Significant figures
More on Significant Figures Understanding the "rules of thumb" for significant figures
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- Based on the examples in the last video
- let's see if we can come up with some rules of thumb for figuring out how many significant figures,
- or how many significant digits,
- there are in a number - or a measurement.
- So the first thing that is pretty obvious is that any non-zero digit,
- and any of the zero digits in between are significant.
- Really the 7 and the 5 here are significant and the zero's in between them, it's also going to be significant.
- So let's write this over here: so, any non-zero digits and zero's in between
- are going to be significant. That's pretty straightforward.
- Now the zero's that are not in between non-zero digits, these become a little bit more confusing.
- So let's just make sure we can rule out some of them.
- So you can always rule out - when you're thinking about significant figures -
- the leading zero's.
- And when I talk about leading zero's, I'm talking about the zero's
- that come before your non-zero digit.
- So these are leading zero's here, these are leading zero's.
- There's no leading zero's here, no leading zero's in this one, this one, and this one.
- But in any situation, the leading zero's are not significant.
- So leading zero's not significant.
- And so the last question, all you have left, I mean, you only have non-zero digits
- and zero's in between; you could have some leading zero's
- which you've already said are not significant.
- And so the only thing left that you have to figure out is what do you do with the trailing zero's,
- the zero's behind the last non-zero, or to the right of, the last non-zero digit.
- So that these trailing zero's here, there's actually two trailing zero's over,
- and then there is three trailing zero's over here.
- So let me make a little... so trailing zero's.
- What do we do with them?
- So the easy way to think about is, if you have a decimal,
- if there is a decimal anywhere in your number, count them.
- If you have a decimal count them as significant.
- they are significant. Count them as significant.
- If there is no decimal anywhere in the number,
- then it's kind of ambiguous.
- You're kind of not sure, and this is the situation.
- So clearly, over here, there's a decimal in the number
- so you count the trailing zeros - these are adding to the precision.
- Over here, there's a decimal so you count the trailing zero.
- There's a decimal here so you count the trailing zero's.
- There are no trailing zero's here.
- And over here, well the way I later put a decimal here,
- here you would count it, so if you have a decimal there you would count all five.
- If you didn't have the decimal, if you just had 37,000 like that
- it's ambiguous, and if someone doesn't give you more information
- you're best assumption is probably that they just measured to the nearest thousand,
- that they didn't measure exactly to the one and just happened
- to get exactly on 37,000.
- So if there's no decimal, let me write it this way,
- it's ambiguous, which means that you're really not sure what it means,
- it's not clear what it means, and you're proabably safer assuming
- to not count the trailing zero's.
- If someone really does measure, if you were to really measure something
- to the exact one, then you should put a decimal at the end like that.
- And there is a notation for specifying:
- let's say you do measure - let me do a different number -
- let's say you do measure 56,000
- and there is a notation for specifying that 6 definitely is the last significant digit
- and sometimes you'll see a bar put over the 6,
- sometimes you'll see a bar put under the 6.
- And that could be useful, because maybe, you're last
- significant digit is this zero over here,
- maybe you were able to measure to the 100's with a reasonable level of precision.
- And so then you would write something like,
- you'd still write 56,000,
- but then you would put the bar above that zero
- or the bar below that zero to say that that was the last significat digit.
- So if you saw something like this, you would say 3 significant digits.
- This isn't used so frequently. A better way to show that you've measured
- to 3 significant digits would be to write it in scientific notation.
- There's a whole video on that.
- But to write this in scientific notation,
- you could write this as 5.60 times 10 to the fourth power, right?
- Cause if you multiply this by 10 to the fourth
- you'd move this decimal over four spaces
- and get us to 56,000.
- So 5.60 times 10 to the fourth;
- and if this confuses you,
- watch the video on scientific notation.
- Hopefully it will clarify things a little bit.
- But when you write a number in scientific notation,
- it makes it very clear about your precision
- and how many significant digits you're dealing with.
- So instead of doing this notation that's a little bit outdated,
- I haven't seen it used much,
- with these bars below or above the high significant digit,
- instead you can represent it with a decimal
- in scientific notation
- and then it's very clear you have 3 significant digits.
- So hopefully that helps you out.
- In the next couple of videos,
- we'll explore a little bit more why significant digits are important
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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