# Unit Conversion & Significant Figures: Crash Course Chemistry #2

2640 lumens. 1 foot.

2.3 kilograms. 9 volts. Aaah! I just closed the circuit with my tongue and

I felt all 9 of the volts. So what do all these things have in common? They’re units. Yes, but they’re also absolutely,

completely arbitrary. [Theme Music] You know who decides how much a kilogram weighs? A hunk of platinum and iridium known as the

International Prototype Kilogram or IPK. The IPK isn’t just how much a kilogram weighs.

In a very real sense the IPK is the kilogram. Every other kilogram is exactly the same as

the IPK, and the IPK is the lump of metal that decides

what that mass is. A kilogram is defined as being the same mass

as the IPK. We made kilograms up just like we made up

seconds and weeks and volts and newtons. There’s nothing about these things that makes

them them. Someone just decided one day that that was

a kilogram. Now the fact that I find units fascinating probably says more about me then it does about units, but I can talk about them all day. For example, did you know that the International

System of Units only includes seven base units and every other unit is derived from those

units? Speed is length divided by time. Acceleration is speed divided by time again,

so meters per second per second. Force is that acceleration multiplied by mass,

cause F=ma remember? Work done in joules is force multiplied by

distance. And power is work divided by time, so how much work can be done per unit of time. Makes sense. It goes pretty deep, and it’s absolutely correct to say that there are an infinite number of possible derived units, just most of them aren’t useful enough to

name. But here’s a bit of trivia for you. When I say watts or hertz, those things are just regular words. No special capitalization necessary. But Hertz and Watt, they were real people

with like last names that were capitalized. So what’s up with that? Well, getting a unit

named after you is kind of the holy grail of science. To quote Richard Hamming: “True greatness is when your name – like hertz

and watt – is spelled with a lowercase letter.” Of course when these geniuses were first piecing

together how the world works they had no idea that there were fundamental

basic units beneath it all. They were basing all of their units on arbitrary

values because, well, how could there possibly be a fundamental

amount of mass or distance. Interestingly, one of the standard base units is derived from an actual value though not a universal one. The second is 1/60th of 1/60th of 1/24th of the time it takes for the Earth to rotate a single time. That’s something, at least but it also illustrates

an interesting point. As fundamental as that seems, when you get down to the dirty details things start to get kind of cloudy. The Earth’s rotation for example is slowing

down. Does that mean that seconds should also slow

down? No. That would mess up every calculation ever. So seconds are slowly becoming less and less

based on reality. Now don’t worry. It’s gonna take forever for

the Earth to slow down noticeably. And when it does we’ll just keep adding leap

seconds to keep things balanced. But units are extremely important in chemistry

and in sciences in general, as we learned when the Mars Climate Orbiter

crashed into Mars because instructions were inputted in the

wrong units. Next time you get a B instead of an A because

you didn’t keep track of your units, just remember at least you didn’t destroy

a 300 million dollar mission to Mars. But what do I mean when I say keep track of

your units? Well. I mean watch them. Do not let them do anything you didn’t tell them to do because they’re sneaky. And a lot of chemistry is just converting

between units. So say you are in a car, and the car is going

60 miles per hour. Now right now everyone who doesn’t live in

America is like: “Boo, miles are terrible. Convert to kilometers

Hank!” Well I’ll do you one better. From a scientific

perspective, kilometers are terrible too. They’re just as arbitrary. We should use something

more universal. Like lightyears. The amount of distance light can travel in a year. And hours, hours is no fun. So let’s convert to lightyears per second.

60 miles per hour. When you say it it sounds like a whole number

with a single unit. But it’s not. It’s actually a fraction. 60

miles over 1 hour. Let’s start with the easy part. Getting to

the seconds. So first we’ve got to get to minutes. So there’s 60 minutes per hour. And also 1 hour per 60 minutes. That fraction once we have it can flip either

way. We want it with the hours on the top, on the

numerator. Why? Because we want the units to cancel. We want

to destroy the hours. We don’t want them in our units when we’re

done. And then the same thing happens again with

1 minute per 60 seconds. Now we go to lightyears. I asked Google, and there’s 1 light-year in

every 5.9 * 10^12 miles. Looking at this we see that the hours cancel

and the minutes cancel and the miles cancel. Leaving us with lightyears per second. That’s

really what matters. We’ve come out with the correct units. The rest is just hammering at the calculator

to discover that a car going 60 mph is also going 9.3 * 10^-12 lightyears per second. Now we perform an important test. The “does

this make sense?” test. And yes indeed it does because 9.3 * 10^-12

is a very, very, very, very small number. Which makes sense because when you’re traveling

in a car you’re going a very, very, very, very, very, very, very

tiny fraction of a light-year every second. Now there are probably gonna be fifty to a

hundred thousand people that watch this video. And I’m gonna guess that maybe a solid seven of you did the math along with me with your calculator out. Now I’m not giving you a hard time. That’s

just my guess. If you want to follow along with your calculator

in the future that might be helpful. It would at very least be very nerdy. But if you have been following along with your calculator, you might maybe have noticed something interesting. I said 9.3 * 10^-12. When your calculator… Your calculator probably said something like

9.3487658140029 * 10^-12. So why, when I had so many more numbers to give, did I only give two? Was I trying to save time? Well obviously not, because now I appear to

be wasting time talking about it. Do you think that it would be too hard for

me to remember all those numbers? Well obviously not, because I just did it.

