## Scientific Notation – Best Explanation

all right this video is about scientific notation scientific notation is a way to write really big or really small numbers in a more manageable format so look I'm gonna show an example here okay so let's say I had the number 24 billion now the reason I know this is 24 billion because it has nine zeros so if it had three zeros would be a thousand if it has six zeros it'd be a million if it had nine zeros would be a billion so I can tell just by looking at this this is 24 billion now let's say I was doing some calculations it's it's really inconvenient to have to write 24 0 0 0 0 0 0 0 0 0 over and over again in your calculator or your computer or god forbid by hand so here's a this is a little trick ok a scientific notation it was developed for the purpose of saving time keep that in mind so I'm gonna rewrite this so what I'm gonna do the steps to doing scientific notation is what you do is you look for the part of the number that has that contains the information it contains the actual numbers instead of just a bunch of 0 see I'm saying so in this case it's 24 so I'm going to write 24 now what I'm going to do is I'm going to count the number of zeros after that point where I cut it off sorry and see how I'm saying see if I if I put my pin right here 24 is to this side of it and all the zeros are to the other side I'm gonna count how many there are 1 2 3 4 5 6 7 8 9 so there's nine zeros so and what I do is I go times 10 to the ninth now why did I do that well because 10 to the ninth is equal to 1 billion so really what I'm doing is I'm writing out in a sort of an expression that says 24 times oops supposed to be 0 times a billion so 24 times a billion is just 24 billion so that's a little proof that this expression here is equal to that same number so that's what scientific notation is it's just a different way of writing numbers all right so this is when you use it for really really big numbers and what about really small numbers it actually works the same way so let's I'm gonna make a little barrier here let's say that I had a number that was like this zero point zero zero zero five seven three okay if I want to write this in scientific notation what I'm going to do is I'm actually going to first choose a place where I would like the decimal place to be so let's say that I I wanted to rewrite this scientific notation excuse me I wanted to regret this number and stamping scientific notation using five point seven three that's kind of a common thing to do is just have the decimal place be one to the right of the first number and then have the decimals following it but in order to do this I need to know now what the what the exponent is going to be on this tin so see how I have the decimal place between the 5 and the 7 that would that would correspond to right here so I'm thinking about how many I want to think about how many spaces I had to move to get there so the decimal place is really here I move the decimal place to here in my scientific notation right between the 5 and the 7 so to get there I had to count 1 2 3 4 spaces so because I had to do that I need to put a negative 4 on the tin as the exponent and let me explain kind of why why you put the negative right there okay well it turns out that raising anything to a negative exponent makes it smaller it makes it get smaller and you'll notice that this number point 0 0 0 5 7 3 is actually very small it's it's it's a minut decimal this number five point seven three is actually very large compared to this so what I need to do this 10 to the negative fourth this is the like the smallness part of that number so just like I used 10 to the ninth up here to make 24 really big I'm gonna use 10 to the negative 4 down here to make five point seven three really small so let me just kind of go over these one more time so for a large number what you do is you put your decimal place right after the part right after the numbers that you want to keep in your initial part okay then you just look at how many zeros are after it in this case it was nine so I went times 10 to the ninth for small numbers what you do is you write out the numbers like this you look at the very end of the decimal and you look at the numbers you put your decimal place right between the first two numbers in that sequence that's that that's the standard way to do it right so I get five point seven thirty then you just consider the number of spaces that you needed to move in order to get to that place in this case it was four so I went ten to the negative fourth because one two three four to get there so that's basically it now let's some thing about going backwards now right what would happen if they gave you a problem like this they said convert to point six times 10 to the negative fifth to expanded form so they just want you to write it in normal form yeah this is in scientific notation right now and you have to write it as a normal number so in this instance what you do is you take 2.6 and you write it down all right and now look at this look at this expression here you see how this is 2.6 times 10 to the negative fifth what this means is that since this is a negative exponent I'm actually going to be writing down a really small number here and since I'm writing down a small number I need to take the decimal place and I need to count actually to the left that's the rule if I have a negative exponent I count to the left when I'm converting into a normal number because I need to create a lot of zeros here in order to make this small because this is very small so what I do is I go to point six I write this down now I look at the exponent says negative five so I just count negative five to the left one two three four five so now this is the new location of my decimal place and what I'm going to do is I'm going to kind of fill in zeros at all the spaces so and I'm gonna put a zero out front okay so it's zero point zero zero zero zero two six in decimal place is not here anymore so if I rewrite this it's just zero point zero zero zero zero two six this is equal to two point six times ten to the negative fifth you'll notice see if I went one two three four five I would get back to this in the procedure that I used to do when I did this problem so anyways that's basically it I guess we can do one more example because I just want to make sure that I'm not doing too much theory here and not enough examples while doing another example involving the large numbers that we did up here okay but this case will try to convert from scientific notation to the normal form of the numbers so let's say that I had a number like I don't know how about 43 times 10 to the third well this is actually pretty easy what I'm going to do is I just want to think of this 43 times 10 to the third as 43 times 1,000 because 10 to the 3rd is 1,000 isn't it it's just a 10 followed by three zeros or excuse me a 1 followed by three zeros boom-boom-boom so 43 times 1,000 is just 43,000 now you don't have to think of it this way you could just do the decimal place counting method right you could go right down 43 and start here at the end and count three decimal places to the right see how I would still get 43,000 but a little comma right here but I don't know whichever way works best with your with your brain to be able to understand this is I mean they're both equivalent mathematically so it's just a matter of personal preference anyways I hope you thought the video was informative I feel like I kind of went all over the place there like a lot of my videos so hopefully was helpful and please check out my other videos and let me know what you think and if you want to leave some like a question in the comments um assuming I don't get too many of them to handle I would be happy to try to get back to you and help you out there so thanks for watching

The first and last examples are incorrect. The first number in scientific notation form has to be greater than or equal to one and less than ten.

thank you, very clear explanations!

This deserves more attention

Excellent video

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