1. Welcome to TechPowerUp Forums, Guest! Please check out our forum guidelines for info related to our community.

Are decimals flawed

Discussion in 'Science & Technology' started by cheesy999, May 7, 2011.

  1. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    First: a maths problem i'm sure most of us know - 0.99 recurring x 10 - 0.99 recurring =9

    this states that 0.99 recurring is = 1 and so does the equation

    1/3=0.3'

    however when you multiply out 0.3' you get 0.9' which means that 0.9' and 1 are the same, however 0.9' is not 1, but slightly less

    my understanding of maths however, is that one numerical value cannot be the same as another

    does this mean maths is flawed?

    if so, is there a number system under which these problems do not occur?
    Last edited: May 7, 2011
  2. 2DividedbyZero New Member

    Joined:
    Aug 2, 2008
    Messages:
    780 (0.36/day)
    Thanks Received:
    202
    Location:
    in retarded hell
    my sig has all the answers you need
    cheesy999 says thanks.
  3. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    too small
  4. lucas4 New Member

    Joined:
    Feb 25, 2011
    Messages:
    232 (0.19/day)
    Thanks Received:
    31
    no, because recurring means there is no end to the number (IIRC)
    u can't do it on a calculator or anything, because when ur typing in the number, it isnt actually recurring unless u type it as a fraction.
    i see what you are saying, but the margin of error is so minute, its practically insignificant.

    at least thats the way i see it :p!

    interesting point none the less :toast:
    cheesy999 says thanks.
  5. lucas4 New Member

    Joined:
    Feb 25, 2011
    Messages:
    232 (0.19/day)
    Thanks Received:
    31
    it = 90 btw :nutkick:
    cheesy999 says thanks.
  6. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    sorry wasn't concentrating i'll fix that
  7. lucas4 New Member

    Joined:
    Feb 25, 2011
    Messages:
    232 (0.19/day)
    Thanks Received:
    31
    its an interesting point, and quite awkward to explain why 0.99 doesnt = 1.

    i think the easiest way to explain it may be rounding error in the apparatus we use :toast:??
    cheesy999 says thanks.
  8. Fourstaff

    Fourstaff Moderator Staff Member

    Joined:
    Nov 29, 2009
    Messages:
    9,154 (5.43/day)
    Thanks Received:
    1,958
    Location:
    Home
    Studying for a maths major here, so I think I have some credibility.

    We know that 0.9 cannot be bigger than 1. Fix 0.9 recurring as a sequence, calling it a(n), where a(1) = 0.9, a(2) = 0.99 etc. Now we make this statement: For any positive number x, there exist an N such that N is a natural number (positive integer) and when n>N |1-a(N)|< x . From that statement, its obvious that a(n) tends to 1, therefore 0.99 recurring is 1.

    Analysis is a bitchy subject, and unless your job/life/education depends on it, its best avoided. We do silly things like finding the limit of 0/0 (0/0 tends to some random things depending on how you define the top and bottom zero).
    digibucc and cheesy999 say thanks.
  9. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    not a rounding error

    if x = 0.9'
    therefore 10x = 9.9'
    10x-x=9x = 9.9' - x

    therefore 9x = 9
  10. mlee49

    mlee49

    Joined:
    Dec 27, 2007
    Messages:
    8,474 (3.55/day)
    Thanks Received:
    2,098
    It's all about being accurate as you need to be.

    Decimals approximations are great for whole number divisions but when you try to approximate pi with decimals you'll fall short every time. However if you'd like to be accurate simply choose your degree of accuracy and there's a fraction to go with it! 22/7 or 355/113 ... it goes on!
    cheesy999 says thanks.
  11. Fourstaff

    Fourstaff Moderator Staff Member

    Joined:
    Nov 29, 2009
    Messages:
    9,154 (5.43/day)
    Thanks Received:
    1,958
    Location:
    Home
    10x - x = 9x =/= 9.9' - x
    9.9' - x = 9.9' - 0.9' = 9
    cheesy999 says thanks.
  12. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    my point is

    why use decimals if their not good?

    i use fractions myself but because there a lot easier
  13. Fourstaff

    Fourstaff Moderator Staff Member

    Joined:
    Nov 29, 2009
    Messages:
    9,154 (5.43/day)
    Thanks Received:
    1,958
    Location:
    Home
    Decimal is good, but it can only do so much. Fractions are neat and easy to work with, but they are much less accurate than decimals.

