 In this video on measurement and precision, we're going to start by doing a little exercise of something you're probably already familiar with from elementary school. We're going to take the measurement of something, measurement of a length of something. So over here to the side, I have a something that I'm measuring represented by this pink section here, and I have a scale that we're going to measure with. We're going to look carefully at that scale. Let me hold it down there. And I want you to do the best that you can to estimate a measurement value for the length of this pink piece, assuming of course that extends off of the edge down to zero and it's lined up with zero. How long is this pink piece of material? Now if you're familiar with this system, you should know that between the five and the six, we have divisions. And based on how old this system is, one of the things about measuring lengths is the only way that it's easy to divide a length is to take it and fold it in half. And that makes it very easy to find the center, and then we can fold that in half and fold that in half and fold that in half. Dividing things into equal units, other equal units like in the thirds or fifths or tenths is actually harder to do without doing some sort of more advanced mathematical calculations. So in this particular case, we have a system, and this is part of the US customary system. Usually this would be measurement of inches where we divide in units of two. So if we look carefully here, we have there's my half, and then between the halves we have quarters. So this would be one quarter and three quarters. And then we have eights and sixteenths and thirty seconds. And if I look carefully here, it looks like the line that's closest to my edge here is going to be the fifteen thirty seconds. So this might be recorded as five and fifteen thirty seconds. Now, this system is very common, and your grandparents or other ancestors may very often have used five and fifteen thirty seconds as a measurement and would be able to very quickly add the fractions together if they had something that was five and fifteen thirty seconds and they wanted to add something that was seven and three-eighths. They could do that math very quickly. We have since moved a little bit away from using this system, but this is typically how you will see things measured on an inch measurement tape. The main thing about this system is the precision of the system is often based on trying to make an estimate as close as possible to that nearest line. Whatever line is nearest, if you happen to be between two lines, you pick the one that's closest to. Now, we have a very different system that we use for measurement when we are measuring in the metric system or the system international. We're going to take a look at that now. Now, let's consider doing a measurement using the metric system. Now, the differences in the metric system, as you can immediately see by looking at the scale here, is that these lines, instead of dividing things in halves and quarters and eighths and sixteenths, etc., there are actually increments, one, two, three, four, five, six, seven, eight, nine, ten. There are decimal increments in here, which makes it very different in how we go about reading it. I'd like you to go ahead and take a moment to see if you can make an estimate for, we'll zoom in here, for how long this particular piece of pink material, assuming again that it's lined up with zero on the other end, how long is this particular piece of material? Measure it, assuming it's zooming in on this scale, and notice there are units of this scale that say centimeters, although they may not look like centimeters on your screen or even in front of me because of the scaling of the system. But anyway, make an estimate. Give me a number. So I'm going to make a guess for the number that you read here. Let me write down the number that you probably wrote. 49.6 centimeters. Okay? It makes sense. Let's take a good look at here. Between 49 and 50, we know that that line there, that slightly longer line, is 0.5. And this line that's next to it is 0.66, so that's 49.6 centimeters. However, as an engineering instructor, I am unhappy with that answer. And here's why. One of the things that we want to do when we write down a measurement is we need to communicate not just the value, but we also communicate the precision with which we measured that value. And what you're communicating here with the number you wrote is you're communicating a certain level of precision. How carefully did you measure that length? However, most engineers, when they see something like this and see 49.6, they picture something very different from what we see here. What they picture is something like this. They picture that that's what you saw, that you saw the 49, that you saw the 50, and that you estimated this piece here as 0.6. Generally, the rule that we want to communicate when we measure is to measure with as much precision as possible, as carefully as possible, and communicate everything we see. We see the 49, we see the 0.6, but then we also will communicate what I like to call a fuzzy digit. What do I mean by fuzzy? Kind of like it's a little blurred. You don't really know exactly what it is. There's a second estimate that says, I can't do any better than this, but I'm going to make a last guess. So here, if we look carefully, and we'll zoom in again, if I look very carefully at that, I can see that it's at the 0.6, but I might estimate that it's a little bit past the 6. Who knows? It's not enough. I can't tell if it's a tenth pass, maybe it's two tenths past, maybe it's right on the zero, maybe I like that. That last thing I write, it almost doesn't matter what I write. I make my best estimate, so I could write 46.2. 49.62. That's what I'm going to record. What that tells anybody who later reads that measurement is, you see the 49, you saw the 0.6, and you made your best estimate at that 2. And I'll put a couple of little lines in there for 49.62, just right now to demonstrate that's what I call, again, my fuzzy digit. Notice I could have written anything in there. 49.62 and 49.61 communicate the exact same thing, because any engineer who looks at that should say that last one was just an estimate. I could put down 49.60 and communicate, again, the same thing. There is a little of a problem with that, though, with putting down that zero at the end. First of all, there's some rules that get forgotten, oftentimes, where that zero, if you record that zero, people might forget that that one is important. Specifically, if you type this into a spreadsheet, for example, the spreadsheet might just eliminate it, thinking that it's not important. And it kind of is. So I actually like to get out of the habit that if I measure with enough precision, and I know that that last one is imprecise, then I will put it, I will never put it as zero. I will often put it as 1 or 0.59 if I think it's just a little bit less. And I won't record that zero. If I'm confident that it's at zero to another decimal place, then I would write 0.601 or 6001, communicating what level I have. Now, officially 0.600 should communicate that, but in practice, those extra zeros often get lost, and so I like to not ever put that last digit being a zero. Okay, so let's practice. Here's another example. Take a look at this length measurement and give me a number value that you think is appropriate. So looking at it carefully, I look there, I see 84 and 85, so I'm going to record 84, and then it looks like we've gone past the 0.5. And now notice in this case, I would be looking and saying, oh, it's pretty obvious that's between the 0.5 and the 0.6. So I can estimate 84.5. Now somewhere between, how close is in between? Well, maybe it's a little more than half, so I could put 84.56. But notice that last one doesn't matter as long as I'm close. It could be 0.55, 0.56, 0.57, somewhere in that range. And so there again is my fuzzy digit where it doesn't really matter. In fact, if I wanted to, I could put 0.5 scribble. And it would contain almost the same amount of information, although the fact that if I put in a 6, I know it's in the upper half of the 0.5 as opposed to the lower half. So I probably want to go with 0.56 or 0.57. One other way you know whether or not you're doing this right is you could ask yourself, would I be okay just writing 84.5 here? Well, I can see it's pretty obvious that it's more than the 84.5. There's still a half in there. And if you would want to capture that half, then you should go ahead and try to capture it even if it was right on 84.5. If it was moved half a unit from what you can see and you would want to record that half, then you should record that precision with a fuzzy digit. So this is a habit I would like you to get into. If you are measuring any length or anything using a digital scale, what you can do is capture that last level of precision Why do you need to do this? Well, as we'll see a little later on, when you start working with these numbers you're going to communicate but you're going to be multiplying numbers together and you've probably heard of rules and we'll see in a later video some discussions about significant figures. Well, you start losing some of the ability to keep significant figures and so one of our goals is whenever we measure we want to get and communicate as much precision as possible because we can always round or reduce our precision and in some cases we'll have to but we can't go back and add precision later. So when you measure, what you see plus what you guess.