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Math Help - Change repeating decimal to fraction

  1. #1
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    Change repeating decimal to fraction

    Please help to solve:
    0.143 (3 repeating) I solved the following way:
    x=0.143 (3 repeating)
    100x=14.3 (3 repeating)
    1000x= 143.3 (3 repeting)
    1000x - 100x = 143.3-14.3
    900x = 129
    x= 129/900

    My question: how to solve this problem using geometric series?
    14/100 + 0.003 (3 repeating)

    I guess we need to find fraction for 0.003 (3 reapeting)

    What is the first term? What is the common ratio?
    Please help.

    Thanks
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  2. #2
    Member Henderson's Avatar
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    You've got the \frac{14}{100} just fine.

    Then you're adding in .003 + .0003 + .00003 + .000003 + ...,

    so your first term is .003, and your common ratio is \frac{1}{10}.

    Also, it's possible to say that .1433333333... is .333333333... -.2+.01, or \frac{1}{3} - \frac{1}{5} + \frac{1}{100}.
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  3. #3
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    Thank you, got it
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  4. #4
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    Simplify

    Henderson, I see you are online now. Can you please tell me whether 8 taken 7 at a time is 56 (it's on binomial theorem) It was not explained in class, but is included in the test review, I do not know what it is about, just used the formula.

    Thank you
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  5. #5
    Member Henderson's Avatar
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    Sure-

    8 taken 7 at a time is the same as the number of ways to leave one guy out, so there are only going to be 8 ways to do this.

    Here's a decent explanation of what you're talking about: Binomial Theorem.

    Hope this helps!
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  6. #6
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    Use Pascal's Triangle and expand

    (2x-3)^4 = 16x^4-96x^3+216x^2-216x + 81

    Is this correct? I did it using binomial theorem, why do I need to use Pascal's triangle?

    Thank you
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  7. #7
    Member Henderson's Avatar
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    Looks correct to me.

    You know the numbers you're getting from combinations that you're multiplying into each term (in your example, the 1,4,6,4, and 1)? Rather than run a combination for each term, Pascal's triangle gives you the whole list of coefficients (since you raised to the fourth power, these numbers are the fourth row of Pascal)
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