[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.01,0:00:04.40,Default,,0000,0000,0000,,In this lesson we're going to learn about significant figures.
Dialogue: 0,0:00:04.40,0:00:08.55,Default,,0000,0000,0000,,When students first learn about significant figures in chemistry or physics class
Dialogue: 0,0:00:08.55,0:00:11.49,Default,,0000,0000,0000,,you always think it's like the most useless thing in the world.
Dialogue: 0,0:00:11.49,0:00:13.95,Default,,0000,0000,0000,,and just a big waste of time.
Dialogue: 0,0:00:13.95,0:00:17.45,Default,,0000,0000,0000,,Most people hate significant figures when they first learn them.
Dialogue: 0,0:00:17.45,0:00:21.11,Default,,0000,0000,0000,,The problem is, the one group of people who don't hate significant figures
Dialogue: 0,0:00:21.11,0:00:23.19,Default,,0000,0000,0000,,are teachers, which love them.
Dialogue: 0,0:00:23.19,0:00:28.37,Default,,0000,0000,0000,,And teachers also, it seems, love to take points off of tests
Dialogue: 0,0:00:28.37,0:00:31.64,Default,,0000,0000,0000,,when people don't get their significant figures quite right.
Dialogue: 0,0:00:31.64,0:00:35.37,Default,,0000,0000,0000,,So no matter what stage you are, in learning chemistry or physics,
Dialogue: 0,0:00:35.37,0:00:37.54,Default,,0000,0000,0000,,even if you're in the middle of the year,
Dialogue: 0,0:00:37.54,0:00:42.02,Default,,0000,0000,0000,,it's a great help to refresh significant figures.
Dialogue: 0,0:00:42.02,0:00:44.60,Default,,0000,0000,0000,,Because there are plenty of points that can be earned
Dialogue: 0,0:00:44.60,0:00:47.60,Default,,0000,0000,0000,,on homework assignments, quizzes and lab reports
Dialogue: 0,0:00:47.60,0:00:51.01,Default,,0000,0000,0000,,by brushing up on this very important topic.
Dialogue: 0,0:00:51.01,0:00:52.72,Default,,0000,0000,0000,,The other thing is - significant figures
Dialogue: 0,0:00:52.72,0:00:57.35,Default,,0000,0000,0000,,just aren't that hard when you really spend a little bit of time practicing them.
Dialogue: 0,0:00:57.35,0:01:00.41,Default,,0000,0000,0000,,One of the most difficult things about significant figures, I think,
Dialogue: 0,0:01:00.41,0:01:03.52,Default,,0000,0000,0000,,is that students don't really understand what they're for -
Dialogue: 0,0:01:03.52,0:01:05.10,Default,,0000,0000,0000,,what the purpose of them is.
Dialogue: 0,0:01:05.10,0:01:08.47,Default,,0000,0000,0000,,Here, let me show you. Here's an example.
Dialogue: 0,0:01:08.47,0:01:10.70,Default,,0000,0000,0000,,Let's imagine that we want to do a pretty simple calculation.
Dialogue: 0,0:01:10.70,0:01:16.61,Default,,0000,0000,0000,,We want to take 62 - divided by 41.
Dialogue: 0,0:01:16.61,0:01:20.96,Default,,0000,0000,0000,,We plug this into our calculator and we get a really ugly answer.
Dialogue: 0,0:01:20.96,0:01:23.63,Default,,0000,0000,0000,,The answer that we get, what the calculator is going to spit out,
Dialogue: 0,0:01:23.63,0:01:32.96,Default,,0000,0000,0000,,is going to be 1.512195122.
Dialogue: 0,0:01:32.96,0:01:34.91,Default,,0000,0000,0000,,How's that for an ugly answer?
Dialogue: 0,0:01:34.91,0:01:38.85,Default,,0000,0000,0000,,Now, here's the thing. You obviously don't want to put this whole thing down on your sheet,
Dialogue: 0,0:01:38.85,0:01:42.79,Default,,0000,0000,0000,,so you're going to ask your teacher - how many numbers do we need to round it to?
Dialogue: 0,0:01:42.79,0:01:45.60,Default,,0000,0000,0000,,Well, that's the thing about significant figures.
Dialogue: 0,0:01:45.60,0:01:49.46,Default,,0000,0000,0000,,If you understand significant figures, you don't need to ask your teacher that question.
Dialogue: 0,0:01:49.46,0:01:53.12,Default,,0000,0000,0000,,Because the answer to that question - how many numbers do we round it to -
Dialogue: 0,0:01:53.12,0:01:57.72,Default,,0000,0000,0000,,is already answered by the numbers you divided in the first place.
Dialogue: 0,0:01:57.72,0:01:59.86,Default,,0000,0000,0000,,Let me show you what I mean.
Dialogue: 0,0:01:59.86,0:02:03.80,Default,,0000,0000,0000,,I'll give you a demonstration first, and then I'll explain the details.
Dialogue: 0,0:02:03.80,0:02:07.07,Default,,0000,0000,0000,,62 has two significant figures in it.
