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## Counting Significant Figures

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Hey, guys. So sometimes some problems, you're gonna 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 gonna give you a really easy process for how we count them. So this some professors 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 is the amount of detail let's given. And that's really just indicated by the number of digits that we get in numbers. So let's say I'm weighing a box and I grabbed two scales. One of them gives me 10 kg. The other one gives me 10.27. Well, this one has more digits, and therefore it's more precise. It gives me more amount of detail, but the actual weight of the box, whereas this one is less precise. But what we're gonna see is that not necessarily all digits and measurements actually matter. For example, let's grab. Let's say I grab another box and I way I get 15 kg on one, and then I grab another scale and I get 0 15 kg for the other. So the number of digits I was given here was to, whereas I was given three 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 to over here and also to 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 0 15 actually have the same number of significant figures. So I'm just gonna 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 we're gonna do is you're always gonna eliminate leading zeros. Leading zeros are gonna be the ones that go in the front. So one way you can think about this is leading is to the left, and I like to think about as leading. If you're leading, you're always coming first, right? So we're always gonna eliminate those numbers. Are those zeros here? And the second rule is if the number has no decimal, then you eliminate trailing zeroes, trailing zeros. There 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 gonna leave those alone for now. And then finally, we're just gonna count up everything else. So now, once we're done, we just count. 123456789 10 11. Notice how I didn't eliminate these zeros over here. These air called middle zeros and they're kind of sandwiched in between two non zero numbers, and we always they're gonna 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 a simple is that? Let's just go ahead and do a bunch of examples. So you see how this works. So we're gonna have We're gonna count of the number of sig figs in each of the following numbers. So let's just check it out. So we're gonna 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 of everything else. 12345 So this one has five significant figures. So in part B, now we're gonna eliminate leading zeros, which there are three. And then there's no trailing zeros, and then we're just gonna count up everything else. So there's two 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 gonna count of everything else. 12345678 So there are eight 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 eight, and now, finally I've got or not. Finally. But party, I've got 100. So here I know. Zero no leading zeros. This does not have a decimal. So I'm gonna eliminate the trailing zeros, and then I don't account everything else. So they actually this has one significant figure here. So I want to take a moment, explain something, so notice how we actually have the same number 100.0 and 100. But the fact that we have a decimal here means that we have more precision and therefore more significant figures. Whereas this measurement 100 just has no decimal, and we eliminate those numbers and only has one significant figure. So even those you represent the same number. The decimal place actually does influence them out of Sig figs than the number has. All right, 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 gonna eliminate the trailing ones and then count up 12345 So this is five significant figures and then last but not least, we've got this number here. We have a leading zeros this number does have a decimal. So we're gonna leave the trailing zeroes alone, and then we are going to, uh, account of everything. So this has three significant figures. Alright, guys, that's all there is to it. Let me know if you have any questions.

2

Problem

How many significant figures are in each of the following numbers?

a) 0.0032

b) 10790

c) 08.02

A

a) 5, b) 5, c) 4

B

a) 2, b) 5, c) 3

C

a) 5, b) 3, c) 3

D

a) 2, b) 4, c) 3

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