 What is uncertainty? Uncertainty is a way to say how uncertain we are about the measurement. For example, if my task was to measure the length of this block here that I copied over here, I will have problems measuring the length because for once it's not perfectly shaped. So I could say, okay, this could be my minimum length, this could be the maximum length. So overall my length with my rule could be anything from 21 to 23 centimeters. Now instead of writing it could be anything from 21 to 23 centimeters. We're going to be writing it is 22 plus or minus 1 centimeter, which includes everything from 21 to 23. Now it's not only the shape of the object that influences the uncertainty, it's also the tool, the method, the measurement. I have another video on that where I explain in detail how you could estimate your total uncertainty of a measurement. So what is the goal of giving a measurement with uncertainty? The goal is to report the measurement or to report an accurate measurement. What does that mean having an accurate measurement? That is a measurement where we're sure that the real value lies within the range of what we're giving. So like 22 plus minus 1, meaning you're absolutely sure that the real value is anything between 21 and 23 centimeters. What is the length between precision and uncertainty? The more precise a measurement is, the lower the uncertainty of it is. The higher the uncertainty is, the less precise it is. Note that there is no direct link between precision and accuracy. I will have another video where we'll be talking about that distinction a bit more. There are two ways of reporting our uncertainties. One is the absolute uncertainty, where you give the uncertainty in the same unit as the value itself. For example here, 10 plus minus 2 meters. The other way of giving your uncertainty is using relative uncertainties, where you give the uncertainty itself in a percentage value. For example, 10 meters plus minus 20 percent. How do we convert from one to the other? Well, if you have the absolute uncertainty, you take the uncertainty, you divide it by the value, you multiply it by 100 percent. For example here, 2 meters over the 10 meters times 100 percent will give me the 20 percent. If I want to go the other way around, I take the uncertainty value, multiply it by the value itself and divide by 100. For example here, I could take 20 percent times 10 meters over 100 percent, and what I will get is my 2 meters. So you can easily convert from one to the other. Now you're probably already familiar with another way of specifying how uncertain you are about your measurement, which is using significant figures. Mostly you use significant figures, I think, in chemistry classes or in physical science, you should have seen this concept. Now what does it mean? For example, if you write 20.0, what you're saying by using significant figures is that you're not certain about the... So this one could have been a 1, could have been a 2, could have been anything else. This is the estimated digit. The last one is almost the estimated. If you only write 20, you're saying already that zero here is uncertain. So we could have had 21, we could have had 19. So this is what we do with significant figures. Now with uncertainties, we're not really doing anything different. All we do is we actually specify plus minus how much is it plus minus in this case. 0.1 meters, is it plus minus 0.2 meters, is it plus minus 0.3 meters. So I'm just a bit more quantifying how much I'm uncertain. But overall, it looks similar to what we did with significant figures. And if you do it correctly, you should kind of write your uncertainty. You should act on the estimated digits. If you write something like this, 20.00 plus minus 0.3, then you're actually creating a conflict between what you're saying with your uncertainty and what you're saying with the significant figures. So if possible, try to keep it consistent so that if someone that doesn't know about uncertainty reads your values, they also get the idea that in this case the second zero was uncertain and estimated and here was the first one that was uncertain and estimated and then somebody that knows about the concept of uncertainty knows what we mean by plus minus 2. Meaning it could have been everything from 18 to 22 while in this one here it could have been anything from 19.7 to 20.3 meters.