what is the molar ratio of 0.114 copper to 0.116 oxygen? Then how do you make an empirical formula from this information?

Well, you could just take a look at the numbers and see that 0.114 to 0.116 is for all practical purposes 1:1 so you would write CuO.

But if you don't see that, an often you can't because the numbers don't come out that well, what you do is divide the smallest number of the set (doesn't matter how many there are in the set) but in this case there are just two. Then divide the other number by the same small number. In this case you have
0.114/0.114 = 1.000 ( note that doing it this way MAKES that number come out exactly 1.000).
Then divide the other number by the same small number. In this case that is 0.116/0.114 = 1.02 so the numbers are
1 and
1.02.
Then you round that 1.02 off to 1.00 because empirical formulas are supposed to be small whole numbers and the ratio is 1:1 and CuO.