Turn on thread page Beta
    • Thread Starter
    Offline

    14
    ReputationRep:
    I just realised something.

    What is 4.4444... to 2 decimal places?
    Offline

    0
    ReputationRep:
    4.44?
    • Thread Starter
    Offline

    14
    ReputationRep:
    hmm. do you see where I'm coming from though. Usually when you see a 4 you look to the next number to see if it makes that 4 a 5, in which case you round up rather than down. but if it goes on forever, you'll never stop looking.
    Offline

    0
    ReputationRep:
    (Original post by mik1a)
    hmm. do you see where I'm coming from though. Usually when you see a 4 you look to the next number to see if it makes that 4 a 5, in which case you round up rather than down. but if it goes on forever, you'll never stop looking.
    I see your point

    It's along similar lines to 0.9999999... = 1 I guess.
    • Thread Starter
    Offline

    14
    ReputationRep:
    yeah I did that in the olympiad handbook... I thought there's no way you can prove 0.999 recurring equals one but you do the algebra and it works :s
    Offline

    13
    ReputationRep:
    But what is the actual theory behind it though?
    Offline

    12
    ReputationRep:
    (Original post by mik1a)
    yeah I did that in the olympiad handbook... I thought there's no way you can prove 0.999 recurring equals one but you do the algebra and it works :s
    :confused:
    Offline

    13
    ReputationRep:
    (Original post by bono)
    :confused:
    Do the a = 0.999999.....

    therefore 10a = 9.999999....

    10a -a = 9a = 9

    therefore a = 1

    ie 0.999999.... = 1
    • Thread Starter
    Offline

    14
    ReputationRep:
    The theory behind what? I just came across this when I was thinking about recurring decimals. How do you round a recurring decimal whose digits' rounding (up or down) depends on the next digit behind that.
    Offline

    12
    ReputationRep:
    (Original post by 2776)
    Do the a = 0.999999.....

    therefore 10a = 9.999999....

    10a -a = 9a = 9

    therefore a = 1

    ie 0.999999.... = 1
    Ahhh right, yes.
    Offline

    13
    ReputationRep:
    (Original post by mik1a)
    The theory behind what? I just came across this when I was thinking about recurring decimals. How do you round a recurring decimal whose digits' rounding (up or down) depends on the next digit behind that.
    I bet theres a deep math theory behind all of this. Or maybe I'm mistaken.
    Offline

    0
    ReputationRep:
    Another approach is to show that between any two real numbers there is another real number. So if .999999 =/= 1 then there is a number such that 0.9999... < x < 1. This contradicts itself, since no number can have a digit more than 9 without going over one, if you get my drift.
    Offline

    2
    ReputationRep:
    (Original post by theone)
    Another approach is to show that between any two real numbers there is another real number. So if .999999 =/= 1 then there is a number such that 0.9999... < x < 1. This contradicts itself, since no number can have a digit more than 9 without going over one, if you get my drift.
    i think the other one is more convincing :rolleyes:
    • Thread Starter
    Offline

    14
    ReputationRep:
    therefore 0.9999... must equal one.. heh.

    I'm usually no good at proofs. I usually make up my own notation and have things like a.bnc where b -n- c are the repeated digits, therefore a, b, c, and n (the set of digits between b and c) are all integers between 0 and 10. But I didn't know how to show an integer. Then I made up some formula where

    x = a + 0.1b + 0.1^(n+1)n + 0.1^(n+2)c

    blah blah

    i could go on forever with these strange things.
    Offline

    18
    ReputationRep:
    I just go on the basis that if the next number is five or more then round up.

    1.046
    1.045
    1.044

    Well 1.046 is closer to 1.05 than 1.04, and 1.044 is closer to 1.04 than 1.05... I just see it very simply...
    Offline

    18
    ReputationRep:
    (Original post by 2776)
    Do the a = 0.999999.....

    therefore 10a = 9.999999....

    10a -a = 9a = 9

    therefore a = 1

    ie 0.999999.... = 1
    But if a=0.9999... then 9a cannot equal 9. Not exactly anyway.
    Offline

    13
    ReputationRep:
    (Original post by ZJuwelH)
    But if a=0.9999... then 9a cannot equal 9. Not exactly anyway.
    But you times it by 10 FIRST so it is 9.9999999999999......

    And so:

    10a - a = 9.99999999999999....... - 0.99999999999999......... = 1

    9a = 9

    a = 1
    • Thread Starter
    Offline

    14
    ReputationRep:
    Write it as an expression with a and n, the number of digits which you take of the recurring decimal 0.999...

    Therefore when n = 2, a = 0.99; when n = 5, a = 0.99999

    As n increases, a tends to 1. THerefore in a recurring decimal, when n nis infinite, a is one.
    • Thread Starter
    Offline

    14
    ReputationRep:
    I guess you can extend it to 0.49999999

    If 0.49999999..... is a recurring decimal then multiply it by two:

    0.9999999999

    and therefore 0.4999999 = 0.5
    Offline

    18
    ReputationRep:
    (Original post by 2776)
    But you times it by 10 FIRST so it is 9.9999999999999......

    And so:

    10a - a = 9.99999999999999....... - 0.99999999999999......... = 9

    9a = 9

    a = 1
    <corrected error>

    I refuse to accept it, there's a flaw somewhere, that ain't supposed to work...
 
 
 

University open days

  • University of Exeter
    Undergraduate Open Days - Exeter Campus Undergraduate
    Wed, 24 Oct '18
  • University of Bradford
    Faculty of Health Studies Postgraduate
    Wed, 24 Oct '18
  • Northumbria University
    All faculties Undergraduate
    Wed, 24 Oct '18
Poll
Who do you think it's more helpful to talk about mental health with?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.