0:00:01.009,0:00:04.403 In this lesson we're going to learn about significant figures. 0:00:04.403,0:00:08.554 When students first learn about significant figures in chemistry or physics class 0:00:08.554,0:00:11.492 you always think it's like the most useless thing in the world. 0:00:11.492,0:00:13.948 and just a big waste of time. 0:00:13.948,0:00:17.446 Most people hate significant figures when they first learn them. 0:00:17.446,0:00:21.109 The problem is, the one group of people who don't hate significant figures 0:00:21.109,0:00:23.194 are teachers, which love them. 0:00:23.194,0:00:28.368 And teachers also, it seems, love to take points off of tests 0:00:28.368,0:00:31.645 when people don't get their significant figures quite right. 0:00:31.645,0:00:35.374 So no matter what stage you are, in learning chemistry or physics, 0:00:35.374,0:00:37.544 even if you're in the middle of the year, 0:00:37.544,0:00:42.017 it's a great help to refresh significant figures. 0:00:42.017,0:00:44.598 Because there are plenty of points that can be earned 0:00:44.598,0:00:47.602 on homework assignments, quizzes and lab reports 0:00:47.602,0:00:51.012 by brushing up on this very important topic. 0:00:51.012,0:00:52.722 The other thing is - significant figures 0:00:52.722,0:00:57.348 just aren't that hard when you really spend a little bit of time practicing them. 0:00:57.348,0:01:00.410 One of the most difficult things about significant figures, I think, 0:01:00.410,0:01:03.518 is that students don't really understand what they're for - 0:01:03.518,0:01:05.102 what the purpose of them is. 0:01:05.102,0:01:08.471 Here, let me show you. Here's an example. 0:01:08.471,0:01:10.698 Let's imagine that we want to do a pretty simple calculation. 0:01:10.698,0:01:16.610 We want to take 62 - divided by 41. 0:01:16.610,0:01:20.957 We plug this into our calculator and we get a really ugly answer. 0:01:20.957,0:01:23.627 The answer that we get, what the calculator is going to spit out, 0:01:23.627,0:01:32.962 is going to be 1.512195122. 0:01:32.962,0:01:34.907 How's that for an ugly answer? 0:01:34.907,0:01:38.853 Now, here's the thing. You obviously don't want to put this whole thing down on your sheet, 0:01:38.853,0:01:42.787 so you're going to ask your teacher - how many numbers do we need to round it to? 0:01:42.787,0:01:45.598 Well, that's the thing about significant figures. 0:01:45.598,0:01:49.463 If you understand significant figures, you don't need to ask your teacher that question. 0:01:49.463,0:01:53.118 Because the answer to that question - how many numbers do we round it to - 0:01:53.118,0:01:57.718 is already answered by the numbers you divided in the first place. 0:01:57.718,0:01:59.856 Let me show you what I mean. 0:01:59.856,0:02:03.804 I'll give you a demonstration first, and then I'll explain the details. 0:02:03.804,0:02:07.066 62 has two significant figures in it. 0:02:07.066,0:02:11.862 A 6 and a 2. Two significant figures. 0:02:11.862,0:02:16.471 41 has a 4 and a 1 - also two significant figures. 0:02:16.471,0:02:21.612 That means that I'm going to round the answer that I got to two numbers - simple as that. 0:02:21.612,0:02:24.701 So that 1 is going to stay and the 5 is going to stay. 0:02:24.701,0:02:26.551 But remember, I'm going to be rounding. 0:02:26.551,0:02:32.285 So I'm going to have to look at the number next to the 5 to determine whether I keep the 5 the same, 0:02:32.285,0:02:35.438 or if it's a big number, if I'm going to round up to 6. 0:02:35.438,0:02:37.603 In this case it's a 1 so I don't round up. 0:02:37.603,0:02:42.520 I keep it as 1.5. 0:02:42.520,0:02:44.368 And that's my final answer. 0:02:44.368,0:02:46.658 The question of how many numbers I need to round it to - 0:02:46.658,0:02:52.515 is already answered by the number of significant figures in the numbers that I divided together. 0:02:52.515,0:02:58.111 Now, the question you may ask is - how did I know that there were two significant figures in the 62 and the 41? 0:02:58.111,0:03:00.116 The answer is pretty simple. 0:03:00.116,0:03:05.698 Any number that isn't zero is always a significant figure. 0:03:05.698,0:03:09.436 We'll talk about zero in the next lesson because it can get a little bit tricky. 0:03:09.436,0:03:11.725 Let's take a look at another example. 