WEBVTT
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welcome to our first example video on significant figures and
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uncertainty. So in this video, we are going
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to look specifically at the rules for using significant figures
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because it is such a common way of handling precision
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and uncertainty and physics classes and in science classes in
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general. Um, you've probably seen some of these
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before. We're just gonna go over them really briefly
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here. So first of all, everyone knows that
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the significant figures in a number like 135 is three
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. We have three SIG figs here, and the
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reason for that is because we have three digits,
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none of which are zero. Now it's the zeros
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that tend to confuse people. So let's go over
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those quickly. First of all, there's a type
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of zero that we would call a leading zero.
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Something like 00.0 25 We didn't even put another 0.25
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It turns out, because thes air leading zeros,
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none of them contribute to the number of significant figures
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. There are only two sig figs in this example
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, and that's because the two digits here, all
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that the zeros air doing, is telling you where
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exactly? Those appear in the number line. Okay
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, What decimal places they occupy. On the other
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hand, if I were to have what we might
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call a captive zero, which might look something like
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this. 0.2005 Notice we still have one leading zero
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. But now these two zero's air in between two
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non zero digits. That means in this case,
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we have four significant figures. Okay, So zeros
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that are captive or included between non zero digits are
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counted into the total number of significant figures. And
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lastly, we have something called trailing zero. So
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, for example, if I have 25 0.0 versus
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25 25 that's just gonna have to Sig Figs.
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But 25.0 that has three sig figs. The reason
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being we have a decimal here. By the same
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token, if we have 100 versus 100 decimal point
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, this is a one sigfig number, whereas 100
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decimal point is a three sig fig number. Okay
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, including the decimal point means that you want to
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count the that particular zero. Now, um,
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that doesn't mean that I could write 25.0 And that
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would be reasonable, necessarily. There are better ways
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to do that. We might use scientific notation or
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something like that instead. Um, but for this
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basic example, here you can get the idea.
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Now, the difficulty with six figure, significant figures
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usually comes when you're trying to do some sort of
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calculation. So, for example, if you have
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1.4 times 4.56 4.56 if we want to multiply these
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two things together when we multiply two numbers that have
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different numbers of sig figs, what we're gonna do
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is we're going to keep the number of significant figures
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of the least precise numbers. So in this case
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, that's 1.4. It only has two significant figures
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. So in our final product, we're only going
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to keep two significant figures. Similarly, if we're
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talking about addition or subtraction, I should say this
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applies to division as well. You only keep the
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number of significant figures of the least precise number in
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the calculation. On the other hand, if you're
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doing addition or subtraction, say you have 12.11 plus
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18 0.0 plus one point 013 and we want to
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know what am I going to keep here? What
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we're actually gonna look at is the decimal place of
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the least precise number. So, for example,
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here we have the least precise number is 18 because
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it has three significant figures, 12.11 has 41.13 also
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has four. So this is the least precise digit
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. Here is this zero. And so we're going
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to say 31 are actually to hear one than 89
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10 11, three. So this is our answer
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without the correct number of sig Figs. Because this
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is, uh because this is our least precise.
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It's are limiting term. It's got the smallest decimal
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place. Then what we're gonna do is we're gonna
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say 31.1. We're gonna only stopped at the tens
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place because this number stops at the tens place.
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If it had gone to the hundreds, say it
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had been 18.1 so we'd end up with three here
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. Then the hundreds place would be where we had
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stopped, and we have 31.13 So these are basic
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rules for using significant figures. Um, in Siris
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of calculations, make sure you pay attention to them
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.