Maths year 11

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    I got one for you. Express  0.\dot{1}2345679\dot{0} as the ratio of two integers.
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    (Original post by Ano123)
    I got one for you. Express  0.\dot{1}2345679\dot{0} as the ratio of two integers.
    \frac{1234567890}{10^{10}-1}
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    (Original post by RDKGames)
    \frac{1234567890}{10^{10}-1}
    In the form  a/b where  \text{gcd}(a,b)=1 .
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    (Original post by Ano123)
    In the form  a/b where  \text{gcd}(a,b)=1 .
    Oh come on, that's not what we agreed on.
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    (Original post by Ano123)
    In the form  a/b where  \text{gcd}(a,b)=1 .
    \frac{137174210}{1111111111}? Division by 9. Can't figure out any more common divisors.
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    (Original post by RDKGames)
    \frac{137174210}{1111111111}? Division by 9. Can't figure out any more common divisors.
    The answer is  10/81 . It's easier to consider the expansion of  \frac{x}{(1-x)^2} . If you make  x=0.1 it gives you want you want,
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    Why do we multiply it by 10x or 100x ?
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    (Original post by z_o_e)
    Why do we multiply it by 10x or 100x ?
    For the same reason why we would multiply 0.5 by 10 while in the process of finding a fraction for it. It makes it easy to find the fraction for it before simplifying it, and it turns the right side into a whole number which is important. We can apply the same idea with 0.5 but we do not need to take anything away because we wouldn't have any repeating decimals.

    x=0.5

    10x=5

    x=\frac{5}{10}=\frac{1}{2}

    and the method you're familiar with is:

    0.5=\frac{0.5}{1}=\frac{5}{10}= \frac{1}{2}

    which has it's similarities if you ignore the x
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    (Original post by RDKGames)
    For the same reason why we would multiply 0.5 by 10 while in the process of finding a fraction for it. It makes it easy to find the fraction for it before simplifying it, and it turns the right side into a whole number which is important. We can apply the same idea with 0.5 but we do not need to take anything away because we wouldn't have any repeating decimals.

    x=0.5

    10x=5

    x=\frac{5}{10}=\frac{1}{2}

    and the method you're familiar with is:

    0.5=\frac{0.5}{1}=\frac{5}{10}= \frac{1}{2}

    which has it's similarities if you ignore the x


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    Not quite.
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    (Original post by RDKGames)
    Not quite.
    Explanation please

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    (Original post by z_o_e)
    Explanation please

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    Because you're layout makes it confusing and nothing there adds up.

    x=0.\dot5\dot8=0.5858...

    10x=5.8585... (NOT 0.58 like you shown)

    100x=58.5858...

    try and work it from there. Think about which ones will make the decimals cancel via subtraction.
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    (Original post by RDKGames)
    Because you're layout makes it confusing and nothing there adds up.

    x=0.\dot5\dot8=0.5858...

    10x=5.8585... (NOT 0.58 like you shown)

    100x=58.5858...

    try and work it from there. Think about which ones will make the decimals cancel via subtraction.


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    That's better.
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    (Original post by RDKGames)
    That's better.


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    Yes
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    (Original post by RDKGames)
    Yes
    How would I do this?

    Question D
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    (Original post by z_o_e)
    How would I do this?

    Question D
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    Well think about it and tell me. Also, you wrote down your x wrong.

    0.\dot24\dot5 means 0.245245245... where the 245's are the one's repeating; i.e. everything in the gap between the two dots.
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    (Original post by RDKGames)
    Well think about it and tell me. Also, you wrote down your x wrong.

    0.\dot24\dot5 means 0.245245245... where the 245's are the one's repeating; i.e. everything in the gap between the two dots.


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    Perfect. I think you got the hang of this now, and I doubt GCSE would often ask you to turn repeating decimals into fractions.
 
 
 
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