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# Multiplying in scientific notation example

Video transcript

Multiple, expressing the product in scientific notation. So lets multiply first and then lets try and get what we have into scientific notation. Actually before we do that lets just try and remember what it means to be in scientifc notation. So to be in scientific notation and actually each of these numbers here are in scientific notation. It is going to be the form: a times ten to some power where a can be greater than of equal to one and is going to be less than ten. So both of these numbers are greater than or equal to one and less than ten, and are being multiplied by some power of 10 so lets see how we can multiply this. so this here is the exact same thing. I am doing this in magenta 9.1 times 10 to the 6th. times, times 3.2 times. Actually, lets use dot notation, it will be a little bit more straightforward. So this is equal to 9.1 times 10 to the 6th. Times (green) 3.2 time 10 to the negative 5th power. Now in multiplication, this comes from the associative property allows us to remove these brackets and says you can multiply that first or these guys first. and you can re-associate them and the communitive property tells us that we can re-arrange these here. and what I want to rearrange is I want to multiply the 9.1 by the 3.2 first. And then multiply that by the ten to the 6 times the ten to the -5. So I am going to rearrange this So I am going to rearrange this using the cumulative property. So this is the same thing as 9.1 x 3.2. and I am going to re-associate so I am going to do these first. Now that times 10^6 times 10^-5. The reason why this is usefull is because this is easy to multiply. We have the same base here, base 10 and we are taking the product so we can add the exponents. so this part right over here is going to be 10 to the ( 6 - 5 ) or just 10 to the 1st power. which is really just equal to 10. and that is going to be multiplied by 9.1 x 3.2 lets do that over here, so we have 9.1 x 3.2 At first I am going to ignore the decimals so I have 91 by 32 So to have 2 by 1 is 2 2 by 9 is 18 have a zero here as I am in the tens place now and am multiplying everything by 30 and not just 3 thats why my zero is there and I multiply 3 by 1 to get 3 and then 3 by 9 is 27 so it is 2 (2+0), adding here 8+3 is 11, carry or regroup that 1 1 +1 = 2 and 2 + 7 = 9 and we have a 2 here. So 91 x 32 is 2912 But I didn't have 91 by 32 I had 9.1 x 3.2 So what I am going to do is count the number of digits behind the decimal point. I have 2 digits behind the point, so that's how many I need in the answer. I will stick the decimal right over there. So this part here comes out as 29.12 So you might say we are done as this looks like sientific notation As we have a number times by a power of ten. But remember this number has to be greater than or equal to one and less than 10 but this is not less than ten, so what we can do is write this number in scientific notation. and use the power of ten part to multiply this power of ten part. so 29.12 is the same thing as 2.912 x 10 notice what I had to do to go from there to there. I just moved the decimal to the left, so what can I do to this to get back I could multiply this (2.912) by 10 or move the decimal to the right. So I want to write this so 2.912 x 10 is the same as 29.12 so 2.912 is in scientific notation but I still have to multiply it by another part times another ten so to finnish up this problem I have 2.912 times ten times ten or 10^1 times 10^1 Whats that, well that is ten Well that is going to be this part over here That's just ten squared. So it is 2.912 times ten to the second power. And we are done.