03 - Significant Figures Rules (Sig Fig Rules) for Calculations in Chemistry & Physics

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In this lesson, learn how to properly count significant figures in calculations for physics and chemistry. We discuss the decimal point, leading and trailing zeros, and scientific notation for significant figures (sig fig) rules.

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[@ekathe85]

Perfectly understood. Thinking about the "weakest link" is the easiest way, for instance in the case where 151 + 4,16 + 0,0220 ends up as just 155, if you had 151,000 + 4,160 + 0,0220 instead then you would keep the whole 155,138 as the final answer. English is not even my main language, yet I find the explanations crystal clear. Keep it coming!

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[@richardserlin1317]

Yeah, FWIW, it seems like that is the central intuition. For a number like 702, if you are confident in the precision of that 2, then you are certainly even more confident in the precision of the zero, and consider that significant. Because with the 2 you’re measuring a precision of how many ones; with zero you’re measuring precision of how many tens. Bigger things are much easier to measure precisely, so if you are confident you can measure the smaller thing quite precisely, then you would certainly be confident that you can measure the bigger thing quite precisely, and even more precisely.

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[@richardserlin1317]

And, I guess I should add that in my previous example, if you think the three is a significant digit, that is your confidence in the precision of that digit, then it should go without saying that you’re also confident in the precision of much bigger orders of magnitude, which is what those zeros to the left are. Those are for orders of magnitude 10 times, 100 times, and 1000 times bigger, then the units being used for the three, which is just three units of 1/10,000.

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Awesome video thank you! The part at the end is really important. I was trying to figure out how we would change 4800 to just 3 significant digits. Thanks!!

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[@benoitdesruisseaux242]

How about these rules for determining the number of significative digits. 1) If the number is in a scientific format, ex: 5 x 10@2, remove the 10@x part from the number. In this example, we remove 10@2 and the result is 5 2) Move the decimal point to the right of your number until the last digit in your number. ex: 55 is 55, 0.023 is 0023, 1.0300 is 10300 3) Remove the leading zeros from your number, 0023 is 23. 4) Count the digits that you now have in your new number, 55 = 2, 23 = 2, 10300 = 5. That is it, you have your significant number.

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[@richardserlin1317]

I think a good intuition for why you don’t count preceding zeros after the decimal point, is that those zeros are represented in the exponent part. Example, .000342 = 3.42 x 10^-4. The -4 gives you the information that there is a decimal point and three zeros. So, adding those zeros elsewhere is unnecessary, a waste of time.

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[@kennylee6271]

According to the rule that trailing zero after a decimal point are counted, can you explain how in 23:49 how that number could be anything else other then 3 S.D? Because, 100 is 3 S.D and, if it were to be 0.000100 it will still be 3 S.D. Unless you mean if there could be more trailing zeros at the end of 100, Which would make sense. Thanks for all your help I've never been good at chemistry or even math at that matter and trying to relearn and you're really helping me out!

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Its just how I circle my final answer. It really means nothing other than "this is the answer".

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[@bb-yo7lq]

At what point do you count significant figures if a problem has multiple steps? The beginning numbers? The numbers in the last step? What if there is both multiplication/division and addition/subtraction? I had a problem with a number that had only one significant figure, but rounding off to one would really throw off the answer, so I’m not sure.

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[@ady2c5]

Hi, let's take a measurement result 123. We have no decimal accuracy. The exact value can either be 122,5 or 123,4 or anything in between. Shouldn't 123 be just two sig digs then? I don't know. Just asking... Thanks.

[@Lishamarriott1]

Your right, if there is no decimal then there is not accuracy and could very well be within those ranges... However this makes it 3 S.D. instead of 4. If the true number was there, it would have the 4th digit (that would have been there as a decimal) because this would have implied accuracy.

[@CaptNaufragio]

I dont understand why significant digita are a thing yet, so far i think this is inane and pointless... But yeah good call on yer part ..

[@jayjulian5215]

At 44.9 minutes I miss where does the teacher get that 4th S.D he added in the result as a zero. Based on the notes the professor gave. I thought the answer would be 480 then 4.80 x 10^2 on scientific notation. Can someone help me understand please.

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[@lenasamuel5869]

It is because you can’t be 100% sure if those 00’s are significant or not and it needs to be 3 significant digits, you apply the scientific notation. Remember with scientific notations only the digits before the x10 are counted as significant. So we need 3 digits only but should be 4800. So 4.80 (that’s 3 significant digits) x10^3 (moving decimal 3 places makes it 4800 while still in the accurate scientific notation formula it’s only 3). It’s science n math so go figure…

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[@jezmarshall9941]

The rule 'zero before a decimal point is not counted' ( sig digits) could prove confusing when the zero is preceded by another digit, eg in the number 10.635, the zero before the DP does need counting. The rule needs clarification here...

[@MathAndScience]

Hmmm yes I agree.

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