So I will tell you why. When you’re doing experimental calculations, there’s two kinds of numbers. There’s exact and measured. Exact numbers are like the number of seconds

in a minute or the number of eggs in a dozen. They’re defined that way and thus we know them in effect all the way out to an infinite number of decimal places. If I say that there are a dozen eggs you

know that that’s 12. It’s not 12.0000000001 or 11.9999999. It’s 12. But that’s not true for the number of miles

per hour my car was going. That car wasn’t going 60.0000-out into infinity

mph. I only know the speed of my car to two decimal

places because that’s all I get from the speedometer. So the car could have been going 59.87390039 mph or 60.49321289 mph; the speedometer would still say 60. And no matter how well I measure the car’s

speed, I will never know it at the same level of precision that I know the number of eggs in a dozen. So that’s the second type of number, measured

numbers. Now the cool thing about measured numbers, because you never ever know them exactly,

is that they tell you two things at once. First, they tell you the number that was measured. And second, they tell you the precision at

which that number was measured. People often get their heads all tangled up

about this, but with a measured number you just have to remember that the actual number goes out to infinite decimal places, you just never know all of them. You can’t.

It’s impossible,. So when my scale says 175 lbs, that doesn’t mean 175.000000 lbs. It means 175.something lbs. And all those numbers after the five? We don’t

know them. And here’s the thing, a measured number can

be pretty unhelpful if you don’t have knowledge of the precision of the measurement. So you have to conserve the precision through

your calculations or else you might end up killing someone with

an imprecise dose of insulin or something. So we have a set of rules for what are called

significant figures: these are the digits in your number that you

actually know. With my speedometer there are two: 6 and 0. But 0 is weird, because sometimes it’s just

used as a placeholder. Like if I said that the fastest plane can

go 13,000 mph, which it can by the way. An unmanned military test glider did it in

2011. That’s not an exact number, those zeroes are

just placeholders. So when a number ends in a zero, or two or three zeroes, it’s hard to tell if those zeroes are significant. But this all gets so much simpler when you use scientific notation, which since it’s science we should. So 60 mph would instead be 6.0 * 10^1. We

get that zero is significant because we wrote it. Otherwise it would just be 6 * 10^1. We keep

that zero around because we actually know it. Scientific notation is awesome by the way,

once you get the hang of it. If you’re having trouble you can always just

type it into Google or your calculator to see exactly what number we’re talking about, but the number of the exponent just tells

you how many places to move the decimal point. So to the 1st power you move it one to the

right and you get 60. To the negative 1st power you move the decimal

point one place to the left and you get 0.60. To the fifth power, one, two, three, four, five, and you get six with five zeroes or 600,000. Of course your significant figures get preserved,

so 2.4590 * 10^-4 is 0.00024590 and you still get the same five sig figs. Now to the magic of figuring out how many

sig figs your answer should have. There are two simple rules for this. If it’s addition or subtraction it’s only the number of figures after the decimal point that matters. The number with the fewest figures after the

decimal point decides how many figures you can have after

the decimal in your answer. So 1,495.2+1.9903 you do the math. First you get 1,497.1903 and then you round

to the first decimal, because that first number only had one figure

after the decimal. So you get 1,497.2. And for multiplication just make sure the answer has the same sig figs as your least precise measurement. So 60 x 5.0839=305.034,

but we only know two sig figs, so everything after those

first two numbers is zeroes: 300. Of course then we’d have to point out to everyone that the second zero but not the third is significant, so we’d write it out with scientific notation:

3.0 * 10^2. Because science! Now I know it feels counterintuitive not to show all of the numbers that you have at your fingertips, but you’ve got to realize: all of those numbers beyond the number of sig figs you have? They’re lies. They’re big lying numbers. You don’t know

those numbers. And if you write them down people will assume

that you do know those numbers. And you will have lied to them. And do you know what we do with liars in chemistry? We kill them! Thank you for watching this episode of Crash

