So, now you know how to properly count significant figures using your sandwich rule and your right, right rule. But now what? Great! You know how to count them, but what are you going to do with them? Well, now we're going to learn how to properly round our answers using some significant figure rules. So when you do calculations on your calculator, it often displays the answer with a large number of decimal places. But in reality, you don't know the answer with that much precision because all of your original measurements have some uncertainty in them. In other words, your calculator will display an answer with 5, 6, 7, 8, 9 decimal places. But if the measurements you took to get those answers have error associated with them, you're not certain about that last digit, right? Well, then how on earth could you display your answer with that many decimal places? It's kind of overstating what you know. So let's say someone's measuring the area of this box below. So I'd like you to take a second if you're watching this video to just pause the video. And in your mind, kind of measure the length and the width of that blue box that you see down below and then calculate the length, the width and the area of that blue rectangle that you see there. And then after you've done it on your own, unpause the video and come back and see where we're going to go with this, okay? All right. So let's say you just paused that video and you just came back. So if I measure the height of that rule of the blue box there, this guy looks like to me it's definitely past the five, but it's not quite at the six. So the height of that blue rectangle there, it's definitely five points something. We just don't know what the something is. So maybe when you're looking at that you think it looks like 5.7 or maybe you say no, I think it looks like 5.8 centimeters or maybe you think it's not quite that big. Maybe you think it's 5.6 centimeters. These are all reasonable guesses. We'll never know the answer for sure because all measurements have some error associated with them. I'll agree on the five, but this number, it's just what does it look like to you? Then if we go and we measure the width of this rectangle here, I can see that it definitely goes past the seven, but it's not quite at the eight yet. So maybe you think that looks like exactly halfway. You think it looks like seven and a half centimeters. Or maybe you say no, it's a little shy of exactly halfway. I think it's 7.4, maybe 7.3. All reasonable guesses. When we do this measurement here, we're not sure about the five, the four, and the three. So your rectangle, when you go to find the area, we would do length times width, right? So when we're multiplying those things together, let's just say let's go on the small side and then look at the large side possibilities. So let's say for that height of that rectangle there, you said it was 5.6 centimeters. And then for the width of the rectangle, let's say you did the small measurement there, two, 7.3 centimeters. That means that when you get your area, we'd have 40.88 centimeters squared. But what if you were on the high side of those measurements there? And you said 5.8 centimeters and 7.5 centimeters. Well, if you throw that in your calculator, you'd get your calculator would spit out 43.5 centimeters squared. So what's the right answer? Is it 40.88? Is it 43.5? Well, the right answer is probably somewhere in between those two numbers. But it kind of overstates what we know to show our answer with a lot of decimal places, because as you can see, the original measurements that we took to get that area have some error associated with them. And so we have to account for that error. So it says down here below, because every measurement you make has at least a little human error, we have to take into account. So it's overstating what we accurately know if you show your answer with a whole bunch of decimal places.