notation is a way of getting rid of all those ambiguous zeros and it's a way of getting rid of zeros that aren't measured it's a way of providing 100% Clarity to whether or not a zero is significant and focusing on just the numbers we want to use in our calculations in scientific notation you're only going to have one number to the left of your decimal and you're going to express place value by multiplying by a power of 10 let's take a look at a couple quick examples for example I have the number 130,000 to place this number in scientific notation the first first thing I'm going to do is I'm going to place a decimal I'm going to move my decimal so that it's after my first nonzero number now this number doesn't have a decimal but we know if it did it would be right here so we're moving the decimal to right there so that's the first thing I'm going to do the next thing I'm going to do is I'm going to drop any ambiguous zeros or zeros that were simply holding place value so remember how we said those zeros were ambiguous and we didn't know about them well it's like with friends when you don't know which friends you can count on you cut them out so when we don't know about a zero whether it's significant or not we cut it out so for scientific notation those ambiguous zeros go byby now we're going to multiply by a power of 10 that power of 10 is going to be equal to the number of spots we moved our zero a number of spots we moved our decimal my decimal started here and I moved it one two 3 four five slots so I'm going to raise to a p the fifth power then I need to determine if it's positive or negative well when I make a large number look small I'm surprising people I'm giving them a lot more than they bargain for and that's a positive thing so when I move my decimal to the left it's positive now if I go to the right then I'm making a really small number look large and we'll look at an example of that in a second and that would be negative so to the left is positive to the right is negative and since I moved my decimal to the left this time it's going to be a positive 5 so 130,000 in scientific notation is 1.3 * 10 5 let's take a look at another example let's say I have this number right here not even going to try to pronounce it 0.123 1 2 3 4 909 centimeters to place it in scientific notation I'm going to move my decimal so that it's after my first nonzero number that's my four so I'm moving it so that's after my four then I'm going to drop all those placehold zeros so I have 4.99 * 10 and um I count the number of places I moved my decimal and I moved it 1 2 3 4 five six seven spots and this time I moved my decimal to the right and when I move it to the right that makes the power of 10 negative so that number is now 4.99 time 10 the7 centimeters chemistry is easy life is hard yes I'm not going to run through well yeah let me run through several of these key examples examples here let's start with this one right here practice D first thing I'm going to do is I'm going to place my decimal after my first nonzero number which is my two so I've got two .3 Z it's real important that you recognize in scientific notation that you do not draw significant digits and that includes zero this zero right here is the zero that's at the end of a number with a decimal point that means it is significant by definition this is between two nonzero numbers so it's significant by definition so we have to include that zero also notice that there's no rule in scientific notation that limits are number of sig figs so we have four sigfigs in this number so our number when we get into scientific notation should also have four significant figures multiply by our power of 10 how many places did I move my decimal one two three places and I moved it to the right so it's negative again this one should be easy but I know examples like this tend to cause people consternation follow your rules place your decimal after your first nonzero number there's my non-zero numbers keep all your significant figures if this is significant and this is significant then all those zeros in between are also significant how many places did you move your decimal you moved it one two three four five spots so five spaces whoops I wound up deleting part of my number and there's my answer I moved my decimal to the left so it's negative notice that writing this number in scientific notation actually made it longer um in terms of the number of things you had to write it didn't save you any hand Strokes or anything so to speak so writing numbers in scientific notation doesn't always save you from writer's cramp um this one pretty straightforward place your digit after your first non-zero number drop your significant zeros these zeros are at the end of a number without a decimal therefore you don't know if they're significant or not and therefore you throw them out when it comes to scientific notation how many places did we move our decimal we moved it one two three four five again and we moved our decimal to the left so once again it's going to be positive chemistry is easy life is hard let me see um oh that's it chemistry is easy life is hard join me for the next lecture after you write down the word Vader write down Vader yeah