>>Hi everyone, and welcome

to the Penguin Prof Channel. Today I’m going to continue

my College Success Series with a math skills review

on dimensional analysis. So first of all what is it? Some people call this

the unit factor method. It goes by several

different names. But it actually is an

essential concept that you use in all areas of life,

really, not just science. Especially if you travel

you’ve run into this. Because you travel to

different countries that use different

currencies and different units. And you are probably

doing dimensional analysis without even realizing it. So, for example, if you travel

to one of my favorite countries, like Italy, and you do some

shopping or you do some eating, you find yourself

wanting to buy things. And wondering, well you know, how much does this

cost in US dollars? And in order to answer

that question, you’re doing dimensional

analysis. Dimensional analysis is based

on one really simple idea. Which is, that you can multiply

anything by the number 1 without changing its value. And you already know that. You can multiply anything by 1, and you get anything [laughs]

whatever that number was. No matter how big and ugly

the number, you multiply it by 1, it doesn’t change. So you’re allowed to do that. And that’s it. Now here’s the thing, you’re

used to looking at the number 1 and seeing it a certain way. But the number 1 can look

very, very different. So these are other

examples of the number 1. 2 divided by 2. 14.5 divided by 14.5. Even a penguin divided

by a penguin [laughs] — you know I had to

get that in there. Those are all equivalent

to the number 1. When you do currency

conversions and you have to look up what the currency conversion

is for a particular country that you’re going

to be travelling to. I just looked this up. We’re going to be travelling

to Peru in a couple weeks. And about 11 US dollars will

give you about 30 Nuevo soles. This is important because

that allows you to travel to countries where they have,

for example, humble penguins. So you’re going to be running

into conversions a lot. There’s a lot of other

ways to be the number 1. A dozen eggs is the

same thing as 12 eggs. So you can put those two values and set them equal

to each other. There’s 60 minutes in an hour. So you know that

that’s equivalent. In one year there’s 365 days. These fractions are all

equivalent to the number 1. And it doesn’t matter

who’s on top. So you can put — for the egg

example, you can put the 12 eggs in the numerator or the

denominator and match that up with a dozen eggs. It’s the same thing. You can put the 60

minutes divided by an hour. Or you can say 1 hour

divided by 60 minutes. Does not matter. Same thing with the

year and the days. So it’s really, really useful

to understand that no matter where you put these

numbers, you can see them as an equivalent so

that it equals 1. One of the most important

things though is that you keep track

of the units. Don’t drop the units,

because the numbers by themselves don’t

mean anything. So let’s see the power

of number 1 in action. How many centimeters

are there in 6 inches? You have to know the

conversion there. 1 inch=2.54 centimeters. So how you’re going to do this

is — this is my suggestion, is that you set up each problem

by writing down what you need to find with a question mark. And I like that because the

question mark shows you that’s what the question is. You’re going to set that equal to the information

that you’re given. And then solve the problem by multiplying the given

data and its units. This is really important

here — its units — by the appropriate unit factors. So that only the units

that you want are left. That means you’re

going to cancel out all the other units

that you don’t want. If you lose the units, you’re

going to lose the problem. You must keep the

units in there. So this question I’m going to

start with how many centimeters. Because that is what

I’m being asked. How many centimeters

are there in 6 inches? So I’m going to set

that equal to the units that I want in inches. I’m going to multiply that

by the conversion factor. 2.54 centimeters per inch. And I choose the

centimeters divided by inches, because I want inches

to cancel out. In other words, when inches

are in the denominator, and also here — this is

a numerator, remember? I can cancel them out. That’s going to leave me

with the units I want. That leaves me with centimeters. So if I do that math. And I do that 6 times 2.54, and

it’s actually divided by 1 — which doesn’t matter —

I get 15.2 centimeters. So that means that in 6 inches, that 6 inches is equivalent

to 15.2 centimeters. And that’s going to three

significant figures. Here’s another example. Express 24 centimeters

in inches. So you’re going to

do the same idea, except that this time my

desired units are different. I want inches. So I’m going to set

it up differently. So I’m going to use? inches=24 centimeters. And I’m going to use