Course Chemistry. Today you learned some keys to understanding

the mathematics of chemistry, and you want to remember this episode in case

you get caught up later down the road: How to convert between units is a skill that

you’ll use even when you’re not doing chemistry. Scientific notation will always make you look

like you know what you’re talking about. Being able to chastise people for using the

wrong number of significant digits is basically math’s equivalent of being a grammar Nazi. So enjoy these new powers I have bestowed

upon you, and we’ll see you next time. Crash Course Chemistry was filmed, edited,

and directed by Nick Jenkins. This episode was written by me, Michael Aranda is our sound designer, and our graphics team is Thought Bubble. If you have any questions, comments or ideas

for us, we are always down in the comments. Thank you for watching Crash Course Chemistry.

my i phone calculator kept sayin 0.00000000003 or something and i was stressed cuz i wasn't getting the answer in the vid or the answer in the comments and i sepent 30 whole minutes and i started thinking OH NO WONDER I FAILED PHYSICS. then i flipped my phone vertically and got 2.8 x 10^-15

You could update this video with the new definition of kilogram

Acceleration has a better equation.

Vf – Vi

A= ————

Delta time

Delta time is Tf – Ti

I have a question regarding this problem you worked out.: 60 x 5.0839 = 305.034. Wouldn't 60 only have 1 significant figure, since there is no decimal place following it. So, then the answer would be rounded to 300?

7:11 Oh really? I would have never noticed

Omgggg this made everything so much better!!!! Thank you I understand everything so much better.

I thought 60 was only 1 sigfig? not 2?

omg i think i love you lol

The addition (@9:40): (1495.2 + 1.9903) = 1497.1903, but becomes 1497.2 because of 1st decimal place precision. (One sig-fig?).

The multiplication ( 60 x 5.0839 ) = 305.034, but because of "two sig figs", becomes 300, then 3.0 X 10^2.

My question: Why did the first calculation ROUND to the required number of Sig figs, but the multiplication did not? (i.e. became 300, not 310.)

I'm I the only one does understand chemistry, I don't know why because i really understand your biology from the first time i watch it, I'm really getting pissed off

how do i even study this course

My chem teacher every day

10:28

6:53 – Hank, why don't u just look where u are going & stop staring at me like that with the creepy background sound ???

the 9.3 is wrong

10:05 i thought 60 has only 1 sig fig?? 🙁

Hank in 2013: "maybe 50-100k views"

2019: 2.7M views

Tells everyone not to run away from Chemistry in the first episode. And says, "do you know what we do with liars in Chemistry? We kill them" in the second episode. Well, THAT escalated quickly,,

The IPK doesn't define the Kilogram anymore

*Previous definition*: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

*2019 definition*: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.

Lmao I love this video

I came here for math…

Hank is 175 pounds LOLOLOLOLOL

My brain died after 8 minutes.

Shouldn't 305.034 be rounded to 3.1 * 10^2? 10:00

I have spent hours doing this problem over and over. 60mph is equal to 2.83*10^-15 ly/s someone smart plEASE CONFIRM

(3:01) That's not what I'm… okay fine. Leap seconds'll do it.

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Because science!!!!

Hank, my awe and pleasure!!!

Ha he said he thought 100,000 people would be probably watching this… YouTube says 2.4 million

I was revising my notes while watching this and the end made my heart stop

omg can you talk in human pace too?

Around 5:30 he says that roughly 50-100,000 people will watch this video. Try over 2 million

How did no one ever teach me how to use significant figures properly

Did not expect that ending

Cool fact "Henry" is an SI unit of Inductance 🙂

Very cute.

Lying dogs because there are actual dogs laying around

Omg please become my teacher, I LOVE YOU!! You're just so entertaining and make it all so easy to listen to!!! I've never enjoyed chemistry so much in my entire life!! Hopefully, I'll be able to get ready for my medicine entrance test thanks to your lessons!

10:30 he said that so sincerely…?

yes yes yes yes. I used hank all of last year to get through bio and I just stumbled upon CC chem. First test is coming up on unit conversions and I was so confused. Not anymore.

my man is not 175 pounds. he looks like a slim Jim lol. much love Crash course you help a lot!

Yay we passed the 7th grade

i thought 60 has 1 sig fig. and the answer would be 3×10^5

I just want you to know I show this every year just to watch my students faces when you tell them we kill liars. Priceless. lol!

Dear Hank, I made my whole class do the math in this video.

0:35 IPK is no longer kilogram definition by the way, it is now derived from plank constant and speed of light so it is defined by the universe.

sorcery

For those in the audience who went to a HS where advanced math (algebra and above) was an elective only afforded to students who were not suspended much of the time – I was hoping you spent more time expanding on the 7 measurements starting around 1:30 or so. I tried to write the equations down so I could apply them but the letters made no sense.

"Next time you get a B instead of an A…."

