Hey, guys. So sometimes in problems, you're going to have to count up the number of significant figures in a number. So in this video, I'm going to introduce you to what significant figures or sig figs actually represent, and I'm going to give you a really easy process for how we count them. So some professors are a little bit more picky about this than others, so just make sure you really need to know this before you watch this video. Let's check it out.

So guys, in physics, measurements have precision. And think of precision as the amount of detail that's given, which is really just indicated by the number of digits we get in numbers. So let's say I'm weighing a box and I grab two scales. One of them gives me 10 kilograms. The other one gives me 10.27 kilograms. Well, this one has more digits and therefore, it's more precise. It gives me more amount of detail about the actual weight of the box, whereas this one is less precise. But what we're going to see is that not necessarily then I grab another scale and I get 15 kilograms for the other. And then I grab another scale and I get 15 kilograms for the other. So the number of digits I was given here was 2, whereas I was given 3 over here. But the zero that's kind of in the front of the number doesn't actually give me any more detail about this measurement. So the number of digits that actually matter in both of these cases is 2 over here and also 2 over here. Remember, the zero doesn't really tell me anything. So we call these significant figures the number of digits that actually matter. So both of these numbers, 15 and 15, actually have the same number of significant figures. So I'm just going to give you a really easy process for how we identify the number of significant figures in a number. Let's just go straight into an example.

So we're going to determine the number of sig figs or significant figures in this number over here, and here's how you do it: The first thing you're going to do is you're always going to eliminate leading zeros. Leading zeros are going to be the ones that go in the fronts. So one way you can think about this is leading is to the left, and I like to think about it as leading, if you're leading, you're always coming first. Right? So we're always going to eliminate those numbers or those those zeros here. And the second rule is if the number has no decimal, then you're going to eliminate trailing zeros. Trailing zeros are just are the ones that go all the way off to the right side. And if you're trailing, you go after everybody else. That's how I like to think about it. So this number in particular does have a decimal place, so we're going to leave those alone for now. And then finally, we're just going to count up everything else. So now, once we're done, we just count 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Notice how I didn't eliminate these zeros over here. These are called middle zeros and they're kind of sandwiched in between 2 non-zero numbers and we always are going to count those. So that's really it. We just count up everything else and it turns out there's 11 significant figures here. So those are the steps. It's really just as simple as that. Let's just go ahead and do a bunch of examples so we see how this works.

So we're going to count up the number of sig figs in each of the following numbers. So let's just check it out. So we're going to eliminate any leading zeros, but there are none. And then if the number has no decimal, eliminate trailing. But this one does have a decimal, so we don't do anything. And then we just count up everything else. 1, 2, 3, 4, 5. So this one has 5 significant figures. So in part b, now we're going to eliminate leading zeros, which there are 3 and then, there's no trailing zeros and then, we're just going to count up everything else. So there's 2 significant figures here. And now, this one, this number over here, there's no leading zeros and there's also no trailing zeros. So we're just going to count up everything else. 1, 2, 3, 4, 5, 6, 7, 8. So there are 8 significant figures here. Notice how I have a bunch of zeros, but these are all middle zeros and we always count those. So this has 8. And now finally, I've got Or not finally, but part d, I've got a 100. So here, I have no zero No leading zeros. This does not have trailing zeros and then I'm going to count everything else. So that actually this has one significant figure here. So I want to take a moment and explain something. So notice how we actually have the same number, a 100.00 a 100, but the fact that we have a decimal here means that we have more precision and therefore more significant figures. Whereas this measurement, a 100, just has no decimal and we eliminate those numbers and only has one significant figure. So even though you represent the same number, the decimal place actually does influence the amount of sig figs that a number has. Alright. So moving on. So we have this number here, no leading zeros And then this this this number does not have a decimal, so we're going to eliminate the trailing ones and then count up. 1, 2, 3, 4, 5. So this is 5 significant figures. And now, last but not least, we've got this number here. We have leading zeros. This number does have a decimal, so we're going to leave the trailing zeros alone and then we are going to, count up everything. So this has 3 significant figures. Alright, guys. That's all there is to it. Let me know if you have any questions.