DO NOT sum the rounded numbers. You're going to have inaccurate results. The total could be off significantly depending on the number of terms and the distribution of fractional parts.
Display the rounded numbers but sum the actual values. Depending on how you're presenting the numbers, the actual way to do that would vary. That way you get
14 48 10 29 __ 100
Any way you go you're going to have discrepancy. There's no way in your example to show numbers that add up to 100 without "rounding" one value the wrong way (least error would be changing 9.596 to 9)
EDIT
You need to choose between one of the following:
Most of the time when dealing with percentages #3 is the best option because it's more obvious when the total equals 101% than when the individual items don't total to 100, and you keep the individual items accurate. "Rounding" 9.596 to 9 is inaccurate in my opinion.
To explain this I sometimes add a footnote that explains that the individual values are rounded and may not total 100% - anyone that understands rounding should be able to understand that explanation.