Why are Significant Figures Important?

So what’s it all about with significant figures?
I mean, really, you learned all these rules about how to multiply and divide with them,
how to do addition and subtraction, when is 0 significant and when it’s not and how to
deal with decimal places. Okay, that’s great but it’s such a pain in the neck. Really!
So what is the point of significant figures? If you’re wondering, I don’t blame you. For
one thing, significant figures are useful because they tell us how to round, so we don’t
have to worry about whether we should round to one or two or three decimal places. So
that’s kind of useful. But the real point is more important than that. The real point
of significant figures is to make sure that the answer you get, like from a math problem,
isn’t more precise than the numbers you started out with in the first place. This is a little
bit tricky so let me tell you what I mean by it. Most of the math we do in science is
with numbers that are measurements, right? So it’s like the amount of liquid in a beaker
that a measurement or the mass of a bunch of chemicals, also a measurement or maybe
like the amount of pressure in a gas sample. All these are measurements. So when we’re
taking measurements, some measurements can be really precise and others can be not so
precise. Let me show you what I mean. Let’s say that I have a rock here, a generic rock,
and I want to find out what its mass is. I can weigh it in a way that’s going to give
me a precise answer or in a way that’s going to give me a not so precise answer. Here’s
what I mean. I could take this rock and I could put it on a plastic toy scale from my
little sister’s Barbie scientist play set, okay? I do that and I get the answer of 82
grams. That’s the mass of the rock as determined by this scale. Or I could take the rock and
put it on an expensive NASA rocket scientist laser scale that cost $10 million dollars
but the laser scale gives me this answer. It’s says 82, similar to the Barbie playset,
.1039217 grams. All these extra numbers are here because the laser scale is much more
sensitive and gives me a much more precise number than I get from over here. So I can
say my Barbie scale number, 82, not very precise as compared to the NASA laser scale which
is super precise. Okay? Now I’ve got these two values for the mass of the rock. Let’s
say that I want to use the mass of the rock to determine its density. To do density, I’ll
do mass divided by volume. Let me take the mass from the Barbie playset here. Okay, so
I’ll take 82 grams, that’s the mass, and then I’ll only need to find out the volume of
the rock, so maybe I’ll use like a graduated cylinder also from the Barbie playset and
find out that the volume of the rock is 82 cubic centimeters. I do this math and the
answer that I get is 1.952380952 grams per cubic centimeter. Now check out your answer
and check out the numbers that I started with. This is a problem and here’s why it’s a problem…
because I started with these two numbers that were not very precise. I measured both of
these with plastic science equipment from the Barbie playset but then the answer that
I got is super, super precise or at least it looks super precise. This answer here looks
like it’s so precise that I only could have measured it with this super expensive NASA
laser instrument, okay? If you think about it, this doesn’t make sense. It doesn’t make
sense to start out with this really imprecise numbers and end up with a number that is so
precise I only could have gotten it with really sophisticated sensitive equipment. So this
is where significant figures come in. If I’m using significant figures or I’ll do the
same calculations but I’ll realize that there are two significant figures in both
of the numbers I’m starting with which means that my final answer here can’t have more
than two significant figures. So instead of 1 point all this stuff, I’m only going to
get 2.0 grams per cubic centimeter. And now in this case, the answer that I get isn’t
more precise than what I started with. So this is what I get without significant figures
and now when I use significant figures, I get an answer that is just as precise but
not more precise than what I started with so it actually makes sense. Now on the other
hand, if we started with two super precise numbers, if we measured both the mass and
volume with super-sensitive equipment, it would be totally fine first to get an answer
that itself is very precise but that’s only because this starting information here was
precise so the answer too can be precise. This is with the correct number of digits
based on significant figures. I hope you’re beginning to get the hang of this and to help
you I want to give you an analogy to the everyday world that might really make this all come
together for you. Okay. so imagine that you’re at home and you’re trying to meet up with
two friends were hanging out somewhere in the city. You give them a call and that’s
the first one. “Hey, where are you? I want to come meet up with you.” Your first friend
is not particularly helpful and they say, “Aw man, I don’t really know where we are…
I think we’re somewhere downtown.” They give you an answer that’s not very precise.
So you’re other buddy is hanging out with him and so you call him and the second friend
is also pretty unhelpful and they say, “Yeah man, I think we’re on some street corner.”
Okay, this is also an answer that’s not very precise. So here is the two piece of information
you’re starting with, that your friends are somewhere downtown and they’re on some street
corner. Now based on these two pieces of information, would it be possible for you to come up with
this answer? Would it be possible for you to hear these two pieces of information and
think, “AHA”, you must mean the southwest corner of Mott Street and Bleecker Street.
Alright, this is an incredibly precise answer. You know exactly where they are. No you couldn’t
do this, right? Based on these two very not precise starting pieces of information, it
would be impossible for you to come to this very, very precise conclusion. Alright? And
so that is exactly what’s going on when you take two imprecise numbers to start with and
you end up with a number that seems more precise than either one of them. It’s why a number
like this doesn’t make sense why you can’t use it and why you have to use significant
figures to make sure that it’s not too precise, alright? So just to review, significant figures
are useful because they help us to make sure that that answer you get isn’t more precise
than the numbers you started with. So even though the rules of significant figures can
be real pain, there is an important point to them.

