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Math Help - First digit after comma

  1. #1
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    First digit after comma

    Find first digit after comma of expression (\sqrt2+\sqrt3)^{2008}
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  2. #2
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    Quote Originally Posted by terafull View Post
    Find first digit after comma of expression (\sqrt2+\sqrt3)^{2008}
    What comma?
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  3. #3
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    Quote Originally Posted by Plato View Post
    What comma?
    I think he means "decimal point" for us US people.

    -Dan
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  4. #4
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    Yes, I meant decimal point.
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  5. #5
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    2008log(\sqrt{2}+\sqrt{3})=999.5728

    Now, take 10^{.5728}=3.7394

    Those are the first few digits of this big number with about 1000 digits.
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  6. #6
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    I dont understand why like this. And 3 is the first digit after decimal point or 7?

    (\sqrt2+\sqrt3)^{2008}=10^{2008log(\sqrt2+\sqrt3)}  =10^{999.5728}=10^{999}*10^{0.5728}
    And what now?
    Last edited by terafull; January 12th 2008 at 07:15 AM.
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  7. #7
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    Quote Originally Posted by galactus View Post
    2008log(\sqrt{2}+\sqrt{3})=999.5728

    Now, take 10^{.5728}=3.7394

    Those are the first few digits of this big number with about 1000 digits.
    But I must know first digit after decimal point.
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  8. #8
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    I pretty much gave you the answer. Look at it. There are 1000 digits in the number. Therefore, counting off blocks of 3 from the far right of this huge number gives us 3,739,..................

    So, the next number after the comma is 7.

    You could even run it through a calculator. My TI-92 gives me

    3.7392622716E999

    So, there are 999 digits after the 3 and the first one is 7.

    BTW, do you use decimal points instead of commas in Europe or wherever?.

    In the US, it's commas to separate the 1000's.

    For instance, 1,000,000,000

    Would you write 1.000.000.000?

    If so, that's wacky and wrong. Do it the right way.
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  9. #9
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    Quote Originally Posted by galactus View Post
    I pretty much gave you the answer. Look at it. There are 1000 digits in the number. Therefore, counting off blocks of 3 from the far right of this huge number gives us 3,739,..................

    So, the next number after the comma is 7.

    You could even run it through a calculator. My TI-92 gives me

    3.7392622716E999

    So, there are 999 digits after the 3 and the first one is 7.

    BTW, do you use decimal points instead of commas in Europe or wherever?.

    In the US, it's commas to separate the 1000's.

    For instance, 1,000,000,000

    Would you write 1.000.000.000?

    If so, that's wacky and wrong. Do it the right way.
    OK, thanks. I mean decimal point, not comma.. So, I must find first digit after decimal point of this expression.
    In Europe are 1/4=0,25 and 10^5=10.000 or =10 000.
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