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multiplied expressing the product in scientific notation so let's multiply first and then let's try to get what we have in scientific notation actually before we do that lets just reven remember what it means to be in scientific notation so it'll be in scientific notation and actually each of these numbers right here are in scientific notation it's going to be the form a times 10 to some power where a can be greater than or equal to 1 and it is going to be less than 10 so both of these numbers are greater than or equal to 1 and they are less than 10 and they're being multiplied by some power of 10 so let's see how we can multiply this so this over here this is just the exact same thing so if I do this in magenta this is the exact same thing as 9 point 1 times 10 to the sixth times times 3 point 2 times I actually don't have to write an 8 I could write let me write it all with the dot notation to make it a little bit more straightforward so this is equal to 9 point doing that magenta is equal to 9 point 1 times 10 to the sixth times times let me do it in this green color times 3 point 2 times 10 to the negative fifth power now in multiplication and you know this comes from the associative property essentially allows us to remove these parentheses it says look you can multiply like that first or you can actually multiply these guys first you can reassociate them and the commutative property tells us that we can rearrange this thing right here and what I want to rearrange is I want to multiply the 9 point one times the 3 point 2 first and then multiply that times 10 to the 6 times 10 to the negative 5 so I'm just going to rearrange this using the commutative property so this is the same thing as nine point one times three point two times three point two and I'm going to reassociate so I'm going to do these first and then that times that times 10 to the sixth 10 to the six times 10 to the negative five times 10 to the negative five and the reason why this is useful is that this is really easy to multiply we have the same base here base to end so we can and we're taking the product so we can add the exponents so this part right over here this part right over here 10 to the 6 times 10 to the negative 5 that's going to be 10 to the 6 minus 5 power or essentially just 10 to the first power which is really just equal to 10 and that's going to be multiplied by nine point one times three point two so let me do that over here so if I have nine point one times three point two so first I'm going to ignore the decimal so I'm just going to treat it like 91 times 32 so if 2 times 1 is 2 2 times 9 is 18 take a 0 here because I'm in the tenths place now I'm multiplying everything really by 30 not just by 3 that's why my zero is there and I multiply 3 times 1 to get 3 and then 3 times 9 is 27 and so it is 2 2 plus 0 so I'm adding here 2 Plus 0 is 2 8 plus 3 is 11 carry or regroup that one 1 plus 1 is 2 2 plus 7 is 9 and then I have a 2 here so 91 times 32 is 2912 but I didn't multiply 91 times 32 I multiply nine point one times three point two so what I want to do is count the number of digits I have behind the decimal point I have one two digits behind the decimal point and so I'll have to have two digits behind the decimal point in the answer so one two I'll stick the decimal right over there so this part right over here comes out to be twenty nine point one two so you might say you might feel like we're done this kind of looks like scientific notation I have a number times a power of 10 but remember remember this number has to be greater than or equal to one which it is and less than 10 but this number is not less than 10 it's not in scientific notation so we can do is let's just write this number in scientific notation and then we could use the power of 10 part to multiply that with this power of 10 so 29.2 or sorry 29 point one two this is the same thing as two point nine one two notice what did i do to go from there to there just move the decimal to the left or another way to think about it if I wanted to go from here to there if I want to go from here to there what can I do to this what I would multiply it by 10 if I multiply it by 10 I would move the decimal to the right it would go from 2.9 to 29 so if I want to write this value this is just this times 10 all right so - 29 point 1 2 is the same thing as 2 point 9 1 2 times 10 and now this is in scientific notation but that's just this part and I still have to multiply it by another 10 so times another 10 and so to finish up this problem we get to point to point nine 1/2 times 10 times 10 or 10 to the first times 10 to the first well what's that well that's going to be this part right over here that's just 10 squared so it's 2.9 1/2 times 10 to the second power and we are done