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Thread: Significant Figures question

  1. #1 Significant Figures question 
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    Physics is something that i know little about, but i am attempting to learn. Therefor i am sure this is most likely the first in many posts i will be making, but i ask that you bare with me during the most simple of questions!

    The book i am reading starts with significant figures, which i grasp except for on point. I will qoute a sentance from the book which is confusing me :

    "When you make a measurement you should record and report the best observation you can make. In order to do that, you should record every digit that you are sure of, given the measuring instrument that you are using, plus one more digit that you estimate"

    And

    "Significant figures are those digits an experimenter records that he or she is sure of plus one very last digit that is doubtful."

    My question is, what is the purpose of the last estimated digit? I am guessing i am missing something because i do not understand why an estimated digit would serve better than leaving a precise figure how it is.

    I hope someone can explain this to me! Sorry for what is most likely a very basic question.

    Regards

    Mike.


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  3. #2  
    Forum Senior silkworm's Avatar
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    This is a very good question, and it is probably best explained by yourself to yourself by measuring something, but I'll try to explain anyway.

    Significant figures always go out to the first uncertain digit because you can see it. Say you're measing something with a ruler and it ends up being 10.8 centimeters but you can see that it is more than 10.8 centimeters because it is somewhere between 10.8 and 10.9 centimeters. And say that it looks right in the middle, after you've looked carefully. Then the measurement is actually 10.85 centimeters, which still is not it's true length. If you had a more precise method to measure maybe the length is really 10.852498321904950042 centimeters. Really though, because you're instrument only goes to millimeters you can only make a measurement to 0.01 centimeters. By recording it this way, not only are you making your best effort to be honest you tell whoever is reading your data about the instruments you used.

    Now you may be like, "But you're not totally sure that it's 10.85 centimeters, you're just eyeballing it, you're lying!" Well, that's true. But to stick to 10.8 or go to 10.9 would make the measurement more inaccurate than being off by ±0.01 by eyeballing that last digit. It's not perfect, but we try our best and it's a lot better than truncating. [/i]


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  4. #3  
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    Thankyou, that was a great example and i am happy to say that i now understand the reason behind it.
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    Forum Senior silkworm's Avatar
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    I'm happy to have helped.

    What sucks is when you have a philosophical argument with an instructor that 200.00 is 5 significant digits and not one. It's only 1 when your best guess is in the 100s place. Otherwise a measurement of 200.00 even could not be done without seriously sacrificing the accuracy of your calculations.

    They set these rules up to illlustrate, it's just a shame when a college professor hasn't taken the time to truly understand significant figures.
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  6. #5  
    Forum Radioactive Isotope mitchellmckain's Avatar
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    Quote Originally Posted by silkworm
    I'm happy to have helped.

    What sucks is when you have a philosophical argument with an instructor that 200.00 is 5 significant digits and not one. It's only 1 when your best guess is in the 100s place. Otherwise a measurement of 200.00 even could not be done without seriously sacrificing the accuracy of your calculations.

    They set these rules up to illlustrate, it's just a shame when a college professor hasn't taken the time to truly understand significant figures.
    But the question about how many significant digits 200.00 has, is not about measurement but about conventions. The convention is that you do not write 200.00 unless you mean that your measurement has 5 significant digits. If it has only 4 significant digits you write 200.0 and if it has only 3 you must use scientific notation 2.00x10^2. Writing only 200 is ambiguous because there is no way of telling if the two zeroes are significant. 200.00 has 5 significant digits because physicists agree not to write 200.00 unless it does in fact have 5 significant digits.
    See my physics of spaceflight simulator at http://www.relspace.astahost.com

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    Forum Senior silkworm's Avatar
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    But the question about how many significant digits 200.00 has, is not about measurement but about conventions. The convention is that you do not write 200.00 unless you mean that your measurement has 5 significant digits. If it has only 4 significant digits you write 200.0 and if it has only 3 you must use scientific notation 2.00x10^2. Writing only 200 is ambiguous because there is no way of telling if the two zeroes are significant. 200.00 has 5 significant digits because physicists agree not to write 200.00 unless it does in fact have 5 significant digits.
    You're preaching to the choir, but it's not "just about measurement but about conventions." If you're looking at raw data and the measurement is 200.00 you know how accurate the measurment could be, but the measurement dictates the significant figures.

    With the 200 example, to show there are 3 sig figs it's a convention to put "200." with the decimal point.

    My first few instructors in chemistry did not understand any of this.
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