Video instructions and help with filling out and completing Where Form 2220 Subtracting

Instructions and Help about Where Form 2220 Subtracting

Okay addition and subtraction with scientific notation as you'll probably remember each number that's written in scientific notation has two parts this which we can call the coefficient or the mantissa and this 10 raised to an exponent we can just call the power when we do addition and subtraction problems with scientific notation we hope so hard that the powers are the same because it makes the problem much easier but if they're not the same it isn't the end of the world I'll show you how to solve those problems too let's look at this it's an addition problem in this case the first thing I always want to look at is the powers and since they're the same ten to the fifth in both cases I'm set here's all I have to do I take the coefficients and since this is addition I add them together three point seven six nine plus four point two one these two guys and I do that math and now since the powers were the same all I do is bring this power down 10 to the fifth and use it my final answer simple is up so my answer is seven point nine seven nine times ten to the fifth all I have to do is do the math and then I just bring down 10 raised to the exponent here's a subtraction problem I'm not even go through the whole thing because I think it's so easy I just look at the powers here they're the same so all I have to do is the subtraction 8.14 minus 2.01 there's the answer and then I take 10 to the negative second I pull it down here and reuse it in my final answer I'm done so you may be asking yourself what do you do if the powers aren't the same like this example here I have 10 to the fifth and I have 10 to the sixth well I can't add these together until the powers are the same so what I'm going to have to do is change around the exponents on one of these numbers so that both have the same exponent 10 now how am I going to do this you may remember these rules that we talked about earlier if I move the decimal place right or left in a scientific notation number that changes the exponent on 10 so we can reverse that I can change this 10 to the fifth to 10 to the sixth by moving the decimal place to the left here's what I mean I take the decimal place and I move it one spot here to get 0.75 8 well according to our rules when I move the decimal place to the left the exponent on 10 gets bigger so I moved at one spot to the left which means that the exponent is going to be bumped up from 10 to the 5th to 10 to the sixth so moving the decimal place one spot to the left now gives me two numbers that have the same power so now I can go ahead and add them just like I did earlier so I'll do two point eight seven one plus point seven five eight add these together three point six two nine ten to the sixth in both cases so I just bring it down and reuse it now as an aside your teacher may be asking you to round your answers using significant figures I'm not rounding using significant figures here but if your teacher is asking you to do that watch my video on significant figures rounding for addition subtraction as well as significant figures rounding for scientific notation but just keep in mind that I'm not following those rounding rules here here's another example we have 10 to the negative 8 10 to the negative 10th in order to subtract them in this case I'm going to have to rearrange some decimal places so that the exponents are the same well I can do the same thing that I did earlier if I move this decimal place to the left it can bump up the exponent on 10 so I can go from negative 10 negative 9 to negative 8 up to by moving this to the left two spots so my new number is going to be point zero five seven two and since it was over to the left it will be up to on 10 times 10 to the negative 8 now both of their powers are the same so since this is a subtraction problem I'll just go ahead and subtract the numbers so I have two point nine seven eight five minus 0.05 seven to do that math there's the answer for the first part and now I just take ten to the eighth and bring it down here for my final answer and there we have it we're done now another problem that people sometimes have when they're adding or subtracting scientific notation is they get a final answer that is not written correctly according to the rules of scientific notation let me show you what I mean let's take this example well we're in luck in one sense because when we look at this the powers are the same so all I have to do is a subtraction I don't have to worry about moving the decimal place to get exponents that are the same on ten so take four point eight six and subtract four point seven two and I get point one four so I could write an answer like that so point one four times bring this down 10 to the third but that can't be my final answer here's why scientific notation as you may remember always needs to be written with one number one digit to the left of the decimal place then you have the decimal point and then