We know that the fractional part must result in zeroes (the fractional part is zero) so we look at the sums of the hundredths digits. They must sum to a multiple of 10. There are three candidates: 1.85, 5.65, 15.55 taken in pairs: (1.85+5.65=7.50), (1.85+15.55=17.40), (5.65+15.55=21.20). We can therefore discard 7.38 and 2.83. The remaining set of 8 is: 28.00, 45.60, 11.50, 1.85, 5.65, 11.30, 15.55, 9.00.
From the three highlighted candidates, we have 3 possible tenths: 0.2, 0.4, 0.5. If we take these in pairs we have (0.2+0.4=0.6), (0.2+0.5=0.7), (0.4+0.5=0.9). None of these sums to a whole number, so we need to look at adding another suitable tenth from the remaining numbers. In order, we would need 0.4, 0.3, or 0.1. The only candidate is 11.30 which would combine with (0.2+0.5=0.7).
Working back we arrive at 5.65+15.55+1.85+5.65+11.30=40.00. Note that 5.65 has been used twice.
To make up the sum 100.00 we need 60.00. The only way we can get this is 28.00+9.00+11.50+11.50=60, which uses 11.50 twice.
Therefore the final answer is:
28.00+15.55+2×11.50+11.30+9.00+2×5.65+1.85=100.00.
This may not be the only solution.