100 thoughts on “Why are Significant Figures Important?

  1. Oh my god, you are the best. today when I went to my physics class and didn't get the explanation, I wasn't procrastinating as I knew about your channel before and also that u must have made a video on significant digit already. now I can confidently walk in class as your lesson made everything crystal clear. one more thing I also really like the way your video are format, they seems so professional, Keep up the good work.

  2. waow..this is soooo cool,am not an experience student in the science class after more than 6years studying management course,but hope this video will help me in the science faculty in my A /AS level programme …thanks alot . Tyler DeWitt.

  3. Excellent explanation, and having lived in Manhattan in my 20s, nice nod to the city with the super precise directions!

  4. When you said the MASS of the rock was 82 grams, I think you meant VOLUME…..

    Just kidding.
    I was pretending to be one of those people that feel the need to correct you over absurdities.
    I'm so thankful for your videos, you're going to be the reason I make it through this semester!

  5. Ooooooooh my gosh I've been so confused on why significant figures are important for so long and they've been so frustrating and this makes perfect sense

  6. You are using the word "precise" instead of accurate. It is better to say accurate because your plastic toy balance can be very precise, meaning that if you measure the rock many -many times you get the same answer 82 g. Getting the same answer is the meaning of precision.

  7. It seems here the answer is one-decimal digit more precise than the dividend and the divisor.  They both are precise to 7 places past the decimal.  But shouldn't the answer be also?

  8. Thank you so much my teacher was trying so hard to explain this to me but I just wasn't getting it. I watch this and it immediately makes sense!!

  9. I have a question, hehe, I've been thinking, let's say you have a big piece of land, and by some reason you want to put 3 division pieces of 3 meters, you have a ruler that can only meassure one decimal of meter, so you meassure 3.0m. So now you multiply 3.0*3 and you get 9.0m right, same precision you begin with, but now that you see that it will only take 9.0m you say, well, I rather make 4 division of 3 meters, so again you multiply 3.0m *4 and now you end up with 12, but, you can only have 2 significant figures, so your result is actually 12.m not 12.0m, but if you instead of multiplying you make the sum, you end up with 12.0m, so what to do?
    I mean from your instruments 12.0 is doable and with the same precision as your instruments.

    Or lets say you have a land of 12.0m and you want to divided in 5 pieces, , now you have a by significant figures, 4.00m but that is way more precise than your instrument, but you have 3 significant figures just as the one you begin with.

    Or in your very example you end up with 2.0 grams per cc, but that .0 is more precise than your instruments, that .0 you cannot know it, because your instruments cannot meassure a decimal of a gram.

  10. I'm in chemistry 1 in sophomore high school right now and I've literally gotten so much extra help with significant figures and I just can't wrap my head around them. With the analogy with the barbie set and whatnot, why do you have to cut the number so short because of the significant figures? isn't the goal here to be as accurate as possible? when you said it doesn't make sense for an "inaccurate" measurement to create such a precise number, that doesn't make sense. Why does it matter how many numbers you started with? When you do the math with the exact numbers you recorded, it makes sense that you would get a large decimal because that's just math. I don't understand why you can only report your answer to the number of sig figs in your measurement. When you round you end up making the number less accurate.
    I may just be WAY over thinking it because I have a quiz tomorrow, but like I understand the math enough to just do it and move on, but that's useless if I don't know it's purpose and how to use it. I'd love if you could reply and clear some of this up. Thank you.