Dialogue: 0,0:02:07.07,0:02:11.86,Default,,0000,0000,0000,,A 6 and a 2. Two significant figures.
Dialogue: 0,0:02:11.86,0:02:16.47,Default,,0000,0000,0000,,41 has a 4 and a 1 - also two significant figures.
Dialogue: 0,0:02:16.47,0:02:21.61,Default,,0000,0000,0000,,That means that I'm going to round the answer that I got to two numbers - simple as that.
Dialogue: 0,0:02:21.61,0:02:24.70,Default,,0000,0000,0000,,So that 1 is going to stay and the 5 is going to stay.
Dialogue: 0,0:02:24.70,0:02:26.55,Default,,0000,0000,0000,,But remember, I'm going to be rounding.
Dialogue: 0,0:02:26.55,0:02:32.28,Default,,0000,0000,0000,,So I'm going to have to look at the number next to the 5 to determine whether I keep the 5 the same,
Dialogue: 0,0:02:32.28,0:02:35.44,Default,,0000,0000,0000,,or if it's a big number, if I'm going to round up to 6.
Dialogue: 0,0:02:35.44,0:02:37.60,Default,,0000,0000,0000,,In this case it's a 1 so I don't round up.
Dialogue: 0,0:02:37.60,0:02:42.52,Default,,0000,0000,0000,,I keep it as 1.5.
Dialogue: 0,0:02:42.52,0:02:44.37,Default,,0000,0000,0000,,And that's my final answer.
Dialogue: 0,0:02:44.37,0:02:46.66,Default,,0000,0000,0000,,The question of how many numbers I need to round it to -
Dialogue: 0,0:02:46.66,0:02:52.52,Default,,0000,0000,0000,,is already answered by the number of significant figures in the numbers that I divided together.
Dialogue: 0,0:02:52.52,0:02:58.11,Default,,0000,0000,0000,,Now, the question you may ask is - how did I know that there were two significant figures in the 62 and the 41?
Dialogue: 0,0:02:58.11,0:03:00.12,Default,,0000,0000,0000,,The answer is pretty simple.
Dialogue: 0,0:03:00.12,0:03:05.70,Default,,0000,0000,0000,,Any number that isn't zero is always a significant figure.
Dialogue: 0,0:03:05.70,0:03:09.44,Default,,0000,0000,0000,,We'll talk about zero in the next lesson because it can get a little bit tricky.
Dialogue: 0,0:03:09.44,0:03:11.72,Default,,0000,0000,0000,,Let's take a look at another example.
Dialogue: 0,0:03:11.72,0:03:17.81,Default,,0000,0000,0000,,Let's do 782 divided by 231.
Dialogue: 0,0:03:17.81,0:03:23.95,Default,,0000,0000,0000,,Put that into the calculator again. We get a really ugly answer out.
Dialogue: 0,0:03:23.95,0:03:27.18,Default,,0000,0000,0000,,3.385 blah blah blah.
Dialogue: 0,0:03:27.18,0:03:29.19,Default,,0000,0000,0000,,I don't want to put that whole thing on my sheet either.
Dialogue: 0,0:03:29.19,0:03:31.36,Default,,0000,0000,0000,,So I look at the numbers that I divided together.
Dialogue: 0,0:03:31.36,0:03:40.16,Default,,0000,0000,0000,,How many significant figures in 782? Well, none of them are zero, so - 3 significant figures here.
Dialogue: 0,0:03:40.16,0:03:41.45,Default,,0000,0000,0000,,They're all significant.
Dialogue: 0,0:03:41.45,0:03:46.52,Default,,0000,0000,0000,,231? No number zero - 3 significant figures here.
Dialogue: 0,0:03:46.52,0:03:51.77,Default,,0000,0000,0000,,What does that mean? It means that I'm going to round my answer to 3 significant figures.
Dialogue: 0,0:03:51.77,0:03:55.71,Default,,0000,0000,0000,,This is going to stay, this is going to stay, and this is going to stay.
Dialogue: 0,0:03:55.71,0:04:00.78,Default,,0000,0000,0000,,As before, I'm rounding, so I look at the number to the right of this 8.
Dialogue: 0,0:04:00.78,0:04:04.12,Default,,0000,0000,0000,,It's a 5, which means that I'm going to have to round up.
Dialogue: 0,0:04:04.12,0:04:06.72,Default,,0000,0000,0000,,That 8 is going to become a 9.
Dialogue: 0,0:04:06.72,0:04:13.86,Default,,0000,0000,0000,,And my final answer is going to be 3.39.
Dialogue: 0,0:04:13.86,0:04:18.68,Default,,0000,0000,0000,,Again - it's 3.39 because that 5 there makes me round the 8 up.
Dialogue: 0,0:04:18.68,0:04:21.53,Default,,0000,0000,0000,,Let's go to one more example.
Dialogue: 0,0:04:21.53,0:04:31.62,Default,,0000,0000,0000,,1219 divided by 3462. Another pretty ugly number.
Dialogue: 0,0:04:31.62,0:04:37.61,Default,,0000,0000,0000,,Dot 352109.
