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    "Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

    What are the subsequent digits of the decimal? -
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    (Original post by RosaA)
    "Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

    What are the subsequent digits of the decimal? -
    That's quite weird. Taken at face value it means: 5.237131313131313131313131313131  \ldots
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    (Original post by Zacken)
    That's quite weird. Taken at face value it means: 5.2371313131313131313131313131\l  dots
    Definitely strange.

    I wasn't sure about what to do with the 7 ... thanks
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    (Original post by RosaA)
    Definitely strange.

    I wasn't sure about what to do with the 7 ... thanks
    I think I'm right, if I am, you're welcome. If not... :lol:
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    (Original post by Zacken)
    I think I'm right, if I am, you're welcome. If not... :lol:
    Feeling extremely confident that the answer will be correct.... *laughs*
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    (Original post by RosaA)
    Feeling extremely confident that the answer will be correct.... *laughs*
    The answer is quite ugly regardless of whether I include the 7 or not...
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    (Original post by RosaA)
    "Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

    What are the subsequent digits of the decimal? -
    If there is a dot above the 3 and 1, it means the recurring part is 371

    i.e.

    5.2371371371371371
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    *bows out in shame*
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    (Original post by Student403)
    If there is a dot above the 3 and 1, it means the recurring part is 371

    i.e.

    5.2371371371371371
    See, that's what I originally thought...
    The dots are above 3 and 1 which means that they cover that region...

    Thank you!!
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    (Original post by RosaA)
    See, that's what I originally thought...
    The dots are above 3 and 1 which means that they cover that region...

    Thank you!!
    Sorry.
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    (Original post by Zacken)
    Sorry.
    All is forgiven
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    (Original post by Zacken)
    *bows out in shame*
    Don't worry about it lol
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    (Original post by RosaA)
    "Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

    What are the subsequent digits of the decimal? -
    5.2371371371... = 5.2 + 0.0371371371... = 5.2 + 0.371371371.../10.

    Now, let x = 0.371371371..., so 1000x = 371.371371...
    Thus 1000x - x = 371.371371... - 0.371371... = 371 -> 999x = 371 -> x = 371/999.

    Hence the original number is 5.2 + (371/999)/10 = 5.2 + 371/9990 = 26/5 + 371/9990 = 52319/9990.
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    (Original post by HapaxOromenon2)
    5.2371371371... = 5.2 + 0.0371371371... = 5.2 + 0.371371371.../10.

    Now, let x = 0.371371371..., so 1000x = 371.371371...
    Thus 1000x - x = 371.371371... - 0.371371... = 371 -> 999x = 371 -> x = 371/999.

    Hence the original number is 5.2 + (371/999)/10 = 5.2 + 371/9990 = 26/5 + 371/9990 = 52319/9990.
    Thank you for explaining the methodology -even though I didn't need help on that aspect of it!
    I just wanted to clarify what the subsequent digits where of the decimal but thank you for the help anyway.
 
 
 
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