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Maths competition

  1. Jul 28, 2008 #1
    these are numbers i could not solve. please help me.

    1. The problem statement, all variables and given/known data

    1) If the repeating decimal 0.8451[tex]\bar{51}[/tex] is represented by the fraction a/b, where a and b are positive integers with no common factors greater than 1, find the sum a + b.

    2) if log(log(log(log x))) = 0 and log represents the base ten logarith, what is the value of x.

    3. The attempt at a solution

    1) i don't understand how to proceed. some hints would be appreciated.

    2)i kno that if, logba = x

    then, a = bx

    i got 10100 as answer but the paper says the answer is 1010,000,000,000 is the answer.

  2. jcsd
  3. Jul 28, 2008 #2


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    For b why don't you show us how you can your answer, writing out every step in full.

    For a, it is the same as finding a number 0.51515151... (and then adding 84 and dividing by 100). Do you know how you would find such a number?
  4. Jul 28, 2008 #3
    2) log(log(log(log x))) = 0

    log(log(log x)) = 100 = 1

    log(log x) = 101 = 10

    log x = 1010

    x = 101010

    oooh ok.... now i see my mistake!!! i tried doing the calculation in my head.... so foolish of my part

    errm, for #1
    d'you mean that i should break the 0.8451515151 into 0.84 + 0.005151515151 ?!

  5. Jul 28, 2008 #4


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    Yes that's how I would approach the problem. Now can you find a fraction to represent 0.005151515.... ?
    If you don't know how, you should read the section entitled "Fraction from a repeating decimal" here
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