# Unit Conversion the Easy Way (Dimensional Analysis)

Learn Unit Conversion the Easy Way The method that we will be using to convert

between units is known as dimensional analysis or the factor-label method or even the unit-factor

method. But what we call it really doesn’t matter. What matters is the fact that this is a versatile

and powerful problem solving technique. So, let’s just do this. We’re going to start with a simple unit

conversion problem. A weightlifter can lift 495 lbs. How many kilograms is that? In order to solve a unit conversion problem

like this, we first need one more piece of information: the conversion factor. For pounds and kilograms, the conversion factor

is 1 kg equals 2.2 pounds. Now, we’re ready to solve this. The first thing you should always do is write

down the quantity that you want to convert. This is the number from the question, not

the conversion factor. Please also include the units. Next, we are going to multiply this number

by a fraction. Inside the fraction we are going to write

the two numbers from the conversion factor. But, how do we know which one goes on the

top, and which one goes on the bottom? To answer that question, all we need to do

is look at the units, which is why we always include the units in the calculation itself. The quantity we are starting out with has

the units of pounds, so we take 2.2 pounds from the conversion factor and write it on

the bottom. Next, because we want to end up with kilograms,

we take 1 kg from the conversion factor and write it on the top of the fraction. Notice that now, the pounds that we started

out with cancel out with the pounds on the bottom, and the units we have left on top

are kilograms, which is exactly what we want to convert to. The only thing left to do now is plug the

numbers in our calculator. You could, of course, put this in your calculator

exactly the way it appears here…but maybe you don’t have one of those fancy calculators

that can do fractions, or maybe you’re like me, and you just want to find a short cut. Because the number on the top of the fraction

is 1, this becomes a simple division problem. In your calculator, type 495 divided by 2.2,

and your calculator should tell you the answer is 225. Our final answer, therefore, is 225 kg. There is one more thing that we should notice

about this problem. The fraction, 1 kg over 2.2 lbs. actually

equals one because 1 kg equals 2.2 pounds. In fact, any time we do unit conversions,

we are simply multiplying our initial quantity by a conversion factor fraction that equals

one. Okay, now that we are experts at this technique,

let’s try a slightly harder problem. A certain car has a mass of 1920 kg. How many tons is that? Just like always, we need the conversion factor

before we can solve this, but this time we need two conversion factors: one to convert

from kg to lbs., and another to convert from lbs. to tons. So, this is going to be a two step problem. We start the problem by writing down the quantity

from the question, 1920 kilograms, and then we multiply this by a fraction. The two numbers that go in the fraction come

from one of the conversion factors, but what goes on the bottom? Because we are starting with kilograms, we

write 1 kg on the bottom of the fraction so that we can cancel out the kilograms. Next, the other half of that same conversion

factor, 2.2 lbs. has to go on the top. The kilograms cancel out leaving us with pounds

as the units of our answer. When you do the math in your calculator, simply

multiply 1920 by 2.2. This time we are multiplying the numbers because

the 1 of the conversion factor is on the bottom of the fraction. Our calculator tells us that the answer is

4224 pounds…but, we’re not done yet. We still need to convert the pounds to tons. The second step works exactly the same way. First, we write down the number that we want

to convert, that is 4224 pounds, and then we multiply this by a fraction. We want to have pounds in the denominator

of the fraction so that we can cancel out the pounds. But which pounds do we choose? 2.2 pounds or 2000 pounds? Remember that we want to convert to tons,

so choose the conversion factor between pounds and tons. We write 2000 lbs. on the bottom, and 1 ton

on the top. Our pounds cancel out, and we are left with

tons for the units of our answer. In our calculators, we type 4224 divided by

2000 because the one is in the numerator of the fraction. Our final answer works out to be 2.11 tons. If you are following in your calculator and

wondering why I rounded my final answer, the reason is that I should have only 3 significant

figures in my answer because the 1920 I started with has only 3 significant figures. Okay, we got the correct answer, but it turns

out that there is an even better way to solve problems that involve multiple conversion

factors. Rather than solving this in two separate steps,

we can combine those steps into one step with two conversion factors. Check this out. Once again, start the problem by writing down

the quantity that you want to convert. Multiply this by a conversion factor fraction,

putting what you want to cancel out on the bottom and what you want to convert it to

on the top. Notice that so far this is exactly the same

as the first step we just did. However, instead of solving this as it is,

we are going to multiply it by another conversion factor fraction. We now need to cancel out the lbs. that are

left on top, so we put 2000 lbs. on the bottom. We chose the 2000 lbs. rather than the 2.2

lbs. because we ultimately want to convert the quantity to tons. This gives us tons as our remaining units

on top while all the other units cancel out. We then proceed to calculate from left to

right. If the one is on the bottom, we multiply. If the one is on the top, we divide. So, we multiply 1920 by 2.2 and then divide

that answer by 2000. Our final answer is 2.11 tons, which is exactly

what we got the first time. But now we can see how powerful this method

is. No matter how many conversions you need to

do, putting the conversion factors in fraction form helps you to know when to multiply or

divide. Thank you for watching. Please comment, vote, subscribe, or check

me out at ketzbook.com.

