If you have a floating point (aka, double) raster, then simply take the Int(eger) of it
Int—Help | ArcGIS Desktop
Now for most scenarios, this won't be a big issue, save the decimals get rounded/truncated, but if that is going to be an issue, then you may need to scale the values up by a factor of 10 to retain the decimal scale you need.
(ie data are between 0 and 1.5... you can scale up to 0 and 15 by multiplying Times—Help | ArcGIS Desktop by 10)
You can do your zonal statistics summaries, but you will have to 'undo' the math because of the scaling.... none is necessary if scaling isn't needed.