8 EE A 4 Scientific Notation Part 1 Introduction and Conversions Lightboard

hello scientific notation scientific notation is way to write very large number with say multiple zeroes into much smaller short-handed way times 10 to the is the first factor it has to be at least 1 and less than 10 okay so must be at least 1 and less than 10 10 to the the second factor is simply power of 10 okay so let's look at example if we have the number 325,000 and we want to write in scientific notation we would put 3 0.25 times 10 to the 1 2 3 4 5 5th power ok all right so let's look at this 3.25 is at least one yes is it less than 10 yes 3.25 that's our first factor our second flower second factor is power of 10 10 to the 5th is power of 10 okay all right now how did we do this let's go over how we did this okay so 450 million that's been written in standard notation so I'm going to show you how to go from standard notation into scientific notation okay so we have decimal point right here we're going to move the decimal one two three four five six seven eight times one two three four five six seven eight times okay so when we write this number in scientific notation we will write it as four point five because the decimal has moved from here to here times 10 to the eighth power okay 10 to the 8th powers because we moved it eight times when you multiply by 10 each time you multiply by 10 you move the decimal one place so 4.5 times 10 to the eighth power four point five is at least one four point five is less than 10 that's our first factor our second factor is power of 10 so this is how to go from standard notation to scientific notation let's do two more okay so we're going to start here with our decimal we'll move it one two three four five six seven eight nine ten eleven spaces so it now becomes three point five times ten to the 11th power at least one less than ten first factor times 10 to the 11th power okay let's look at this one one two three four five six seven eight nine 10 11 12 13 14 15 16 17 18 so it's 4 times 10 to the 18th power least one less than 10 times 10 to the end 10 to the 18th power okay notice on this one up here had 3 6 9 10 zeros but it's 10 to the 11th power common mistake is to say 10 to the 10th power is not the number of zeros is how many spaces you move how many decimal points you move okay so we again we moved at 11 spaces so it's three point five times ten to the eleventh we moved at 18 so it's 4 times 10 to the 18th power ok let's look at some different ones ok these examples we're still written in standard notation some people call it decimal notation you may see that also written we've still got to get to point where we have times 10 to the nth power and has to be at least one and less than 10 so how can we do that well we got to move the opposite direction if we start out with fraction something that's less than 1 we're going to move the opposite direction so we're going to move one two three four five six seven now that becomes eight times now if we're moving the opposite direction it still can be power of 10 but it's going to be one two three four five six seven to the negative 7 okay ten to the negative seven all right let's do another one okay got that nine on there all right so let's go one two three four five six seven eight nine 10 11 12 13 so now it's going to become nine times 10 and again if we're moving the opposite to the right it could be to the negative 13 okay at least one less than 10 and to power times of 10 to power all right all right now let's go we went from standard to scientific now let's learn how to go from scientific to standard okay so in this example we'll starting out in scientific notation and we're going to convert it to standard notation okay so how do we do that well we're starting out with three point seven nine I'll write that right here now I'm gonna leave the decimal point off times 10 to the eighth power remember every time you multiply by 10 you're going to move the decimal place one time so this case we're going to move it eight times so we start here we're going to go one two three four five six seven eight one two three four five six seven eight so our decimal goes here we're going to fill in with zeros and our new number becomes 379 million okay let's do another one four point eight times 2n to the 12th this is in scientific notation so we're going to move the decimal tip twelve places so let's write four eight we start here we're going to go one two three four five six seven eight nine 10 11 12 go back fill in our zeros okay and our new number then will become comma comma comma comma okay so this is our new number becomes four eight zero zero zero zero zero zero zero zero zero zero zero okay so again we moved decimal 12 places so we started out with four point eight we moved it with twelve places here's our new number okay now let's do something with negative modeling scientific notation we have seven point five times ten to the negative nine all right so we want to convert that into the standard notation so we'll start out with seven 5.5 now again if we're going to the negative nine we're going to become smaller so it's going to have to move nine places one two three four five six seven eight nine we go back and add zeros okay so our new number becomes point zero zero zero zero zero zero zero zero seven five okay let's do another one all right so let's write our number eight seven four three we're going to start with decimal here and we're going to be moving 11 places one two three four five six seven eight nine 10 11 at our zeroes okay and our new number becomes point zero zero zero zero zero zero zero zero zero zero eight seven four three okay okay let's look at this example we have three hundred and fifty million okay another way to write that is right here 35 times 10 to the seventh the question is is that in scientific notation well let's look our first factor has to be at least one yes has to be less than ten note so that is not in scientific notation so we have to change that by moving the decimal one place here that becomes three point five and if we make this number smaller we have to make our power of 10 one larger so now this becomes scientific notation so be careful if you see an answer such as this it has to meet these qualifications of at least one but less than ten to be written in scientific notation okay hope you enjoyed this video so we had an introduction to scientific notation we converted from standards scientific and from we converted from scientific to standard we used positive exponents and we use negative exponents all right in the future video we'll be using the operations addition subtraction multiplication and division of scientific notation all right thanks for watching please subscribe see you in the next video