# Maths competition

1. Jul 28, 2008

### Kushal

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

1) If the repeating decimal 0.8451$$\bar{51}$$ 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

thanks

2. Jul 28, 2008

### nicksauce

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?

3. Jul 28, 2008

### Kushal

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 ?!

thnks

4. Jul 28, 2008

### nicksauce

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
http://en.wikipedia.org/wiki/Recurring_decimal