Dialogue: 0,0:04:37.61,0:04:39.88,Default,,0000,0000,0000,,How many numbers do I round it to?
Dialogue: 0,0:04:39.88,0:04:42.70,Default,,0000,0000,0000,,I'm sure you've already gotten the hang of it.
Dialogue: 0,0:04:42.70,0:04:46.63,Default,,0000,0000,0000,,Four significant figures here, four significant figures here -
Dialogue: 0,0:04:46.63,0:04:50.46,Default,,0000,0000,0000,,That means I round my answer to - you guessed it - four significant figures.
Dialogue: 0,0:04:50.46,0:04:53.45,Default,,0000,0000,0000,,This stays, this stays, this stays, and this stays.
Dialogue: 0,0:04:53.45,0:04:58.77,Default,,0000,0000,0000,,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.
Dialogue: 0,0:04:58.77,0:05:04.38,Default,,0000,0000,0000,,My final answer is going to be .3521.
Dialogue: 0,0:05:04.38,0:05:07.46,Default,,0000,0000,0000,,There you go. Rounded to four significant figures.
Dialogue: 0,0:05:07.46,0:05:11.25,Default,,0000,0000,0000,,Now, we can do this exact same thing with multiplication.
Dialogue: 0,0:05:11.25,0:05:15.60,Default,,0000,0000,0000,,All we have to do is round, and then we add a couple zeros if we need to.
Dialogue: 0,0:05:15.60,0:05:17.94,Default,,0000,0000,0000,,Let me show you what I mean.
Dialogue: 0,0:05:17.94,0:05:26.53,Default,,0000,0000,0000,,When I take 56 and multiply it by 28, the answer that I get is 1568.
Dialogue: 0,0:05:26.53,0:05:31.55,Default,,0000,0000,0000,,But as with division, I look at the significant figures in the two numbers I multiplied together -
Dialogue: 0,0:05:31.55,0:05:34.20,Default,,0000,0000,0000,,two here and two here -
Dialogue: 0,0:05:34.20,0:05:38.10,Default,,0000,0000,0000,,which means that I'm going to round my final answer to two numbers.
Dialogue: 0,0:05:38.10,0:05:39.78,Default,,0000,0000,0000,,This one stays and this one stays,
Dialogue: 0,0:05:39.78,0:05:42.70,Default,,0000,0000,0000,,and I look to the right of it to decide whether I round up or down.
Dialogue: 0,0:05:42.70,0:05:45.21,Default,,0000,0000,0000,,It's a 6, so I round up.
Dialogue: 0,0:05:45.21,0:05:50.45,Default,,0000,0000,0000,,My final answer becomes 1,6 - because these two numbers stay -
Dialogue: 0,0:05:50.45,0:05:57.90,Default,,0000,0000,0000,,and I just fill everything else in with zeros. So I get 1,600.
Dialogue: 0,0:05:57.90,0:06:10.31,Default,,0000,0000,0000,,If I multiply these guys together, 4833 times 1741, I get a really big number -
Dialogue: 0,0:06:10.31,0:06:16.11,Default,,0000,0000,0000,,8 million, 414 thousand, 253.
Dialogue: 0,0:06:16.11,0:06:19.46,Default,,0000,0000,0000,,Again - how can I round this using significant figures?
Dialogue: 0,0:06:19.46,0:06:23.41,Default,,0000,0000,0000,,4 significant figures here and 4 significant figures here, so -
Dialogue: 0,0:06:23.41,0:06:27.33,Default,,0000,0000,0000,,You guessed it - I round my answer to 4 digits.
Dialogue: 0,0:06:27.33,0:06:29.86,Default,,0000,0000,0000,,I look here to find out whether I round up or down.
Dialogue: 0,0:06:29.86,0:06:37.82,Default,,0000,0000,0000,,It's a 2 so it stays the same - 8,414 - and I fill the rest of the number in with zeros.
Dialogue: 0,0:06:37.82,0:06:39.28,Default,,0000,0000,0000,,I don't need them.
Dialogue: 0,0:06:39.28,0:06:41.77,Default,,0000,0000,0000,,Round it to four digits.
Dialogue: 0,0:06:41.77,0:06:46.96,Default,,0000,0000,0000,,Now, if you're smart, you've already realized that I'm doing something pretty simple.
Dialogue: 0,0:06:46.96,0:06:52.23,Default,,0000,0000,0000,,All the numbers that I have been multiplying together or dividing have the same number of significant figures.
Dialogue: 0,0:06:52.23,0:06:55.02,Default,,0000,0000,0000,,So maybe you're asking yourself - OK, this seems easy enough,
Dialogue: 0,0:06:55.02,0:07:02.10,Default,,0000,0000,0000,,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?
Dialogue: 0,0:07:02.10,0:07:06.31,Default,,0000,0000,0000,,What if, like for example, one had 5 and one had 2 -
Dialogue: 0,0:07:06.31,0:07:09.00,Default,,0000,0000,0000,,How would I round then? Let's take a look.