    Your sig proves the => but not the <= which is what we want. You might as well say W1zzard is either a guy or a girl or both.
    cheesy999 says thanks.
  14. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    how are they accurate if the system has errors?

    i mean - 1/3 is precisely a 1/3 of the object
  15. Fourstaff

    Fourstaff Moderator Staff Member

    Joined:
    Nov 29, 2009
    Messages:
    9,154 (5.43/day)
    Thanks Received:
    1,958
    Location:
    Home
    The system has no errors ;)
    cheesy999 says thanks.
  16. Frick

    Frick Fishfaced Nincompoop

    Joined:
    Feb 27, 2006
    Messages:
    10,382 (3.40/day)
    Thanks Received:
    2,084
    That is not an error. It's an infinite number so you can't express it in decimals.

    I don't really get your point btw. Since when is 0.99 recuring = 1? And 1/3 has never been 0.3. At least not in my schools.
    cheesy999 says thanks.
  17. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    sounds like a problem with the system if you can't use it for something

    i mean you couldn't do one calculation on an pentium processor and that was counted as an error - http://en.wikipedia.org/wiki/Pentium_FDIV_bug

    there's one problem with a calculation in decimals - doesn't that mean their broken?
    lucas4 says thanks.
  18. Fourstaff

    Fourstaff Moderator Staff Member

    Joined:
    Nov 29, 2009
    Messages:
    9,154 (5.43/day)
    Thanks Received:
    1,958
    Location:
    Home
    You will need to work with symbolic to ensure no rounding error problems, and x86 does not do its math symbolically. Well, in that sense fractions is better than decimals, contradicting what I said earlier :/
    cheesy999 says thanks.
  19. Kreij

    Kreij Senior Monkey Moderator Staff Member

    Joined:
    Feb 6, 2007
    Messages:
    13,881 (5.12/day)
    Thanks Received:
    5,615
    Location:
    Cheeseland (Wisconsin, USA)
    1/3 is not a number, it is a divisional proportion.
    All fractions are estimates based on what they are derived from, and when converted to their decimal equivelents are rounded as to be useful.

    When you do something 1/2 assed can it be equated to 0.5 assed? Not necessailry. ;)
    digibucc, erocker and cheesy999 say thanks.
  20. lucas4 New Member

    Joined:
    Feb 25, 2011
    Messages:
    232 (0.19/day)
    Thanks Received:
    31
    i dont think it means they broken.

    they are fit for their purpose, and we all know that they cannot be 100% accurate when we have a recurring answer or pi.
    this is why we round our answers to a certain number of decimal places which is considered to be an accurate enough margin.

    eg, sometimes rounding earlier answers to 4dp if u need a 2dp final answer is perfectly acceptable level of accuracy, whereas rounding to 4dp if we need a 10dp final answer isnt.
    we know when to use the appropriate degree of accuracy which doesnt make them broken IMO
    cheesy999 says thanks.
  21. Fourstaff

    Fourstaff Moderator Staff Member

    Joined:
    Nov 29, 2009
    Messages:
    9,154 (5.43/day)
    Thanks Received:
    1,958
    Location:
    Home
    An engineer's point of view. :nutkick: We can sit here all day arguing who is right, but I have weapons in my arsenal to make me right. ;)
    cheesy999 says thanks.
  22. lucas4 New Member

    Joined:
    Feb 25, 2011
    Messages:
    232 (0.19/day)
    Thanks Received:
    31
    no need for a gun fight :p
  23. cheesy999

    Joined:
    Jul 2, 2010
    Messages:
    3,881 (2.64/day)
    Thanks Received:
    572
    Location:
    UK
    so is there such thing as a number system where things like this are not a problem (say Roman numerals/attic numerals for example)
  24. lucas4 New Member

    Joined:
    Feb 25, 2011
    Messages:
    232 (0.19/day)
    Thanks Received:
    31
    *swoosh* now the talk goes above my head :roll:
    cheesy999 says thanks.
  25. Frick

    Frick Fishfaced Nincompoop

    Joined:
    Feb 27, 2006
    Messages:
    10,382 (3.40/day)
    Thanks Received:
    2,084
    IMO numbers and math is above such worldly things as usefullness. Just because we can't pin them down doesn't mean they're not useful. Think about pi.
    cheesy999 says thanks.

Currently Active Users Viewing This Thread: 1 (0 members and 1 guest)

Share This Page