions

just for this lesson because I don’t want to add another thing in here to confuse you.

There will be a lesson later about how to do significant figures with unit cancellation

but I don’t want you to worry about sig figs now, just worry about figuring out how to

do the unit conversions. So anyway, 1560 grams is our final answer, let’s do a couple more.

How many miles is 15,100 feet? The conversion we’re going to be doing in this problem is

for units of feet into miles. We will be starting with 15,100 feet. We got to go to our unit

conversion table or find information on the Internet to figure out what the relationship

is between miles and feet. We got it right here so this is going to be the statement

we’re going to use to write our conversion factors. Let me pull this off the table here.

Now don’t freak out that miles is on this side and feet is on this side. It doesn’t

matter what unit is on what side of the equation because you can just easily flip it, okay?

You don’t care what unit is on what side of the equation, all you care about is being

able to have this so you can write the conversion factor. So let’s write the two conversion

factors that we can get from this statement. I’ll take 1 mile and I’ll put it on top here

and I’ll take the other side, 5,280 feet, and I’ll put that on the bottom. And I’ll

write what we could call the reciprocal of this, where we take it and flip it up so that

5,280 feet is on the top and 1 mile is on the bottom. We’re going to be multiplying

our measurement in feet by one of these two conversion factors. Which one is it going

to be? We have feet not as part of a fraction, so you assume that feet is on the top of a

fraction, it’s the same as if it’s on the top of a fraction which means that we

are going to want a conversion factor that has feet on the bottom of a fraction so they

cancel out. So it is going to be this one here. And now, feet on the top and feet on

the bottom cancel out and they leave me units in miles which is what I’m looking for here.

Now how do I do the math? I’ll do 15,100 times 1 divided by 5,280 because it’s on

the bottom of the fraction or if you can plug larger expressions into your scientific calculator,

you can do 15,100 times and in parentheses you can do one divided by 5,280. Again you

might wonder why you have to keep doing the 1, you can leave the 1 out if you want to

but remember this isn’t always going to be a 1 so it is a good thing to get in to

the habit of multiplying by whatever is on the top of the fraction and then dividing

by whenever is on the bottom of the fraction even if it’s 1 for right now. You can do

either one of these expressions and you’re going to end up with an answer 2.86. Units

are in miles. Again, I’m not really paying attention to significant figures for these

calculations. That’s how you do this, let’s do two more problems so you really get the

hang of this. This problem is about units of money. On a certain day, the exchange rate

between the US dollars and Euros is 1 US dollar equals 0.78 Euros. On that day, how much is

125 Euros worth in US dollars? So we will be going from Euros to US dollars here, starting

with 125 Euros and the question gives us this relationship between dollars and euros which

I write it in bigger letters here. In the two previous problems, I took this statement

and I wrote two conversion factors top and the bottom but I flip the top and the bottom.

What I’m going to do here though is I’m going to look at what I’m starting with I’m

just going to write the one conversion factor that I need, okay? So I’m going to take

125 Euros and what do I want to multiply that by to cancel out Euros? I’m going to want

the version of the conversion factor that has Euros on the bottom so they’ll cancel

out. So I’m going to take this thing that has Euros, 0.78 Euros and that will be on

the bottom which means that then this 1 US dollar will be on top. See you don’t always

have to write out both of the conversion factors, you can figure out which of the two you need

based on what should be on the top and what should be on the bottom. Now, Euros up here,

Euros down there, they cancel out which leaves us with dollars which is good because that’s

what we’re looking for and the math is going to be 125 times 1 divided by 0.78 or 125 times

(1 divided by 0.78). This is going to give us 160 US dollars so the dollar is doing pretty

well compared to the Euro on this day. One more. How many liters is 23,500 milliliters?

These are both metric units and you know a lot of times people ask me this unit canceling

method, can I use it for metric units? Of course, you can use it for any type of units.

All you got to do is figure out what the relationship between your two units is. So we are going

from milliliters (mL) to liters (L) and you may already know this but there is 1000 milliliters

(mL) in 1 liter. That’s what I mean, this is all you need. You can convert any two units

that you want just as long as you know the relationship between them. So we have this

here for liters and milliliters. So 23,500 mL… which conversion factor am I going to

want to use here? Since I want to get rid of milliliters, I want to use a version of

this that puts milliliters on the bottom. So I’ll put 1000 mL down here so that they’ll

cancel out so that means that I’ll put 1 L on the top. Cancel, cancel, I’m left with

liters so this is going to be, I’m not even going to write it out because I think you’re

getting the hang of it, it’s going to be 23,500 times 1 divided by 1000 which is going to

be 23 .5, final units are in liters. So that’s how you can convert from one unit to another

by setting up your conversion factors and canceling your units. So where do you go from

here? There are two more videos that may be of interest to you. The first is to show how

to string multiple conversion factors together because you don’t just always have to use

one. Here I’m converting from days all the way to seconds by setting up a bunch of conversion

factors where all the units cancel. So I’ll show you how to do that in one of the next

videos and then another video you might want to watch is about understanding unit conversion

where I talk about the rationale, the reasoning behind why you set up conversion factors the

way you do, why the units cancel, and how this relates to things you might be able to

more easily understand.

Thank you!!!!! I completely understand what is going on now

You really helped me out 🙂 Thanks so much! I have more confidence that I will ace my test on Tuesday :)))

sha

How is it 160 usd? I got 97.5

Thanks so much man!

shout out to tyler, who taught me when my teachers wouldn’t

Before watching this video I was a sobbing wreck of a human being because I didn't understand this concept at all. I finally get it now, thank you SO much.

for the conversion factors, would you get the same answer if you switched the two? for example, 1 mile = 5,280 ft. what if you were to use 1 ft = 0.000189394 miles?