0:03:11.725,0:03:17.811 Let's do 782 divided by 231. 0:03:17.811,0:03:23.952 Put that into the calculator again. We get a really ugly answer out. 0:03:23.952,0:03:27.180 3.385 blah blah blah. 0:03:27.180,0:03:29.187 I don't want to put that whole thing on my sheet either. 0:03:29.187,0:03:31.355 So I look at the numbers that I divided together. 0:03:31.355,0:03:40.155 How many significant figures in 782? Well, none of them are zero, so - 3 significant figures here. 0:03:40.155,0:03:41.453 They're all significant. 0:03:41.453,0:03:46.516 231? No number zero - 3 significant figures here. 0:03:46.516,0:03:51.769 What does that mean? It means that I'm going to round my answer to 3 significant figures. 0:03:51.769,0:03:55.712 This is going to stay, this is going to stay, and this is going to stay. 0:03:55.712,0:04:00.776 As before, I'm rounding, so I look at the number to the right of this 8. 0:04:00.776,0:04:04.115 It's a 5, which means that I'm going to have to round up. 0:04:04.115,0:04:06.715 That 8 is going to become a 9. 0:04:06.715,0:04:13.857 And my final answer is going to be 3.39. 0:04:13.857,0:04:18.683 Again - it's 3.39 because that 5 there makes me round the 8 up. 0:04:18.683,0:04:21.534 Let's go to one more example. 0:04:21.534,0:04:31.615 1219 divided by 3462. Another pretty ugly number. 0:04:31.615,0:04:37.614 Dot 352109. 0:04:37.614,0:04:39.882 How many numbers do I round it to? 0:04:39.882,0:04:42.702 I'm sure you've already gotten the hang of it. 0:04:42.702,0:04:46.626 Four significant figures here, four significant figures here - 0:04:46.626,0:04:50.456 That means I round my answer to - you guessed it - four significant figures. 0:04:50.456,0:04:53.451 This stays, this stays, this stays, and this stays. 0:04:53.451,0:04:58.766 And I look at the number just to the right of the 1. It's a zero so I certainly don't round it up. 0:04:58.766,0:05:04.377 My final answer is going to be .3521. 0:05:04.377,0:05:07.464 There you go. Rounded to four significant figures. 0:05:07.464,0:05:11.252 Now, we can do this exact same thing with multiplication. 0:05:11.252,0:05:15.604 All we have to do is round, and then we add a couple zeros if we need to. 0:05:15.604,0:05:17.941 Let me show you what I mean. 0:05:17.941,0:05:26.530 When I take 56 and multiply it by 28, the answer that I get is 1568. 0:05:26.530,0:05:31.546 But as with division, I look at the significant figures in the two numbers I multiplied together - 0:05:31.546,0:05:34.202 two here and two here - 0:05:34.202,0:05:38.103 which means that I'm going to round my final answer to two numbers. 0:05:38.103,0:05:39.780 This one stays and this one stays, 0:05:39.780,0:05:42.702 and I look to the right of it to decide whether I round up or down. 0:05:42.702,0:05:45.214 It's a 6, so I round up. 0:05:45.214,0:05:50.449 My final answer becomes 1,6 - because these two numbers stay - 0:05:50.449,0:05:57.901 and I just fill everything else in with zeros. So I get 1,600. 0:05:57.901,0:06:10.308 If I multiply these guys together, 4833 times 1741, I get a really big number - 0:06:10.308,0:06:16.111 8 million, 414 thousand, 253. 0:06:16.111,0:06:19.460 Again - how can I round this using significant figures? 0:06:19.460,0:06:23.411 4 significant figures here and 4 significant figures here, so - 0:06:23.411,0:06:27.328 You guessed it - I round my answer to 4 digits. 0:06:27.328,0:06:29.860 I look here to find out whether I round up or down. 0:06:29.860,0:06:37.821 It's a 2 so it stays the same - 8,414 - and I fill the rest of the number in with zeros. 0:06:37.821,0:06:39.277 I don't need them. 0:06:39.277,0:06:41.772 Round it to four digits. 0:06:41.772,0:06:46.958 Now, if you're smart, you've already realized that I'm doing something pretty simple. 0:06:46.958,0:06:52.229 All the numbers that I have been multiplying together or dividing have the same number of significant figures. 0:06:52.229,0:06:55.024 So maybe you're asking yourself - OK, this seems easy enough, 0:06:55.024,0:07:02.105 but what would I do if I had to multiply together or divide two numbers that didn't have the same number of significant figures? 0:07:02.105,0:07:06.314 What if, like for example, one had 5 and one had 2 - 0:07:06.314,0:07:09.000 How would I round then? Let's take a look.