  11. I really need to watch this vid but idk what is the prob with my YouTube!! Whenever I try to watch a vid it just stops at 00:00 just stops there!! I really need it !! The only why I hate using today's digital devices they can never be trusted!!! I wish I had a book with me right now!!

  12. Your analogy is brilliant. Really made this concept click for me–I only wish teachers could explain it as easily and clearly as you did…then we could all avoid the headache of students complaining that this concept doesn't make sense. Teachers set themselves up for failure when they present sig figs as this obscure and bizarre concept that no one understands. Thanks so much for this video!

  13. awesome tyler is the man! But question??? is accuracy a better term than precise for the locations downtown, since precision means close relative to other measures, whereas accuracy refers to close to true measure (like the actual location)? (which I learned from tylers other videos haha)

  14. That was an EXCELLENT example!
    I understood the whole of the concept becoz of just that one real life example…..do try to include examples like these….makes us understand better! Thanks a lot! may gid bless you….

  15. my chemistry teacher told us that on some problems we shouldn't use sig figs or else we will get a really inaccurate answer and when i asked her how will we know she said you just will. and sure enough on a test there was one such problem and of course i didnt know and used sig figs getting the answer wrong

    and i still dont quite understand. so you use imprecise measurements and get an imprecise answer that just looks precise so you need to make the imprecise answer less precise just to make it so that it doesnt look precise?

  16. significant figures have a major downside. what if you do actually get exactly 82/42 from a super NASA laser scale. by the rules of this stupid system your answer has to be rounded horribly

  17. this is the most idiotic thing I've ever seen. you assume that there is never a time when whole numbers can be an exact amount. if I have 3 apples and wan to split them between 2 people by the logic of this each person would get 2 apples. which is impossible

  18. I hate Sig Figs so much, I don't understand how it would be 2.0, since 2.0*42 gives you 84g instead of 82 if you're solving for g algebraically

  19. 2017 BRO THIS GUYS IS awesome!!!! and HELPFUL!!! thx bro I am in high school and its the biggining of the school year u teach even better than my teacher's ur awesome:) thx for the help

  20. This man single handedly carried me through high school when my teachers would get mad at me trying to explain everything. Thank you so much.

  21. I'm sorry to tell you but I don't think that's a real rock but that can be excused. BTW Great video. So good in fact that my teacher required us to watch it for homework. But for real.Great video, you explained it perfectly

  22. Question : Sir, shouldn't you use the word "accurate" instead of "precise"? (as accuracy is the measure of the closeness to the actual value)

  23. wow. thank. you. I FINALLY UNDERSTAND WHY IT MATTERS!!! I asked my college professor to explain this and he wasn't able to explain it in an hour lecture… as great as you did in 7 minutes.

  24. I've always been confused by this bc I'll get an answer then have to round up +20,000 or something crazy like that. How is that more precise?

  25. Thank you for this! My maths teacher is actually a Food Tech teacher because our school doesn't seem to have enough maths teachers xD

  26. seems like being more accurate than starting numbers isn't worse than being as accurate than your starting numbers. it may be unnecessary, but it isnt anymore wrong than if i didn't use sig figs. say they were measuring how much space ship fuel they needed to travel to another galaxy. would you rather them be unnecessarily precise, or round the fuel down with sig figs? i myself would rather not get 999/1000 the way there and run out of fuel.

  27. Hi Tyler, you are an awesome teacher and thank you for making all these videos! I only have one question about one of the words you used in this video. Why did you use the word precise instead of accurate? Based on the definitions of the two words, isn't it better to use the word "accurate" since the rocket laser scale can measure something closer to the actual value?

  28. Hey man, awesome video. So essentially the heart of the problem lies in the fact that in chem/physics we often measure things and it is basically impossible to get a measurement that is 100% correct right?

  29. When we estimate mesurement uncertainty in chemical measurement the general rule is that we put the final answer in only either one or two significant figures. Are we being more conservative here because some of our measurements that we used may have only one or two significant figures while others may have more significant figures?

  30. I'm a teached. Watched the whole playlist of SF. You explain what an ambiguous numbers are, and adding them. Example: 7000 + 1

  31. I’m very sensitive, but your passion for educating made me tear up at the end of the lesson. Thank you for your help!

  32. BUT WAIT

  33. Thanks, u r such a good teacher, u r better than my highly graduated chemistry and maths teachers, love from india

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