Finally, I can do my homework. Love you man no homo

Now i get it

To all the students here Les chat pls, related studies of course but still Les chat!!

yeet

Soon as he called it easy I just felt like my mom was giving me a hug, I've never felt so confident and relaxed

Edit: failed the test 🙁

Will I need to memorize the conversions chart?

Do you have a video that shows measuring units in both metric system and English system? I have a problem that contains both metric and English system. I don't know how to get from the metric system to the English.

Thanks for making Chemistry soooo much more fun to learn.!

Are you somehow related to a certain female teacher in the 8th grade by the name of JoAnna DeWitt?

2 hour class on conversions at school, still don't understand anything. 12 min video with Tyler i understand everything.

Straight Forward, and Brief! Excellent video!

This guy is the best

YAYAYAY now I understand

you sound like seth green. also, thank you.

When I watch these videos i just see how much I'm over thinking it

You are truly gifted. Your videos are a big help to me thank you so much

My teacher is so bad that when she teaches she does the problems wrong and then after we write it down she’s like “OH WAIT I DID IT WRONG” and she confuses everyone by doing this and then she’ll be like “OH I FORGOT TO TELL YOU SOMETHING” and goes back to something we did 20 minutes ago and it confused us even more. And then she asks for the answer to a problem and nobody says anything because she can’t teach

Love u man thank u

ok for the first problem you did with the 3.45 x (453.6/1) isn't 1560. no matter how i redid the problem my answer was always 1564.92 > 1,565. i'm just curious of how you got that answer because i did not

Thank you so much! I am SO ready for my Engineering Unit Test :)))

How come when I computed 3.45 X 453.59 it equaled 1564.885 or 1565 and not 1560?

Loved it you're my angel during my exams and lessons ??

Can you please be alive forever? World needs teachers like you!

Good teacher

Thank You

Great guidance for teaching students with learning disabilities

on the last problem, I got 23 not 23.5, did I do something wrong?

I know this is irrelevant but last term I got an A in chemistry because of you!!!!!!!!!!!!????????????

omg thank youuuuuu!

(2:57) All numbers are fractions. All numbers have an invisible 1 in the denominator. For example, 3 is the same as 3/1 and 4 is the same 4/1.

on families im from the P

You are awsome! I get it now. Thanks!

I love you.

How was it doing pretty well when a dollar is cheaper than a euro? You have 160$ and you go to France, do the exchange and get 125 euro…. means that dollar is doing pretty not that great.

the 3.45×453.6/1 is 1564.92 how did you get 1560?

This video, like the others, is just so good. Previously mystifying concepts become sensible and easy. Love the opening line "some people call this dimensional analysis, some people call this the factor-label method, but you're going to call it easy" – ha!! Great!

Thank you!!!

My teacher didn’t teach this good at all omg

this guy is amazing

2018 Anyone ?

he just condensed a 3 hour lecture of confusion into 13 minutes of A+ 🙂

he is good

I swear my teacher teach things by jumping to the end of the video and be like " oh why dont you understand

Your awesome dude!!! Thanks!!

I swear to God, I need you as my teacher……for life, bro!

thank you knockoff milo yiannopolous

WOW!!!! Thank you Thank you Thank you!!!!! you have just made this so easy to understand. You are great at what you do. Please don't stop.

You are the inspiration for many student god bless you

i swear he is a god

this dude is awesome

Thank you! Thank you! Thank you! I think the biggest mistake that teachers make is assuming that students already know certain things. I am doing an online course which does not have any math prerequisites yet they explain this stuff as if everyone is a mathematician. I haven't studied math in more than 10 years so it was a struggle until I found your lectures.

Why… Why…. WHY

Thank you ‼️‼️

This guy kicks ass!

Awesome intro…lool

tyler

am really appreciated your nice teaching , May God be with you in any temptation

best lessons god bless u

y'all might use this later in life. I did when I converted from inches to yards I believe for being a new piece of table cloth.

Please make a video on 'equivalent weight and n-factor in redox reactions'

here for my bio class

you are the LITERAL bomb.com !! thank you!

For the last question, if I were to use significant figures would the answer be 20?

Thank you for the lesson!

he looks like peter pan ?

This was sooo helpful!!! Thank you so much!!

Thank you, This made metric conversions really understandable. .

Thanks man, what a life saver!

I found a better idea

loads gunHello Sir deWitt (sounds dutch). Could you bundle up alll your vids and sell it. I know its free but I want my own Tyler DeWitt chemistry/physics/biology dvd bundle. I would pay for it. Lets say $5.99. Make your sell accessible for the world, because I live in the netherlands. Because if youtube stops working one day. I dont mind. Because my dvd is right there in de cupboard. Smiling at me?. (This is NOT a joke)

Who would bye his dvd, or blu-ray or the link to download everything?

I have a chem test tomorrow and this is helping so much omg

Wow thank you so much. I finally understand. My chemistry professor is terrible at explaining anything. I was so lost and confused

Thank you soooo much for this !!!!!

It’s 2019 and your videos still make a HUGE impact on student’s lives.

Who tf uses pounds anyways

I liked this video it helps me learn more on my study

Thank you for existing.

My AP chemistry teacher won’t let my class use a conversion chart. She said she wants us to remember it. Any suggestions or tips to remembering? Even thought it sounds impossible ??♀️

3.45lb x453.6g= 1564.92 How did you get 1560 grams?

You have saved my life and grades so many times! THANK YOU!!!!!

I used my calculator in the first problem n i got 1564.92 ??

My teacher sucked at teaching this cus you can’t pause them wen you want to or go back thanks

I love this guy, like seriously. I only understand things when you explain it. Thank you!