C8H8O3
Lookup the atomic weights of the elements involved:
Atomic weight carbon = 12.0107
Atomic weight hydrogen = 1.00794
Atomic weight oxygen = 15.999
Now determine the relative moles of each element by dividing the weight percentage by the atomic weight of each element.
Carbon = 63.15 / 12.0107 = 5.257811784
Hydrogen = 5.30 / 1.00794 = 5.258249499
Oxygen = 31.55 / 15.999 = 1.97199825
So we have a ratio of carbon : hydrogen : oxygen of
5.257811784 : 5.258249499 : 1.97199825
We want to create a ratio of small integers that comes close. So start by dividing all the numbers by the smallest. Getting:
2.666235523 : 2.666457488 : 1
Not quite there. We could multiply the above values by 1, 2, 3, etc until we get some values close to integers, but the .666 values looks rather close to 2/3, so let's multiply the values by 3 and see what we get.
7.998706568 : 7.999372463 : 3
And this looks good. The ratio looks to be
8:8:3
So the empirical formula is C8H8O3