First write out the fraction as follows:
0.324 0.324
--------- = -----------
3.6 3.600
Now move both decimal points 3 spaces to the right:
324
-------
3600
You must now find a way to divide this fraction. I would start by looking for the largest possible factor of both 324 and 3600 and then reduce the fraction by cancelling the common factor. While not large, 2 is such a common factor, so from 324/3600 we'd get 162/1800 = 81/900.
9 is a factor common to both 8a and 900, so continue reducing your fraction:
9/100. This cannot be reduced further.
9/100=0.09 (which does not repeat).