Welcome to, METRIC PREFIX CONVERSIONS! We will review the various metric prefixes, and then take a look at how to convert from one prefix to another. So the prefixes are given here on the left, and each prefix has a symbol. The base (circle) is the metric unit used with the prefix, which we will get to in a moment. Each prefix represents a specific number, and that number can be expressed using a power of 10. The base units are the metric units used to measure some quantity. And so they can be attached to any prefix according to the quantity. For example there can be a megagram, symbolized Mg, which is 10⁶ grams, or 1 million grams. At the other end of the scale let’s say meter is our base unit. So we could have a nanometer, which would be symbolized nm, which is 10⁻⁹ meters, or 1 billionth of a meter. You can see that expressing the amount as a power of ten is much more convenient than writing out the zeroes in very large or very small numbers. So any metric unit can be attached to any prefix which gives the unit a specific numerical value. And we use the prefixes to represent any number. For example, 2.6 million grams would be 2.6 megagrams, or 2.6 Mg or 2.6 times 10⁶ grams or 2 million 6 hundred thousand grams. 18.2 billionths of a meter is 18.2 nanomters. So now let’s take a look at how we can convert from one metric prefix to another. To gain an easier perspective let’s put everything in a horizontal table and we will begin with meters and grams for our base units. The table allows for an easy view of each exponent, which we will need in the conversions. For example, how many decigrams are in 2.6 kg. We will use a specific algorithm that uses the dimensional analysis set-up, as follows: First step, write amount and unit given in the problem, then multiply by fraction with the given unit on bottom and wanted unit on top. Now we need to fill in the numerical relationship between: Decigrams and kilograms (which is where we now refer to the chart). We put a 1 with the larger unit, which is kilograms, and the smaller unit gets a power of ten, determined simply by subtracting the exponents represented by the prefixes. Kilo has an exponent of 3, Deci is -1. And so the difference is 4, which becomes the exponent. There is 10 to the 4th, or 10,000 decigrams for every 1 kilogram. With this set-up the kilograms cancel, leaving the desired unit decigram. Do the math and we get 2.6 x 10⁴ dg. We have determined there are 26,000 dg in 2.6 kg. Click on this link if you need to review dimensional analysis beyond what is presented here. Let’s try a problem where we are converting from a smaller unit, nm, to a larger unit, cm. The set-up is the same as before: Write what is given, multiply by a conversion factor with given unit on bottom, wanted unit on top, larger unit gets 1. The number for smaller unit is determined by subtracting the exponents represented by the prefixes. nm cancels, leaving cm. 18.2 nm=1.82 x 10⁻⁶ cm or 1.82 millionths of a cm. But the purpose of scientific notation is to forget about dealing with lots of zeroes, so we can ignore this. So any metric unit can be used with the prefixes: E.g., liters or seconds or joules or pascals or Watts. A common volume unit is milliliter, or 10⁻³ liters; Or microseconds, a very short span of time; Or terrajoules, a lot of energy; Or kilopascals, a common unit of pressure in chemistry; Or gigawatts, a billion watts. If you’re a fan of “Back to the Future,” you may remember Doc Brown speaking in terms of jigawatts to power his deLorean. He may have pronounced it oddly, but jigawatts probably has more levity than gigawatts. The last part of this video is concerned with unit conversions of squared and cubed unit lengths. Length units such as meters or inches are interesting because squaring them gives us area and cubing them gives us volume. And so that changes the conversion because numerical relationships also have to be squared or cubed as well. Let’s look at a couple of examples. What’s the relationship between square meters and square kilometers? The initial set-up is the same as before: Units given on bottom, units wanted on top. What changes is their numerical relationship. First we add the LINEAR relationship given by the table. There are 10³ meters in a kilometer. However, squaring the linear units requires that we square the numerical relationship. There are 10³ squared m per km², a million square m in 1 square km. Last, let’s look at cubed lengths, here, the relationship between cm cubed and dm cubed. Note that a cubic decimeter is 1 liter. This is how the liter is defined. The problem is how many cubic decimeters are in 44.5 cubic centimeters. Again, same set up: Using a conversion factor with given units on bottom, wanted on top, with the larger unit getting 1. Subtracting the exponents of the LINEAR relationship gives an exponent of 1. But the units are cubed, and so we cube the numerical relationship, giving us 1 cubic dm for every thousand cubic cm. 44.5 divided by 1000=0.0445 cubic dm. So for squared length, which is area, the linear relationship is squared. For cubed length, which is volume, the linear relationship is cubed. You should memorize the prefixes and the exponent each one represents. These prefixes are used extensively in science and you should have them in your head for immediate recall. You won’t get to use this chart on a test. Seeya!

EXCELLENT! Thanks you so much for posting this. Very clear, very usable method.

I've seen too many "methods" and "explanations" for prefix conversion. Thanks so much for posting. This makes sense!

Thank you so much for posting this. This was one of the first lessons in chemistry, which I was not getting at all until seeing your video, and my teacher continues to give us problems that require conversions and I'm getting them every time. You have saved my grade.

Thank you…. This was so helpful

GREAT! Thanks so much! Best method I've seen.

keep on the good work

Another good one! Thanks for posting!

Thank you!!

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Thank you soo much for this video! currently studying for a final and this video just might have saved my grade 😀

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can u be my teacher?..lol

how was 10^7 came up to be 10^-6..when you just moved one decimal place to the right?

Thanks man

Thank you so much for uploading this video. Big help!

Why does he sound like the guy who narrates darkmatter2525 episodes, unless…………

Thanks!! I spend one hour searching for a good explanation video!! and I can say that this is the best explanation

How do you decide the order in which to subtract exponents? Does the result always have to be positive?

