Lesson 8 4 Scientific Notation part 1

all right ladies and gentlemen we're going to go on lesson 84 scientific notation okay we're going to compare numbers written in scientific notation so we need to begin with talking about what scientific notation is this you'll notice is going to be done in couple parts so so be prepared for that so first of all scientific notation is method of writing very large very small numbers using powers of 10 okay so for example when we're talking in our scientific notation here we are talking about things that are like say the distance between galaxies okay things that are very very large or the size of atoms things that are very very small and we do so using powers of 10 okay it's to help us shorten up numbers and not have to write them to the full length but also being being able to function using them so first of all we need to talk about what happens to number when you multiply it by 10 or multiples of 10 like 100 or 1,000 and one of the common things that people try to tell me is that well we simply add zero that is incorrect we do not add zero okay that is the that is the elementary version of of what we are actually doing and it it's half correct but it's not completely correct all right the correct answer to what happens to number when we multiply it by 10 is we move the decimal one place to the right for every 10 that is being multiplied okay and yes because of this you may be adding zero or multiple zeros depending on how many places you have to move the decimal but it is not simply add zero okay so we have to first of all get away from that Elementary level mentality okay not to pick on it it it's fine way for young students to learn how to deal with multiples of 10 but now we're taking it to the next level okay so now dealing with multiples of 10 and and what happens when we multiply by values of 10 have chart here and we're actually going to start over here on this side of the chart and then we'll move the other way okay so 10 to the first Power what does that mean well that means yeah well it's just 10 okay 10^ SAR well what does that mean well that is 10 * 10 okay 10 the 3 power is 10 * 10 * 10 and 10 4th power is 10 * 10 time 10 know my boxes are little small here times 10 okay now what is the value of 10 well that's just 10 what is the value of 10 * 10 well that is 100 and 10 * 10 * 10 is th000 and 10 4th power is 10,000 okay so talking about what all those values mean and helps us because when we're multiplying by these things well multiplying by 10 what do do to the decimal well move the decimal one place to the right okay and if continue that pattern 10 the second power move the decimal two places right okay and three places I'm going to abbreviate here to the right and four places right sorry I'm going to use an arrow to the right that's very poorly written Arrow let me fix it because don't like again it is hard to write with this mouse sometimes okay but when I'm multiplying any of these things here I'm multiplying and I'm moving the decimal given number of places to the right right and how do determine that well one it could be the exponent because you'll notice here let me get my highlighter out here again okay 10 to the first Power went one place to the right 10 squar went two places to the right 10 to the thir three places 10 to the fourth four places or you could go by number of zeros one zero one place two zeros two places three zeros three places four zeros four places and so on okay so those are some of the shortcuts now let's go back the other way and fill in the rest of the table going the other way well 10 the 0o power we've already talked about 10 the 0o power is one okay and if we're using our pattern here in this particular case obviously have to divide by 10 moving to the left so what does it mean well 10 the 0o power is one talked about that you know also you could go one over if you really want it to one over 10 the 0o power you're still going to end up with 1 over one okay when multiply by one do move the decimal anywhere no so it doesn't go anywhere so no movement at all all right no right no left or anything and if continue that those things going the the other way sorry messed up here this is zero which gives us one okay now I'm now I'm comfortable again my fault hate it when mess up like this this would be 1 over 10 to the 1 power but what is 1 over 10 to the 1 well that's 1110th okay and what's going to happen then to my decimal well that's going to go one place one place left okay one place to the left one over squared well that's one 100 which will be two places left all right and again our shortcuts for those if you notice let me move this out of the way 10 to the first Power one left one zero one left 10 to the second power two left two zeros two places left so we have those shortcuts that help us and so what we're dealing with is is dealing with these ideas of what happens when multiply by multiples of 10 all have to do is Slide the decimal to the right and left based on the exponents so all of that to get to that understanding so when we're converting from scientific notation into standard notation now this is number in scientific notation 4.36 * 10 4th power so what that is telling me here is am taking this number this 4.36 and I'm multiplying it by 10 four times so my decimal will go from where it starts four places to the right okay if we're multiplying with negative exponent we will move the decimal three places to the left again going back to our table what happens when we multiply by negative exponents we go to the left now the important part of that is once we move to the right or left is we may have to add zeros this one here you'll notice had to add two zeros in order to give me my four places in this particular case you notice had to add two zeros to get me my three places to the left so we're we are going to add zeros if necessary but it's not always necessary so now go ahead and let's multiply we're going to convert from scientific this is in scientific notation into standard notation so I'm going to multiply 4.62 * 10 four times so that's telling me moving the decimal four places to the right because multiplying by 10 four times four 6 two okay that gets me one two places but am going to have to add two zeros to get me the full one two 3 four places so 4.62 * 10 4 is 46200 all right 3.31 * 10 7th so the decimal has to go seven places to the right right and need to add the appropriate number of zeros to get there well one two places gets me the decimal behind the one so will need five additional zeros so 3 3 1 and 1 2 3 four five so the decimal now is way down here at the end which you don't have to put it if it's at the end so my number now you'll notice is 3, 310,000 and know this number here is not written terribly smaller than or vice versa this is not terribly smaller than that but when we're talking about numbers that are say 10 to the 20th power those get very very long so okay 2.42 * 10 the -3 the -3 I'm multiplying Now by one10 three times so that's going to move my decimal to the left three times so got one there need two zeros in front 0 0 2 42 and in this case make sure that you do absolutely place your zero all right 10 the -4 is moving my decimal four places left there's one I'm going to need three more zeros one 2 three and again definitely placing my zero in front and my 3 32 so there we go just matter of sliding decimals left and right so that gets us to the end end of scientific notation part one so stop this video and if you want to even you go to the assignment and work on this that part of of the assignment and then come back and watch the part two or you can begin the part two video now