von kumold » Sa Jun 02, 2012 1:45 am
if your decimal is written as a cycle, like a.abc..zabc..zabc..z......
then there is one simple way to write it as fraction. first we'll get numbers after point
0.abc..zabc..zabc..z ...
and call it, for example, number x
so, x=0.abc..zabc..z...
ab..z is n-digit number
let's multiply each side of x=0.abc..zabc..z... to 10^n
we'll get
10^n*x=abc..z(point mark)abc..zabc..z...
10^n*x = abc..z + 0.abc..zabc..z... or 10^n*x=abc..z+x
so
10^n*x-x=abc..z
from that, we'll get our x
x=abc..z/(10^n - 1)
let me show it in example
let's write as fraction number 0.625625625625625625625625625....
here our abc..z is 625, and 625 is 3-digit number
from here
we'll use our formula x=abc..z/(10^n-1)
abc..z=625 and n=3
x=625/(10^3-1)
x=625/999
so, number 0.625625625625.... in fraction will be 625/999
