here's addition and subtraction with significant figures um the rules are different than those for multiplication division but I actually think they're simpler so you'll probably catch on pretty quickly here's an addition problem that I'm doing just like multiplication division the first thing that I want to do is the math and then I'll round second so I add these guys up and here's the answer that I get now for rounding my final answer can't have any more decimal places than does the number I started with that has the fewest number of decimal places o that's not easy to say it's probably not easy to understand it's a lot easier to demonstrate what I mean than to try to explain it okay so this number up here 13.01 98 it has four decimal places this guy here 1.2 only has one decimal place that means that my final answer can only have one decimal place too I find it easy to draw a line vertically um just to the side of the number with the fewest number of decimal places okay so right here right next to the two just like that that means that this number here um is the last that I'm going to have I'm going to get rid of all the others so I'm going to round to 14.2 and just as we've done before uh look to that one to see whether I keep the two to the same or whether I round up it's a one so I'm going to keep the two the same that means my final answer is going to going to be uh 14.2 it has one decimal place and the number I started with with the fewest number of decimal places also has one so that's how I know I did it correctly now it doesn't matter if we're adding more uh than one number the rules are the same here I'm adding three but I could be adding five or seven or 10 the first thing that I do is the math and the next thing that I do is look at the number of decimal places in each of the numbers I added together okay two decimal places here because these zeros to the right of a decimal place of a decimal point are always significant 15 here doesn't have any decimal places at all and this number here has three decimals places that means that the line that I'm going to draw is going to be just to the side of this 15 and it shows us where we round that means that it's going to be 291 look next door here it's a one so I'm going to keep it the same 2 9 1 this left us with zero decimal places with no decimal places at all but it's correct because the number here 15 didn't have any decimal places so our final answer can't have any more decimal places than this guy had here adding a whole bunch of numbers together follows the same rules subtraction also follows the same rules so when I do this subtraction fraction problem I get 40. 3378 two decimal places here four decimal places here that means my line goes just to the side and three will be the last digit look to the right of it to the seven that means I'm going to round the three up to a four so the answer I'm going to get is going to be 40. 34 I'm only going to do one more example because I think is probably making a lot of sense sometimes addition and subtraction problems are written like this horizontally when I'm given a problem like this I find it easier to stack the numbers up vertically on top of each other just so I can see how the decimal places uh relate to each other so what I mean is this I'll take 8.67 9 and 0.3 and 5.88 and stack these up vertically like this okay when I do this math here's the answer that I'm going to get and then I look at the number of decimal places 3 has uh the least so my line is going to go just like this showing me where to round the eight is the last decimal place I look to the right of it there's a five which means that I'm going to round this eight up to a nine so the final answer is going to be 14 18.9 which has one decimal place just like this number here is 0.3 which also had one decimal place so that's how we do addition and subtraction uh with rounding for significant figures