WCLN Sig Fig Rules Overview 📊

Significant Figure Rules summary

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0:00so we know that sig figs are all about determining how accurate number really
0:06is communicating so you have the rules above now if you just like memorizing
0:14rules that's fine you've got what you need
0:17personally I don't like to memorize the rules like that I like to remember
0:21things by making sense them so here's a different way to understand remember
0:27sigfig rules to better understand these rules let's consider that they are way
0:34of trying to determine what a person out there somewhere wrote down must have
0:41meant with their number
0:43keeping this in mind let's consider the first rule as the main one if they wrote
0:49down a number other than zero there must have been some reason for this digit
0:54that is it must be significant
0:58it must have mattered to the person who wrote it down
1:01they must've been telling you something with that digit you don't just randomly
1:04right down to Herr five for no good reason
1:08so really it's the other rules that we have to consider what is meant by the
1:14zeros note that all the other rules after real one or all about the zeros so
1:21what we need to determine is for each 0 is it significant or is it just a
1:28placeholder for example if we have the number 0.05 to $OPERAND centimeters we
1:37look at it we say well we know for sure that the five and the two are both
1:41significant that's a rule one so we just have to think about the zeros now this 0
1:48was needed to show that it was a small number you see there's no way to show
1:54how smaller number is without reading the decimal and the 0 here it doesn't
2:01make the number any more accurate it's just a placeholder telling us about the
2:07magnitude of the number
2:09nothing about its accuracy
2:12now let's take a look at the first 20 here you've probably noticed that you
2:19don't often see numbers that just start with a decimal for instance like this in
2:26your math and science courses as well as in modern society in general we
2:31typically write a 0 in front of the decimal like this
2:37the reason for this is about making the decimal more noticeable weather in a
2:42sentence with a bunch of periods involved or even in a list in fact if
2:48you dig into legal guidelines for engineers and pharmacists and scientists
2:53and so on you often run into a rule or recommendation to never leave a decimal
2:58point naked that is out by itself as you don't want to miss the decimal point and
3:06accidentally prescribed say five milliliters when someone intended to
3:12write down . 5 milliliters but the decimal got smudged now that would be a
3:1810-fold overdose and suddenly the little error gets really serious
3:24therefore it's always good practice to put that proceeding 0in of course then
3:32that zero out front of a decimal by itself is never significant but
3:39something like an extra place holder so as a result our number example here has
3:46two sig figs
3:51let's look at another example this time 0.05 20 so what we already know is that
4:03the five and the two are both significant so this 0 is just a
4:10placeholder as we discussed showing how small the measurement is and this 0 is
4:16just there to help us not miss the decimal so we only have to consider this
4:220 at the end now this one's not a placeholder as it doesn't help show the
4:30number is being any bigger or smaller
4:33therefore if the person who wrote this number down didn't have it to show
4:38bigger smaller there must be some other reason they wrote that number it must be
4:43to indicate accuracy therefore it must be a significant digit so this example
4:52has three sig figs
4:57now what if we had a zero in the middle of some significant digits like this
5:040.050 to now this zero right in the middle here isn't there show magnitude