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Rounding Doubt

  1. Sep 21, 2012 #1

    nebbione

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    Hi everyone, i didn't understand how to round up a number when i'm having a five,
    for example if i have a number with the last digit greater than 5 like 12.76 i know that i can round up to 12.8 and if the last digit is less than 5 for example 12.74 i know that i can round up like this 12.7, but i didn't understand how to round up if i have a number like this : 12.65.

    my book says:
    " If the last digit dropped is equal to 5, the remaining digit should be rounded to the nearest even number. (This helps avoid accumulation of errors in long arithmetic
    processes.)"

    Can you explain me what is the meaning (english is not my mothertongue)? I can't understand it, and can you make me some examples ? please
     
    nebbione, Sep 21, 2012
  2. jcsd
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  3. Sep 21, 2012 #2

    someGorilla

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    even = pari
    odd = dispari
    :smile:
     
    someGorilla, Sep 21, 2012
  4. Sep 21, 2012 #3

    jbriggs444

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    The rule means that 3.5 should be rounded up to 4 (an even number) and that 2.5 should be rounded down to 2 (an even number).

    The idea is that if you consistently follow this rule, you are likely to round up and down with equal frequency. If you always rounded up when the last digit is five then long calculations would tend to produce results that are too high. If you always rounded down when the last digit is five then long calculations would tend to produce results that are too low.

    Rounding to an even number tends to balance things out.
     
    jbriggs444, Sep 21, 2012
  5. Sep 21, 2012 #4

    nebbione

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    thank you very much!! now I understand how it works! Thank you!
     
    nebbione, Sep 21, 2012
  6. Sep 21, 2012 #5

    mfb

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    2016 Award

    Staff: Mentor

    Rounding to an odd number or throwing dice would do the same. But the even numbers have another advantage: You can divide by 2 afterwards (if that is required in some way), and do not need to round again.


    3.5 => round to 4 => divide by 2 => 2
    3.5 => round to 3? => divide by 2 => 1.5 => round to what? 2 is better than 1.

    2.5 => round to 2 => divide by 2 => 1
    2.5 => round to 3? => divide by 2 => 1.5 => round to what? 1 is better than 1.
     
    mfb, Sep 21, 2012
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