so scientific notation we're going to talk about what it is why it's important and then we're going to do some example problems so that you'll get really good at this stuff so scientific notation is like an abbreviation it's a shorthand way to write numbers that are really big and really small here's why that's important in science we spend a lot of time dealing with really huge numbers for example this is the number of miles that it is from Earth to the closest star outside of our solar system really big number we also look at a lot of really small numbers this tiny number is the amount of time that it takes for light to go from one side of an average siiz bedroom to the other side that's about 30t okay and these numbers aren't even the biggest and smallest that we use a lot this is the number of atoms in an average size glass of water and this number is the weight in pounds notice there's a decimal place here so it's a really tiny number this is the weight in pounds of a proton in an atom look at all these zeros these zeros are such a pain right imagine having to multiply this number by this number or do division do any of this by hand it would be such a pain even if you're using calculator or computer just typing in all these zeros and making sure that you haven't for forgotten one or added in a couple more that's really a big pain so scientific notation comes in handy because it lets us take numbers like these really big ones and these really small ones get rid of all the zeros and write them in a very compact very simple way that's much easier to use let me show you how we do it let's start with this really big number in Miles here's what we do to compress it down and write it in scientific notation the first thing is we figure out where would the decimal place be a lot of these numbers won't actually have a decimal place written but you know that it should be right here so I'll write in where the decimal place would be there it is now I move it and I count the number of spots watch what I do I go 1 2 3 4 five 6 7 8 n 10 11 12 13 and here is the new spot I move it until the decimal place is sitting here and there is only one number one digit I should say one digit to the left of the decimal place so the decimal place is here and then one digit there so I moved it 13 spots in this direction to move it to a place where there was only only one digit to the left of it so after I do that I write the number with a decimal place in the new position so it's going to be 2.53 and then I get rid of all of the zeros after this three here so this is the first part of the number now I need to account for the fact that I moved the decimal place 16 spots I mean 13 spots in this direction so I say that I moved at 13 spots in this direction by writing 10 raised to the 13 power you see this number here the exponent on 10 is the same number of spots that I move the decimal place to its new position so 2.53 * 10 13 I move the decimal place in this direction and I get a number 13 on 10 okay now here's a very small number I do the same but instead of getting bigger the exponent on 10 is going to get smaller let me show you what I mean decimal place is here it's already written in the number watch what I do I'm going to move it one 2 3 4 five 6 7 eight spots okay so now the decimal place is here and there's one digit that's not a zero to the left of it okay so 1 2 3 4 5 6 7 8 I had to move it eight in this direction now I rewrite my number with a decimal place in its new position okay so it's going to be 2.03 and now to show that I've moved the decimal place eight spots in this position in this direction I'm going to do 10 to the 8 so when I move the decimal place in this direction I get a positive number the exponent on 10 it goes up on the other hand when I move the decimal place in this direction the exponent on 10 goes down so I have positive3 in this direction and I have -8 in this direction so I've summed up these rules here here's a decimal place you move it left the exponent goes goes up you move it right the exponent goes down it's negative in this direction positive in this direction this is the kind of thing that is best learned by just getting a lot of practice so now we're going to do some example problems first we're going to take numbers like this and we're going to write them in scientific notation and then we're going to take numbers that have already been written in scientific notation and show how to turn them back into regular numbers okay let's start with this we'll write it in scientific notation the first thing that I want to do is find out where the decimal place is decimal place is here I'm going to keep in mind that when I move my decimal left the exponent goes up now I think it's easiest to think about starting at 10 to the 0 okay when the decimal place is right here the exponent part of the number is 10 the 0o I move at one spot okay that's 10 the 1st move it again 