Gee, I was also wondering that when I got a B instead of an A in US History. Oh well. At least I passed Junior Year

Who even is this video for? I dont think you really hit any target audience with this one, its so basic and barely teaches anything on many subjects

You know what we do to liars in chemistry? we fail them

Still confused what an IPK is?

10:27 Now that got dark…

HELP so I got this question and I ended up having to put 4300 in 3 sig figs but I can’t use scientific notation…any advice?

Didnt help me, it went too fast

your shoulders are too big for your head so it looks like your a puppet

I hate to say this about a CC video, but this one isn’t helping me at all. I’m not sure what to do here.

the ISU is the measurement system used officially by scientists; the reason the Imperial System (English Units and US customary units) is still being used by the average public and institutions of only few countries is just because of force of habit. It is more than known that the metric system is elegant, accurate and based on universal physical standards.

Somehow I can't believe that a chemistry video is helping with my construction math class class

So…. I put in your calculation at the 5:00 mark of the video and got a different answer than yours (I got 2.8 x 10^-15).

This is after typing in the calculation multiple times on 2 different calculators.

I then asked Google to convert 60 mph into light years per second and received the same answer as my calculations (2.835 x 10^-15).

Can someone please explain how you got the answer 9.3 x 10^-12 because I'm confused.

50-100k people watching this video? Wrong by a lot Hank. Millions in fact.

Say goodbye to the IPK, it's the planck constant now

10:04 60 only has one sig. Fig.

Hank: "Now there are probably gonna be fifty to a hundred thousand people that watch this video."

Youtube: 2,834,220 views

?

Hank Green does a better job of explaining things than my actual chemistry teacher, part 1.50 x 10^15

What are units anyways, and how do they work? 0:30

Unit Conversion 3:26

Scientific Notation/Precision of Measurement/Significant Figures 5:36

Lmao he thought only 50-100k idiots would watch this video but turns out almost 3 million did. Also anyone 2019 gang?

I got the calculation of the car as going 2.8×10^-15 is this correct, or can someone explain how he got to 9.3×10^-12 which seems waaaay too fast!

I'll remember that next time when I fail my test: "At least you didn't fail your mission to Mars" lmao

Hey i just discovered this channel and i think iys awesome. Quick question about the rules for the lying figs. In his example for multiplication he used the equasion 60 × 5.0839 = 305.034 however since our least precice number was 60 we then turn everything after the first two figs in our answer to zero making our answer 300.000. I was just wondering why it is that we do not know so to speak about the 5.034 and we should get rid of it. It just seems like when making calculations its a lot to leave out of your answer and im just wondering why it is better to convert it to zeros instead?

Sooooo technically it would actually be 9*10^-12 because according to significant figures the 0 isn’t trapped in the decimal, technically. Because you only get 60mph not 60.mph So technically speaking it would actually just be 9*10^-12

We kill them

5:00 The result is wrong. It should be 2.8351×10^-15

okaaaaay that was the best science video ı have ever watched!! thank you !! 🙂

THANK U I WILL WATCH

Whoa

Because science

Dude just get to the point!

I think you guys should link the scishow video where the new definition of the kilogram is discussed.

You thought there would only be 50,000 to 100,000 people who would watch this video? You are currently at over 2,800,000!

"there are probably gonna be 50 to a 100 thousand people watching this video"

Have you done physics

is this a maths class or a chem class ? maybe both . excellent !!!!

I love that you give us the reason behind all the units before jumping into the hows of it all. It makes everything much more interesting. Thanks man!

“Being able to chastise people for using the wrong number of significant digits is basically math’s equivalent to being a Grammar Nazi.” ??

Kilogram is not based on IPK anymore tho *they updated it just this year

9:55 shouldn’t it be 310 instead of truncating the number? ?

i love him???

hurray for significant figures

"True greatness is when your name- like Hertz and Watt- are spelled with a lowercase letter"

Me: Hank green…John brown….

how can such a smart guy be using apple lmao

I love this series. Thank you!!!

Could you try my creation, thanks! Spot: androidcircuitsolver/app.html

50-100K

2.8M!!!!!!

The math is wrong: 60 mph in light years/second is actually 2.83513 x 10^-15 while 9.3 x 10^-12 light years/second is actually 196,816 mph.

Yeet

I am so confused on the speed the car goes in light years I got SO MANY different answers

I'm giving this channel a shout out when I graduate college

I kinda hoped that you had pointed out the difference between sidereal and synodic day and the fact that a second hasn't ever been 1/86,400 of Earth's rotation time. But then again, the class is about chemistry, not astronomy.

As a mathematician as well as a scientist, I now know the reason why I hate myself.

so there are probably gonna be fifty to one hundred thousand people watching this video

2,800,000 million views

like if your in 2019

this video could’ve easily been 2 minutes at the most why did u have too talk so much like i just skipped through it at because of all the talking, the video didn’t help a bit