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Really Big Numbers

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alright let's talk about some really big numbers like really really big numbers that's what we're going to look at today what the real topic here is is something called scientific notation but for now let's just think of this as really big numbers what kind of big numbers like the number stars like if you were trying to count the number of stars how many stars actually exist and not just the ones that you can see in the sky but how many bars actually are there in the whole entire universe probably a lot right well nobody really knows for sure exactly how many stars there but there's a lot in the latest greatest estimates by astronomers are that wow there's not many stars in the universe that's a big number okay I 3 with a ton of zeros behind it and that's not the only astronomically big number there other large numbers is wow that we might deal with like if you wanted to get from our Star to the nearest other star how far away would you have to go will you have to go this many kilometers that's a long long distance at a really big number and if you were traveling that distance the fastest you could go is the speed of light and how far does go well let's say you let a particle of light go for a whole year at full speed this is how far it would go it would go really really far that's a lie 4 in kilometers numbers are just straight-up crazy our human brains can't really comprehend how large is numbers are and if you were going to start trying to do math with these numbers addition subtraction multiplication division then it's can start getting pretty tricky pretty fast and we're going to man if you had to show all your work all those zeros Okay so  in order to take these crazy large numbers can make them a little bit easier to work with what we do is we use what's called scientific notation and it's a way to shorten long numbers and it's kind of like when we abbreviate things scientific notation isn't abbreviation of a really long number into a shortened form like writing Mr. Instead of mister so this is the number of stars in the universe written in intific notation it's a shorter sweeter version of the same number it's an abbreviated version of the same number and understand where we came up with that 3 x 10 to the 23rd power we first have to understand how the powers of ten work so check this out you know what 10 to the zero is cuz anything to the zero is one and you know what 10 to the 1st power is that's just 10 and you know what 10 squared is 10 * 10 is 100 and if you multiply that by 10 you get a thousand and then 10 to the 4th would be a thousand times 10 which is 10,000 and intended V to be $100,000 and guess what the powers of 10 have as Zero's as the exponent so the number of zeros in each of these matches the exponent in each of these this one has 5 zeros for zeros then 30010 and no zeros okay crazy so if I wanted to write 100 billion all I have to do is count the zeros and write it out as 10 to the 1 2 3 4 5 6 910 11th power  okay isn't it a lot easier to write 10 to the 11th power then it is to write 100 billion so it's an abbreviation we're going to use that  to help us later but first what is 10 to the 7th power do you have really use a calculator for this or could you use the shortcut yes and then what's a shorter way to write 100 million alright once you think you've got those let's talk about how to write really big numbers in scientific notation 10 billion is a really big number but it's just 10 to the 10th power cuz there are 1 2 3 4 5 6 7 8 9 10 0 0 70 billion will isn't 70 billion just 10 billion times 7 so if 10 billion is 10 to the 10th and 7 billion is 7 * that couldn't we just right need billion as 7 x 10 to the 10th power  can the standard way to write 70 billion is a 7 with 10 zeros behind it scientific notation is an abbreviation it's a shorter version but it still means the same thing so how would you write cool boy look at that number that's a really big number how would you write that in scientific notation well that's the standard way to write it we're going to do is notice that we could write this green number  and this would be that * 9.37 and then since that green number with all the zeros in the one in front of it is 10 to the 12th couldn't we just say that the blue number at the top and standard notation can be written as 9.37 x 10 to the 12th power yeah okay that's the same number written in scientific notation can you the rule with scientific notation is instead of writing it is 937 or 93.7 or point 937 you have to have one digit in front of the decimal so we make it 9:37 and then we count the zeros for that green number right here's an easier way to do it if you had $60,000 one two three four so it's 10 to the 4th time 6 that's easy okay if you have 89 million one hundred thousand are going to count the zeros but  notice that would be 891 x 10 to the 5th we don't want 891 we want 89.1 so we're going to put 89 no sorry 8.91 we don't want to 89 one we don't want 891 we want 8.91 and since we went one two three four five six seven places we're going to say it's 8.9 1 x 10 to the 7th power so actually writing things in scientific notation is really pretty easy you just count how many spaces you have to move the desk can you put that number as the exponent on the 10 so the decimal goes there and that is how we do it okay hundred 23 alien where do we want the decimal we want the decimal to be between the one and the two so it's 1.23 but it's going to be 1.23 x 10 to the what set 1 2 3 4 5 6 7 8 1 2 3 x 10 to the 8th power is can you would write in this number in scientific notation really easy wasn't it alright you try it  convert this really big number to scientific notation okay what if you have a number in scientific notation can you want to scientific notation the lies it or something what if you want to write it in standard notation well could we move the decimal two 8431 yeah and then we moved the decimal twice right but that six phone it says we still have four more spots to go so one two three four five six what are we set those blank spots we put zeros in them right so 4.31 x 10 to the 6 power in standard notation is 4310000  can notice the decimal moved six times because of the six Expo so try that here write 2.2 x 10 to the 5th power in standard notation see what you got okay once you got that we're all set and we will try this some more tomorrow Sia

Uploaded by Jeff Marbut.

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