the same conversion, but notice how I

choose to put inches over centimeters in this case. That’s because I want

centimeters to cancel out. So I have centimeters

in the denominator here. I have centimeters in the

numerator here, that realize that a whole number,

that is a numerator. Centimeters cancel and I

end up with 9.45 inches. So hopefully you’re kind of

getting the hang of that. You can use multiple

unit factors at once. And we’re going to

do this example. How many seconds are

there in two years. So I’m going to start

with what I want, how many seconds

in equals 2 years. Now I’m going to have to

somehow get rid of years and end up with seconds. And I’m going to do

that by multiplying by several different

ways of saying 1. I’m going to get rid

of years by multiplying by 365 days divided by a year. That’s 1. I’ve got to get

rid of years now by — or excuse me, days — by multiplying 24 hours

in a day — that’s 1. I’m going to get rid of hours by multiplying how many hours

there are in a minute — 60 minutes divided by an hour. And finally I’m going

to get to seconds by converting how

many seconds are there in a minute, which is 60. So if you do all the math

— and this is a big number. 2 times 365 times 24

times 60 time 60 — I didn’t need to

divide by anything, because all the denominators

here are 1. I get 63,072,000

seconds in two years. And if your instructor is like

me, you really need to convert that to scientific notation. So I’m going to make this 6.3 — I’m going to put a little

decimal point there. And I need to count how

many places I’m going to be moving this decimal. So this is going to be from 6.3, I’m going to be moving

it 1, 2, 3, 4, 5, 6, 7. So that’s going to be 6.3

times 10 to the 7th seconds. And again, I’m using

the same number of significant figures

as is appropriate. We can do another module

on significant figures at a later time if you want. So that’s the idea. And here you can use multiple

unit factors in order to get to the answer that you want. The key is going to be

hold onto those units. Because if you find yourself

multiplying by, you know, for example, 365 divided by 1,

and you don’t put the units in, that’s actually not 1 is it? That number would be 365. So if you kill the units,

you’re going to kill it. I don’t give any credit if

my students drop the units. The units are everything. So some things to know. It can be really helpful

to get comfortable with prefixes in

the metric system. Most of us in science,

we focus on kind of one side or the other. Usually in biology —

or in physiology anyway, we focus on kind of

the lower part of this. Most of you will probably

be focused somewhere here. These are just helpful in

knowing how many places over, you know, you move from

the basic unit of 1. So this would be, for example,

you know, 1 meter or 1 liter. Then you can change

your prefixes, and then very easily

indicate how many powers of 10 you’re talking about. So that’s really useful to know. It’s also useful to

have some references. Especially conversion

tables like these. You want to have

access to these. All of these conversions

are different ways of saying 1, right? So if you have a question, like how many kilograms does a

90-pound Emperor penguin weigh? You’re going to look at the

section of the table under mass. And you’re going to use the

conversions where you see pound, and then you see kilograms. So if you use 0.45 kilograms per

pound, that’s going to allow you to answer this question. How many kilograms does a

90-pound Emperor penguin weigh? This is something that of

course, everyone needs to know. Now I want you to be careful. I know that online you can get

all kinds of widgets and apps which will do the

conversions for you. And that’s great if you

happen to have access to them. But I do require my

students to be able to use the conversion

factors that I give them on an exam to do it themselves. So just be aware that you do

need to know how to do this. Once you master it, of

course, then you know, it’s easy to plug in values. If you have the power of

conversions, you’ll be able to travel and enjoy your life. And convert anything you

want into anything else. And buy your pizza. This is my favorite pizza. This is a beautiful medieval

town called Siena, in Tuscany. This is not Photoshopped. I know — people say

this picture looks fake. But it was real. I was just eating my pizza

and put it on the wall there. It was just perfect. And anyway, it was the power

of conversion that allowed me to know how much this pizza

cost in US dollars [laughs]. Oh, it’s hard to make

math sexy isn’t it? Thank you so much for visiting

the Penguin Prof channel. Please rate and subscribe. Visit on Twitter and

the Facebook page. Good luck.

Ms Penguin, you're one of the best profs ever. Please never tire of making these videos.

Oh that is soooo… full of inaccuracy I've lost hope in getting you up to date.

I'd like to hire you to tutor me in everything; how to clean a spoon, the physiology of goosebumps, differential calculus, how to correctly use a semicolon. Unfortunately for us both, I cannot afford the $430/hr rate your individual instruction is obviously worth.

Wish I could take your class!

Would it be possible to get the link to the conversion chart resource you showed in the video (9:18)? I am trying to print a copy of it. Thank you for the videos

you have a voice for narrating like no other. I could not imagine these videos with out your voice. and such a great voice it is. I thought I tell you. and the videos aren't bad either. thank you.

Who's here for stem in ltms