Okay, in the last video we saw how to count how many sig figs there were, and we saw a few examples of each type. Now we're going to learn how to do these calculations, or how to apply sig figs to calculations. There are two different types of calculations that we care about.
There's multiplication and division as one option, and addition and subtraction as the other. Multiplication and division is the easier option, so we're going to start with that. So multiplication. and division. This also applies to exponents because it's literally just a variation of multiplication and division.
So if you square something you're multiplying two numbers together. Okay, so I'm gonna try my best to word this properly. Here's how it goes. So if you're multiplying two numbers or dividing two numbers, the result We'll have the same amount of sig figs as the measurement with the fewest.
So in other words, what it comes down to is whatever your worst piece of equipment is, it's going to limit how accurately you can record your final answer after you do a bunch of calculations. Okay. So, not so... super difficult but it has to do with counting sig figs on the fly so all the stuff we did in the last video where we learned how to count sig figs we're going to need to kind of do that in the background while we're doing all the other math that we do in this class and there's going to be enough math that you're gonna need to get good at this okay so let's try a few examples All right, so let's take 17.491 divided by 4.556.
Okay, I didn't put any zeros in just to make it really easy as to how many sig figs things have. So this has 5 sig figs. This has 4, correct?
1, 2, 3, 4, 5. 1, 2, 3, 4. Okay. Here's one of the biggest problems with sig figs is that your calculator has absolutely no idea what a sig fig is. So just type it in. 17.491 divided by 4.556.
And I got not a nice whole number. Okay. I got a bunch of decimals.
Oh, I can't see it because of the glare. Okay. I got...
I'm going to put this calculator so you can still see it. 3.839113257. I will not need you to write every number out every time.
That is a complete waste of your effort. But we do need to... keep however many sig figs we're allowed to keep. The rule says, we're assuming these are measurements, the rule says that whichever one has the fewest amount of sig figs is how many your answer is going to get. So essentially, since this has four sig figs and this this has 5, we can only keep up to 4 sig figs for our answer.
So 3.839, and that's 1, 2, 3, 4 sig figs. And now we just follow the typical rounding rules. If this is 5 or above, we...
sorry, if the next number is 5 or above, we round up. If it's... lower than...
if it's 4 or below, we round down. Okay, so since this is a 1, we would round down, and basically that all drops off, and we get 3.839. If this was like 3.8397, we would round up.
this would be 3.840. Okay, but the idea is this has one, two, three, four sig figs, and it has four sig figs because our measurement with the fewest had four. Whenever we do... Whenever we do multiplication or division, your calculator is going to spit out every decimal it can get. It has no idea what a sig fig is.
You have to be able to interpret this with the correct number of sig figs. Okay? I do take off points if your sig figs are off.
All throughout the entire year if you have Chem 1 and Chem 2 with me. Okay? All through the labs.
This is one of those things that's not worth a lot of points, but it will nickel and dime you if you don't get good at this. Okay? Um... So basically, whichever one has the fewest, that's how much that one's going to have.
I do want to point out something, though. This is an example that I think is funny. I know it sounds stupid to have funny, fake examples, but if we do 3 times 5, okay, most of you are going to say 15. Well, this has one sig fig and this has one sig fig, so this would round up to 20. If you do 3 times 6, that's 18. That also rounds up to 20. 3 times 7 is 21. That's low enough. One sig fig, this would round down to 20. 3 times 8 would be 24. That's low enough. that it would round down to 20. So the moral of this story...
Oh yeah, gotta keep track of sig figs. There we go. Okay, the moral of this story is if you basically are in the lab and you get to the point where you're doing measurements that have one sig fig...
your answer is going to be a guess at best. It's going to be terrible no matter what you do. This is why you try to get as many decimals as you can, so you can accurately know your answer.
If you end up just doing like one sig fig or two sig figs, your answers are going to suck. Okay. All right.
So the other option, we've seen multiplication and division, the other option is addition and subtraction. And it's going to sound really similar. I'm going to write these rules so that they intentionally sound similar, but they are not exactly the same. So anytime you're adding or subtracting some numbers, the result will have the same... I'm trying to make it space the same as the other one too.
Same amount of decimals as the measurement with the fewest. So like we saw with that ruler that I drew in the previous video, we can only know the number of decimals on our measurements so accurately. We're just kind of limited by the equipment itself. So the same is true when we add and subtract things. However, whichever one has the fewest decimals is what's going to be the limiting factor.
So for example, if we took, I don't know. 13.491 minus 6.04. I can't think of a reason that you would have two things that can be added and subtracted that have different numbers of decimals because typically you use the same instrument, but whatever.
Okay, so if we plug this in the calculator, I probably should be able to do this in my head, but, you know, I'm tired. I'm blaming COVID. 13.491 minus 6.04. Your calculator...oh, I typed here wrong. I'll just retime it.
13. 13.491 minus 6.04. Okay. And the answer comes out at 7.451. As per usual, your calculator doesn't understand how sig figs work, so yeah. In terms of decimals, this has three decimals.
This only has two decimals, so this only gets two decimals. So this means we round right there. So the answer you would write on your paper is 7.45. Okay.
The other way to visualize it is I have seen some textbooks do it like this. Whichever one has the fewest amount of decimals, put a line after that one, and that's where you cut off everything. You do round at this point, but that's where you make your decision. Okay, whichever version of this makes more sense to you, that's what you should do.
Okay, we will see more examples of all of this stuff in class, but these are the basic rules of how to do sig figs. All right, thank you.