10 the second 10 the 3 10 the 4th 10 the 5ifth 10 the 6th the 7th 8th and 9th okay so I move it nine spots here and it's going to be 10 to the 9th now I'll rewrite my number with a decimal place in its new location it's going to be 3.7 7 4 9 * 10 9th so what I did here it's like I put the decimal place here and I imagine that I was starting at 10 the 0o and then that number on 10 went up each time I moved the decimal place to the left let's try it with this but instead of going up the exponent is going to be going down okay so we start at 10 the 0o and now we go down 10 the 1st 10 the2 10 the 3 10-4 10 to the5th so 5 in this direction time 10 to the5th because I just counted down from 10 the 0o and my new number is going to be 5.2 69 * 10 5 okay this one right here put in the decimal place and start at 10 the 0o 10 the 0 10 the 1st second 3D four 4th fifth 6th 7th 8th 9th 10th 11th 12th 13th 14th 14 in this direction so 10 to the 14th as I was counting up and I stop right here so there's one digit to the left of the decimal place and I write it as 8.13 * 10 14th this one here I'm moving it in this direction so we're starting at 10 to the 0o and then the exponent is going to be going down so 10 the 0o 10 the 1 -2 -34 5 -6 -7 8 8 in this direction time 10^ -8 and my number I keep the decimal place here so there is one nonzero digit to the left of it it's going to be 2.14 * 10 8 so that's how you take a number that's written kind of like regularly we call it in decimal notation how you take a decimal notation number and transfer it into scientific notation I'm going do a couple more practice problems at the end of this video if you want a little B more practice on this but now I want to move on to numbers that are written in scientific notation and I want to undo it and turn them back into you know regular numbers numbers that are written in decimal notation okay here's how I do this I like to think that we need to take the number and get the exponent back to 10 to the 0o here's what I mean by that let's start up here 7921 right now we're at 10 to the 8 we want to get this 10 8 back down to 10 the 0 so when we move the decimal place right the exponent goes down so watch this okay here it is at 10 the 8 10 the 7 when I move it to the right one spot okay 10 to the 6th move it down another spot 10 to the 5th move it down another spot now I'm going to have to move it a few more times and I'll add in the zeros after I'm done okay so I went 10 to the e8th 7th 6th 5 4 3 2 1 Zer so I had to move the decimal place a few more spots and I ran out of numbers so for each of these places in between where I move the decimal place I can write in a new zero here you see how I did that I just put a zero in between every place where I had to move the decimal and so now my new number is this I just took the exponent and move the decimal to the right until I got it back to 10 the 0o okay now for this one here 8.2 * 105 I want to get this exponent back to zero so I want the number to go up because it's a negative number so I want to move the decimal place to the left okay so right here it's 10 the 5th move it one spot it's 10 the4th it went up one okay 10 the -3 10 the2nd 10 the 1st and 10 the 0o so I'm going to put in a new zero between each one of these decimal places and then to be neat I'll rewrite this number 0.0082 is how you write this in decimal notation okay two more 4.13 * 10 3r so that means that the decimal place is at 10 the 3 now I want to get this three back down to zero 10 the 2 10 the 1st 10 the 0o that's my new spot and I add in a zero there so my answer is 4,130 here's the last one 52216 when the decimal place is here we're at 10 the -9th so I want to go up to get it back to zero so I'm going to be moving the decimal place to the left to get this X component up so 9th here8 -7 -65 -4 -3 -2 -1 0 there's my new decimal place location and I fill in all of the space in between the points with zero and then I can rewrite my number just like this and here it is written in decimal notation so that is how you take a number that's written in scientific notation and get it back into kind of a regular a decimal notation number now I'm just showing you how to do this here I'm not talking about the math behind it what's actually going on with this expon with this number with this 10 with the exponent so this it's really good if you can do this now but I hope that you'll find the time to watch the video called really understand scientific notation all right because it's one thing to just be able to work through this conting one type of number into another it's it's a more important thing to be able to understand how the math is actually working so please watch that video so you can actually understand the math so many people hate scientific notation and I think that's because they don't really understand so please watch that video if you have time about really understanding scientific notation