526.9, 00821(Garrett Richardson)

230.45 kg 00811

347.72 , 00119

82.554 00804

193.6 lbs., 00213

345.5 Kg, 00103

82.72 kg, 00704

255 kg, 00212

34.09 kg, 00108

68.2 kg 00115

135.91 kg, 00818

134.09kg, 00123 (Dane Zimmerman)

00118 : 135.91 kg

00101 , 150kg

26.3kg, 00122

00107

346.99

230.5kg, 00111

53.6 kg, 00705

34.1 kg, 00708

109.09 lbs, 00602. Ay whats Gucci

87.73kg 00609

346.998, 00219

135.9 kg, 00418

639 kilograms is 289.85 lbs

34.09 kilograms, 00808

415 pounds, 00809

68.1818, 00415

26.36 kg, 00422

347.72 kg, 00707

229.971 kg , 00611

254.92 kilograms, 00812

346.998 Kilograms, 00207

thanks

I have a quiz tomorrow on this

you saved my life

How many kilograms of phosphorous are in a sample containing 4.00E+30 phosphorous atoms? Use “E” for “×10" and use significant figures. how would you solve this problem?

THANK YOU! My chemistry teacher could not explain this properly!

Thanks to you I understand !!thank you thank you

This is helpful

1 tonn is 1000 kilogramms if I am not mistaken…which means that 1920 kilogramms is 1.920 tonn and certainly not 2.11

I just watched 6 different YouTube videos on help with conversion factors and now I can stop searching because you actually explained it thorough and simple way! Thank you!

Got it

My chemistry teacher said when we walk into her class room there are no more pounds..deg. F……gallons and so on…..PROBLEM solved…….I hated conversions anyway….I found them useless and confusing

THANK YOU I've been watching Khan Academy and this is much more my speed. Quick explanation and clean visuals! Looking forward to watching more of your vids.

thank youuuu

Now I am understand

Thank you. You explained this well, another way to rember the unit conversion is

What comes up must come down, 1920 kg must be below in the converison factor.

Thank you!!! I get it now!!!!

Awsm??

Thank, you help me to teach my son in a simple way.

I love you so much

Super helpful!!

doing 2 hour lectures on this topic in college.. But it only took me 5 minutes to actually understand how to do it and why it's important

The only problem I have is I don’t know conversions like kilometers to miles what should the second step be? Miles to meters to kilometers

Muscle pounds or sugar Punds?

This video really helped me! Thank you so much!

i never thought it was this easy

Very helpful. Thank you!

still don't get it

thank you so much I had a quiz on it tomorrow and was really nervous thanks a lot!

THANK YOOOOOOU!

omg why cant my chemistry teacher make it make sense like this

This video helped me so much, thank you!!!!!!

Superb

very nice, khan academy didnt do a good job at explaining this in my opinion, but you nailed it

Hey PHOENIX! #XRDS

Really helpful loved it

OMG TYY

THANK YOU!!! I am getting ready for nursing school and learning how to do conversions is a big deal. You made it sound so simple!!

2:13 ¿how is this possible? ¿are units numbers?

Guess who is gonna ace her quiz tm

shut up libtard

awesome video! its extremely helpful

what do we do if there isnt a question, but just the numbers?

Hodgin send you here?

saving my College Chem grade lmao thank youuu

Thanks a lotttt

this just saved my chem grade

Thanks my teacher made this sound so confusing but its actually pretty simple!

i know how to do it but how can we know the numbers we need to use to convert?

Wow, thanks. My teacher explains none of this, you're a lifesaver I have a quiz tomorrow

You see, my teacher didn’t do this. She decided the best way for us to learn conversions was find the height of André Robinson in coke bottles.

Awesome!

SOMEBODY HELP I HAVE A QUIZ ON THIS TOMORROW AND I CANT DO UNIT CONVERSIONS IM GONNA FUCKING FAIL

i have a unit test on this in ab an hour ty

YOUR VOICE IS EUPHORIC ????????? DO ASMR PLEASE ?????

Thank you!!!! You simplified everything in less than 10 min!!!!

I just had to learn about dimensional analysis and I didn’t really get it. Thank you so much!!!! ❤️

Excellently explained

How do u do Mph to inches per second, or something along those lines?

We have an exam in this today

I notice they have several ways you can convert and some come with different answers

Thank you so much. This was a major gap I was seriously struggling with. It's amazing how useful the internet is, especially when your lost about something.

Thanks baby daddy

In my book it says 1 kg is equal to 2.205 Ib?

You answered every single one of my questions, thank you so much!!!!!!!!!!!!!!!!!! 🙂

HOLY SHIT DUDE! THANK YOU! My teacher had us learn this absurdly longer method where you break down everything into something else

You sir save my brain to having Alzheimer Disease.?

Thank you

Thank you but I still have one question what if you have two things you want to convert, for example 15 cm per min, so you have to convert cm to meters, but also have to convert min to hours so you get meters per hour.

F**k my math teacher (teaching me more complicated way)