250 divided by 30

Discussion in 'Math' started by Lightfire, Apr 30, 2011.

  1. Lightfire

    Thread Starter Well-Known Member

    Oct 5, 2010
    690
    21
    Hello,

    250 divided by 30 is results to 8 point unlimited three (like 8.33333333333) base on my math calculation.

    I used pencil and paper for calculating instead of a calculator.

    So guys, it is unlimited point three. Is there any rules in that to make it not unlimited point three. I mean to make it not unlimited. Just like 8.33333333333. But in some calculators, the results is 8.333333333333334.

    What is the correct?
     
  2. magnet18

    Senior Member

    Dec 22, 2010
    1,232
    124
    It seems that the calculator is rounding the last number up, calculators like to do funny things.
    There are no rules that make it do that other than differences in the rounding rules, division is division.
    If you don't want unlimited numbers, it's technically 8 and one third, or 25 thirds
    (8 1/3 or 25/3)
     
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  3. retched

    AAC Fanatic!

    Dec 5, 2009
    5,201
    312
    The accuracy of math you use is dependent on the accuracy you need.

    If you need accuracy to the 3rd place past the decimal, then use 8.3334

    There is another way to represent the "forever 3s" and that is to draw a line over the top of the 3s to show they go on forever...like this:
    Code ( (Unknown Language)):
    1.  
    2.   __
    3. 8.33
    4.  
     
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  4. Lightfire

    Thread Starter Well-Known Member

    Oct 5, 2010
    690
    21
    Hello,

    What if I will use the answer 8.33333333333 by multiplication.

    Like 8.33333333333 times 30.

    Is it rally needed to make it 8.33333333333? Or just make it 8.3. Or what?

    Thanks. :)
     
  5. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    @ Bill
    One overlined 3 is enough. You only need to overline the shortest period of the endless part.

    @ Lightfire
    You need to shed away the misconception that calculators will always give you the correct answer. You might have noticed a thread not long ago about the 4*24/(9+3) operation (or something like that).

    Use your basic math to determine the result.
    If you want to multiply 8. \bar3 by 30, you need to remember that the actual operation is
    \frac{25}{3} \cdot 30 =\\<br />
\frac{750}{3}=\\<br />
25

    Anything else is just an approximation to a different degree.
     
    Last edited: Apr 30, 2011
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  6. retched

    AAC Fanatic!

    Dec 5, 2009
    5,201
    312
    Like I said, It all depends on the accuracy you need.

    In cutting wood for building, 8.3inches is fine.

    If you are working with atoms, you may want to use 8.33333333333333333 inches

    For standard work, 2 places is fine.. so 8.33x30 willl do... and it usually gets the point across to anyone who reads it that it is 1/3rd and not 3 tenths.
     
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  7. Papabravo

    Expert

    Feb 24, 2006
    10,136
    1,786
    What you are asking about is precisely the difference between an exact representation and an inexact one for rational numbers. Some rational numbers have an exact decimal representation and others do not. Most calculators have 8 or 9 digits of significance to work with and apply rounding rules to those numbers that do not have exact decimal representations.
     
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  8. Lightfire

    Thread Starter Well-Known Member

    Oct 5, 2010
    690
    21
    Okay, thank you.
     
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