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Math Help - Rounding

  1. #1
    MHF Contributor Quick's Avatar
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    Rounding

    I'm taking physics this year and the first thing my teacher says to us is how to round, or to be more precise, how to round when the last digit is 5.
    Quote Originally Posted by My Physics Teacher
    If anything is beyond the five then you will round up. If there is nothing beyond the 5 and an odd number in front of the 5, then round up. If there is nothing beyond the 5 and an even number in front of the 5, then round down.
    I firmly disagree with this statement. Is this just some querky physicists thing though? or is it just my teacher...
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick View Post
    I'm taking physics this year and the first thing my teacher says to us is how to round, or to be more precise, how to round when the last digit is 5.

    I firmly disagree with this statement. Is this just some querky physicists thing though? or is it just my teacher...
    One thing I know, because I am a teacher...You'd better do what your teacher says, because as far as the class is concerned, he/she is God!

    As far as the rounding is concerned, there are several "standard" ways of rounding. They are used in Math, but not as much because Math classes generally tend to use exact numbers, not rounded.

    I have heard of the rounding method you describe and it probably works as well as any other I've heard of. The one I generally subscribe to is a bit simpler:
    If the number ends in a 5 exactly then round down. If there are any numbers after the 5 then round up.
    This sounds like it's perfectly reasonable, but there is a hidden problem: significant digits. You probably won't run into these until High School. The problem is there is generally some uncertainty in the last digit of any measured number. When in doubt, the last digit has an uncertainty plus/minus 1. So the number 10.5 is really 10.5 \pm 0.1. How do you round this using my method? You can't. (However we can just drop the last digit and say the number is 10. \pm 1, so we don't really have to worry about it, either.)

    Basically you'll see a lot of arbitrary definitions used in your Physics classes. You'll find that the rounding scheme is going to be the least of these, so don't worry about it too much.

    -Dan
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  3. #3
    MHF Contributor Quick's Avatar
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    Why would you round down? 5 should always go up.

    Although I won't try debating with my teacher, I only do that to teachers I feel will give up
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  4. #4
    dan
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    Quote Originally Posted by Quick View Post
    Why would you round down? 5 should always go up.

    Although I won't try debating with my teacher, I only do that to teachers I feel will give up
    i've always used this method:

    "if the digit after the digit you are rounding to is <=5 then round up, if it is less then 5 then round down..."
    it may not be right but it has always worked for me


    dan
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  5. #5
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    Hello, Quick!

    I was taught that even-odd routine for "rounding on 5" many years ago.

    Since 5 is exactly halfway, the rounding is evidently arbitrary.
    So to be "fair", someone invented that scheme: Odd-Add.

    Since then, however, I have "rounded up on 5."
    Here is my reasoning . . .

    The digit can be any of ten possible digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

    For half of them {0, 1, 2, 3, 4}, we round down.
    For half of them {5, 6, 7, 8, 9}, we round up.

    To me, that is "fair".

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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick View Post
    Although I won't try debating with my teacher, I only do that to teachers I feel will give up
    Though I deeply feel with you on this statement, I DO in fact debate with my teachers. I wouldn't recommend doing so until late Undergrad, though. I've been quite happy to leave a number of my teachers behind, though, Godlike though they may have been in their classrooms.

    -Dan
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