This is very helpful! Thank you so much for sharing!!! God bless! 🙂

What I'm still confused about is for example..if you were to convert a cubed unit to a unit that is not cubed..such as converting 0.50mm^3 to L.

omg! it was amazing lecture i had! thank you for enlightening me

how many cubic centimeters are there in exactly one cubic mete??

My proff took 2 lectures to explain and still managed to confuse everyone. Thank you so much.

Where was deca and hecto.

First!

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Cubic centimeter is same as milliliter. One does not use prefixes larger than kilo with meter or gram. One does not use even kilo with the liter. 1000 kilograms is a tonne and 1000 liters is a cubic meter. Prefixes deci and centi should be avoided especially on technical contexts. They have some established uses – especially sound volume is always given as decibels and never just bels.

luv yer vids!! This is great, clear, to the point, easy to use.

where did he get this "-6" in one problem? please help, we have exams and I still don't get this metric prefixes.

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howd u get 1.82

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Excellent method! I've been struggling with how we were taught in class and this toppled my hours of confusion in just a few minutes. Thank you!!

THANK YOU

when you were converting nanometers to centimeters, why did it suddenly change from 10^7 to 10^-6????

You should not use upper case K for kilo in the introduction. Kilo is always abbreviated with k.

Thank you so much!! I've been struggling to understand how to do this and have watch so many other videos, yours made to so simple and easy to understand!! THANK YOU!!

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I have an exam tomorrow, you saved me, I finally got it!

Thanks for the help

Best method!!!

How would you convert 355 km/s to cm/s and m/ms? When we have 2 units in the given unit. Can you please explain that.

wish my teacher made videos like this for people who forgot the subject entirely. Nobody asks questions and I'm sure its because they are to shy. anyways thanks for making this video it helps lots.

Finally someone who explains it sensibly!

Am I the only one that doesnt get it even after watching tons of videos? Like i dont get the multi step one because no body specifies why we chose that unit to get to the one we want

I cannot thank you enough my chem professor could not explain this to me for shit and you just saved my mind from endless hours of frustration THANK YOU

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i can't understand how 10^6=1,00,000 that it should equal 1,000,000 in minute 6:04?

Love this video!!!

Will this technique always work because I’m trying in on homework and then I look it up and I’m off by a zero for example I was figuring out how many meters are in a kilometer and I got 100 meters in one meter and I looked it up to be sure and it’s 1000 meters in one kilometer, am I doing something wrong

plz made such a video which has a shorttrick to remember multiple and submutiple prefixes .ok

Im a bit confused with why the decimal was moved. it went from 10^7 … 10^-6. I was with you until that part

thank you soo much!!

Wow, out of the 20 videos regarding metric conversion your method is the one I'm going with, took me 2-3 tries but I got it now no problem, thank you!

thank you so much

Too hard to understand

This is the first time I liked all the comments because the video was just awesome. My lol teacher was still confusing me. But I am just cleared now. Thanks sir.🙏🙏🙏😃

I am the latest comment

this help so much thank you so much

Hi I may just be pulling a complete blank but I'm still confused on how he is getting the exponent in the conversions by subtracting from said prefixes. How does he know which prefixes to use?

This is way too confusing especially if you are new to prefix conversation. if you have the list memorized it's easy to multiply or move the decimal point to the right when you move each step up the list and divide each step down the list or move the decimal to the left.

He forgot some

bro my mind is blown!!! this made it super easy I was not getting it one bit , you my friend are like baby jesus!

i love you!😭😭😭♥️thank u very much!

do u make vids about probability?

The best…

100th comment

This helped me understand this concept so much! Thank you for the video!

Stuff you missed:

Hecto = 100

Deca (Deka) = 10

For storage (Bytes)

Each conversion is 1024 not 1000 because it is a binary number (2^x, and if you have ever played 2048 those numbers all of them)

How did the 10^(7)nm turn into 10^(-6)cm?

really good vid

My teacher taught us this topic awhile ago and I was left dumbfounded. Finally I get it and I'm just so happy I found this video!! Thank you so much!!

I am really love this so much

Ty for saving my life

I swear the textbooks just converted and never explained and it looked so simple but I was still so confused and this broke it down perfectly. Thanks!!

Yassss you are a lifesaver 🙏🏼🙏🏼 better explanation than my prof and the book!!

U dont have hecto and deka…

thank you so much, you literally saved my life

Holy crap! After going through several YouTube videos and meeting with my professor to explain the metric system, you by FAR explained it so I can understand. Thank you, thank you, thank you!!!!!!

I wonder why nm to cm is 10^-6 and not -7…

Very good

You are the true MADDO SCIENTIST!!!!

I never write comments, but this just saved my butt! Thanks so much!

did you have a tutorial on how to rules of the exponents? This is why I kept getting the answer wrong, I didn't know you had to add the exponents. I thought I could just times it by the 10 to whatever.

U made it sooo easy

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thank you so much for the video!!!! this is the best method i've come up across in converting si units and i'm very sure it's going to benefit me well, thanks a whole lot!

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do you always subtract from the larger exponent???? or the larger unit (PREFIX) exponent is where the ONE is ?? thank you

Thanks a lot sir again.

This video really helped me with understanding how to go from unit to next. Thank you so much.

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Thank you, thank you, thank you, thank you! You've saved my life!

that's good but i understand some

Brilliant! Thank you for this clear explanation. I never thought of it this way before. I have just accepted the 10 to the power as given. Now it all make sense!

Does it matter which one you put to subtract first? That confuses me

Thank you very much for producing this video. It is very easy to follow with clear understanding