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Intro to significant figures

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers. Created by Sal Khan.

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  • aqualine sapling style avatar for user 15HayashiN
    Can anyone help me because I got more confused watching the video...
    (26 votes)
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    • aqualine ultimate style avatar for user eyrzeke
      All non-zero digits are significant; 1, 2, 3, 4, 5, 6, 7, 8, and 9;

      Zeros between non-zero digits are significant, like 705 and 80008;

      Leading zeros are never significant, like in 0.03 or 0068;

      Trailing zeros are significant ONLY if a decimal place is present; examples where the zeros are not significant include 100, 380; those that are include 38.00, 590.0, and 280.190;

      I hope this helps! Realizes that the post was made 8 years ago Oh well
      (164 votes)
  • mr pants teal style avatar for user Raelina
    What if the number is 0? Would that just be 0 significant figures?
    (23 votes)
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  • hopper cool style avatar for user FluffMania
    At , Sal covers the number 370. and how many significant figures there are in it. I'm confused about why someone would put a decimal after a number and not put any numbers after it. What is the purpose of this? If the measurement is exactly 370 anyway, why can't the number be 370.0 instead?
    (11 votes)
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    • scuttlebug yellow style avatar for user pineapple282
      From what I understand, '370.' shows that the number is accurate up to the ones place (e.g. that it is 370 and not a rounded 373 or 368). It could actually represent 370.4, but '370.' is still a correct representation of 370.4 as '370.'is accurate up to the ones place and 370.4 rounded to the ones place is 370.

      370 and 370.0 mathematically represent the same number but with significant figures, 370 is accurate up to the ones place and 370.0 is accurate up to the tenths place. Referencing the previously mentioned example, 370.4 can be accurately represented as '370.', but not 370.0.
      Hope that helps!
      (5 votes)
  • winston default style avatar for user User_E
    I don't really get it is it just like : 00.30000 mean it's has 4 significant figures?
    (9 votes)
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  • leafers ultimate style avatar for user Tesha Bair
    Why are the trailing zeros in a decimal number significant?
    (7 votes)
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    • male robot johnny style avatar for user Thomas B
      Because they indicate that you measured that value to a higher degree of precision. If I measure something as exactly 100 millimeters and record it as 0.100 meters, that represents something different than saying 0.1 meters since in the later case it may of actually been 0.12m or 0.9m and I just rounded it off. By adding the extra 0s you know that the only rounding would have been to the nearest mm.
      (15 votes)
  • purple pi purple style avatar for user Devika
    If we have a number like 14.03 and we need to round it to one significant digit, how would we do this?
    (5 votes)
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  • starky ultimate style avatar for user .
    i thought all digits were significant....
    Protest for the rights of 0's!
    (9 votes)
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  • piceratops ultimate style avatar for user Luke Spooner
    How would we do this for a number like .3 repeating? Is the number of significant digits infinite?
    (2 votes)
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  • mr pants teal style avatar for user jones316496
    So basically.... the numbers that are not 0 AFTER the 0 will be counted as significant EVEN if there are more 0's after it?
    (3 votes)
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    • leaf green style avatar for user Will
      Perhaps someone has already mentioned this, but I don't have time to read all these posts, so if I've been redundant...my apologies. Anyway, some have tried to argue that 0.00 has three significant figures because to write it using scientific notation, you would need three zeros (0.00 × 10^1). However, from what I understand, writing a number using scientific notation requires the first factor to be a number greater than or equal to one, which would seem to indicate you NEVER use zero. I still contend that 0.00 has three significant digits though, but only because placing a decimal point AFTER a zero indicates that the zero is significant, and placing zeros at the END of a decimal number indicates they were MEASURED or else they would have been omitted. Yeah!
      (2 votes)
  • leaf green style avatar for user Brenton Anderson
    I have a hard time getting what is significant and what isn't... Like, it's hard for me to grasp the concept of what MAKES a sig-fig, a significant figure.. Can someone explain it to me like I'm five years old?
    (3 votes)
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Video transcript

Let's see if we can learn a thing or two about significant figures, sometimes called significant digits. And the idea behind significant figures is just to make sure that when you do a big computation and you have a bunch of digits there, that you're not over-representing the amount of precision that you had, that the result isn't more precise than the things that you actually measured, that you used to get that result. Before we go into the depths of it and how you use it with computation, let's just do a bunch of examples of identifying significant figures. Then we'll try to come up with some rules of thumb. But the general way to think about it is, which digits are really giving me information about how precise my measurement is? So on this first thing right over here, the significant figures are this 7, 0, 0. So over here, you have three significant figures. And it might make you a little uncomfortable that we're not including these 0's that are after the decimal point and before this 7, that we're not including those. Because you're just like, that does help define the number. And that is true, but it's not telling us how precise our measurement is. And to try to understand this a little bit better, imagine if this right over here was a measurement of kilometers, so if we measured 0.00700 kilometers. This would be the exact same thing as 7.00 meters. Maybe, in fact, we just used a meter stick. And we said it's exactly 7.00 meters. So we measured to the nearest centimeter. And we just felt like writing it in kilometers. These two numbers are the exact same thing. They're just different units. But I think when you look over here, it makes a lot more sense why you only have three significant figures. These 0's are just shifting it based on the units of measurement that you're using. But the numbers that are really giving you the precision are the 7, the 0, and the 0. And the reason why we're counting these trailing 0's is that whoever wrote this number didn't have to write them down. They wrote them down to explicitly say, look, I measured this far. If they didn't measure this far, they would have just left these 0's off. And they would have just told you 7 meters, not 7.00. Let's do the next one. So based on the same idea, we have the 5 and the 2. The non-zero digits are going to be significant figures. You don't include this leading 0, by the same logic that if this was 0.052 kilometers, this would be the same thing as 52 meters, which clearly only has two significant figures. So you don't want to count leading 0's before the first non-zero digit, I guess we could say. You don't want to include those. You just want to include all the non-zero digits and everything in between, and trailing 0's if a decimal point is involved. I'll make those ideas a little bit more formal. So over here, the person did 370. And then they wrote the decimal point. If they didn't write the decimal point, it would be a little unclear on how precise this was. But because they wrote the decimal point, it means that they measured it exactly to be 370. They didn't get 372 and then round down. Or they didn't have kind of a roughness only to the nearest tens place. This decimal tells you that all three of these are significant. So this is three significant figures over here. Then on this next one, once again, this decimal tells us that not only did we get to the nearest one, but then we put another trailing 0 here, which means we got to the nearest tenth. So in this situation, once again, we have three significant figures. Over here, the 7 is in the hundreds. But the measurement went all the way down to the thousandths place. And even though there are 0's in between, those 0's are part of our measurement, because they are in between non-zero digits. So in this situation, every digit here, the way it's written, is a significant digit. So you have six significant digits. Now, this last one is ambiguous. The 37,000-- it's not clear whether you measured exactly 37,000. Maybe you measured to the nearest one, and you got an exact number. You got exactly 37,000. Or maybe you only measured to the nearest thousand. So there's a little bit of ambiguity here. If you just see something written exactly like this, you would probably say, if you had to guess-- or not guess. If there wasn't any more information, you would say that there's just two significant figures or significant digits. For this person to be less ambiguous, they would want to put a decimal point right over there. And that lets you know that this is actually five digits of precision, that we actually go to five significant figures. So if you don't see that decimal point, I would go with two.