In image compression using transforms, how to deal with the transformed coefficients as they are not integers?
Oftentimes some rounding occurs in storing the coefficients. This is why many image compression algorithms are lossy, i.e. they lose information when converting the floating point coefficients to integer format. The process of rounding is called quantization. See this wikipedia article for an example. 

http://en.wikipedia.org/wiki/JPEG#Quantization