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# Subtracting in scientific notation

CCSS.Math:

## Video transcript

what I want to do in this video is get a little bit of practice subtracting in scientific notation so let's say that I have 4 point 1 times 10 to the negative 2 power 4 point 1 times 10 to the negative 2 power and from that I want to subtract I want to subtract 2 point 6 2 point 6 times 10 to the negative 3 power and like always I encourage you to pause this video and see if you can solve this on your own and then we could work through it together all right I'm assuming you've had a go at it so the easiest thing that I can think of doing is try to convert one of these numbers so that it has the same it's being multiplied by the same power of 10 as the other one and what I could think about doing well what can we express 4.1 times 10 to the negative 2 can we express it as something times 10 to the negative 3 so we have 4 point 1 times 10 to the negative 2 well if we want 10 to the negative 2 to go to 10 to the negative 3 we would divide by 10 but we can't just divide by 10 that would literally change the value of the number in order to not change it we want to multiply by 10 as well so we're multiplying by 10 and dividing by 10 I could have written it like this I could have written 10 over 10 times let me write this a little bit neater I could have written 10 over 10 times this and then you take 10 times 4.1 you get 41 and then 10 to the negative 2 divided by 10 is going to be 10 to the negative 3 so this right over here this is equal to 10 times 4.1 is 41 times 10 to the negative 3 and that makes sense 40 one thousandth is the same thing as 4.1 hundredths and all we did is we multiplied this times 10 and we divided this times 10 so let's rewrite this we can rewrite it now as 41 times 10 to the negative 3 minus minus 2.6 minus 2.6 times 10 to the negative three so now we have two things we have 41 10 to the negative 3s minus 2.6 10 to the negative 3s well this is going to be the same thing as 41 minus 2.6 minus 2.6 let me do that same color that was purple minus 2.6 10 to the negative 3s 10 whoops 10 to the negative 3 is 10 to the negative 3 there 10 to the negative 3 there one way to think about it I have just factored out a 10 to the negative 3 now what's 41 minus 2.6 well 41 minus 2 is 39 and then minus 0.6 is going to be thirty eight point four thirty eight point four and then you're going to have times 10 to the negative third third power times ten to the negative third power now we this is what the product or if this is what the difference of these two numbers is but this is no longer in scientific notation in order to be scientific notation this number right over here has to be has to be between 1 has to be greater than or equal to 1 and less than and less than 10 so what we could do is we could divide this number right over here by 10 we can divide this by 10 and then we could multiply and then we could multiple can do this we could kind of the the opposite of what we did up here we could divide this by 10 and then multiplied by 10 so if you divide by 10 and multiply by 10 you're not changing the value so 38.4 divided by 10 is 3 point 8 4 and then all of this business 10 to the negative 3 10 to the negative 3 times 10 is 10 to the negative 2 power so this is going to be 3 point 8 4 times 10 to the negative 2 power