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Math Help - Recurring decimals

  1. #1
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    Recurring decimals

    Hello everyone!

    Question
    Change 3/11 into a recurring decimal. (no calculator).

    I started by thinking what 1/10 was and trying to work from there, but it didn't help. Help!
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  2. #2
    Moo
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    Hello,

    Do you remember how to do a division at school ?

    First, you divide 3 by 11. The quotient is 0, the remainder is 3. Then, put a coma and calculate 30/11. The quotient is 2, the remainder is 8.

    etc...

    And there will be a time when you will have 3 as a remainder. It'll be the same numbers as previously, and here is the period.
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  3. #3
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    so, it's like a sequence

    3/11 , 30/11 , 300/11
    0 r3 2 r8 27 r3

    giving 0.27...

    thats about as far as I could do it without a calculator!

    there is always a remainder, so it will always carry on, but i don't understand the bit about 'there will be a time when you will have 3 as a remainder'

    thanks.
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  4. #4
    Moo
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    Ouap, that's not like this i meant to do ^^

    D'you see the thing ?
    Attached Thumbnails Attached Thumbnails Recurring decimals-boo.jpg  
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  5. #5
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    Sorry, I don't understand what you have done there.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    I think

    the easiest way to do it if you are trying to do what I think you are is this...to get a repeating number you must have it over all nines...so to have a repeating number that repeats every two numbers you must have it over 99 so rewrite \frac{3}{11} as \frac{27}{99} and now you know that the repeated decimal equivalent is .2727272727
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  7. #7
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    Quote Originally Posted by Mathstud28 View Post
    the easiest way to do it if you are trying to do what I think you are is this...to get a repeating number you must have it over all nines...so to have a repeating number that repeats every two numbers you must have it over 99 so rewrite \frac{3}{11} as \frac{27}{99} and now you know that the repeated decimal equivalent is .2727272727
    Yes. I got it now! Thanks.
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