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Math Help - How do I convert 7.54147813E^-4 into an integer or fraction.

  1. #1
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    How do I convert 7.54147813E^-4 into an integer or fraction.

    I was doing a probability tree and you have to take the probability tree like this (1/52)*(1/51)+(1/52)(1/51) = 7.54147813E^-4

    They want it in integer or fraction form. They tell me the answer is 1/1326, and when I do that I get my answer 7.54147813E^-4

    However, I have no idea how to arrive at 1/1326. Math--Frac didn't work on my ti83 calculator neither did math--dec

    This is so dumb because I know how to everything, but this last part is tripping me up.
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    \dfrac{1}{52} \cdot \dfrac{1}{51} + \dfrac{1}{52} \cdot \dfrac{1}{51} = \dfrac{2}{51 \cdot 52} = \dfrac{1}{51 \cdot 26} = \dfrac{1}{1326}
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Quote Originally Posted by InceptSean View Post
    I was doing a probability tree and you have to take the probability tree like this (1/52)*(1/51)+(1/52)(1/51) = 7.54147813E^-4
    Here's your problem. The calculation on the left is NOT equal to the number on the right. (1/52)(1/51)+ (1/52)(1/51)= 2(1/52)(1/51)= \frac{2}{(52)(51)}= \frac{2}{(52)(51)}= \frac{2}{2652}=  \frac{1}{1326}. If you want exact answers, do the exact arithmetic from the start- do not convert to decimal form and round off.

    They want it in integer or fraction form. They tell me the answer is 1/1326, and when I do that I get my answer 7.54147813E^-4

    However, I have no idea how to arrive at 1/1326. Math--Frac didn't work on my ti83 calculator neither did math--dec

    This is so dumb because I know how to everything, but this last part is tripping me up.
    Thanks from InceptSean
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Quote Originally Posted by Jester View Post
    \dfrac{1}{52} \cdot \dfrac{1}{51} + \dfrac{1}{52} \cdot \dfrac{1}{51} = \dfrac{2}{51 \cdot 52} = \dfrac{1}{51 \cdot 26} = \dfrac{1}{1326}
    I have not done long arithmetic like this in forever. So, 52/2, only because...that's the only number that can go into 52, right?
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    I don't know what you are trying to say here. I don't know what "long arithmetic" is but this really involves only multiplying integers. There is no "52/2" in this. Are you referring to \frac{2}{52}= \frac{1}{26}? I don't understand what you mean by "that's the only number that can go into 52". By "only number" do you mean "2"? No, it certainly is not the "only number" that divides evenly into 52. 4 divides into 52 13 times, 13 divides into 52 4 times, and 26 divides into 52 twice.
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Quote Originally Posted by InceptSean View Post
    I have not done long arithmetic like this in forever. So, 52/2, only because...that's the only number that can go into 52, right?
    Huh, you do not need long division.

    $\dfrac{1}{52 * 51} + \dfrac{1}{52 * 51} = \dfrac{1}{2652} + \dfrac{1}{2652} = \dfrac{2}{2652} = \dfrac{2}{2 * 1326} = \dfrac{1}{1326} \approx 0.000,754,149$

    Remember calculators usually give approximate answers when there is division involved.
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Quote Originally Posted by HallsofIvy View Post
    I don't know what you are trying to say here. I don't know what "long arithmetic" is but this really involves only multiplying integers. There is no "52/2" in this. Are you referring to \frac{2}{52}= \frac{1}{26}? I don't understand what you mean by "that's the only number that can go into 52". By "only number" do you mean "2"? No, it certainly is not the "only number" that divides evenly into 52. 4 divides into 52 13 times, 13 divides into 52 4 times, and 26 divides into 52 twice.
    Well, 2 cannot go into 51 is what I mean. So, 51 stays 51. Yes I am referencing the 2/52, I mean in this problem, not the "only number" on the broad spectrum of things.

    If it was 2/(52 x 52), the 2 would affect both in the denominator, giving 1/(26 x 26). Am I right?
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Quote Originally Posted by JeffM View Post
    Huh, you do not need long division.

    $\dfrac{1}{52 * 51} + \dfrac{1}{52 * 51} = \dfrac{1}{2652} + \dfrac{1}{2652} = \dfrac{2}{2652} = \dfrac{2}{2 * 1326} = \dfrac{1}{1326} \approx 0.000,754,149$

    Remember calculators usually give approximate answers when there is division involved.
    This just gives me 7.54147813E^-4 again on a calculator, I think I just need to get a ti84 calculator instead of a ti83...
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Actually no. If you write it as

    \dfrac{2}{51 \cdot 52} = \dfrac{2}{51 \cdot 26 \cdot 2} then you see the two's cancel giving \dfrac{1}{51 \cdot 26} = \dfrac{1}{1326}.

    Got it?
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Quote Originally Posted by InceptSean View Post
    Well, 2 cannot go into 51 is what I mean. So, 51 stays 51. Yes I am referencing the 2/52, I mean in this problem, not the "only number" on the broad spectrum of things.

    If it was 2/(52 x 52), the 2 would affect both in the denominator, giving 1/(26 x 26). Am I right?
    No. You are wrong.

    $\dfrac{2}{52 * 52} = \dfrac{2}{2 * 26 * 52} = \dfrac{1}{26 * 52} = \dfrac{1}{1352}.$

    The fact that 51 is not evenly divisible by 2 is irrelevant.

    $\dfrac{1}{52 * 51} + \dfrac{1}{52 * 51} = \dfrac{2}{52 * 51} = \dfrac{2}{2 * 26 * 51} = \dfrac{1}{26 * 51} = \dfrac{1}{1326}.$

    This is third or fourth grade arithmetic.

    Please remember what I said about calculators. They give APPROXIMATE answers for many problems, including many division problems. If you want an exact answer, you cannot rely on a calculator.
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    Re: How do I convert 7.54147813E^-4 into an integer or fraction.

    Quote Originally Posted by Jester View Post
    Actually no. If you write it as

    \dfrac{2}{51 \cdot 52} = \dfrac{2}{51 \cdot 26 \cdot 2} then you see the two's cancel giving \dfrac{1}{51 \cdot 26} = \dfrac{1}{1326}.

    Got it?
    Got it, thank you =]]
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