We have been working with Gibbs factors and the grand partition function in my thermodyamics class. There is an example in the text that deals with a system that is either occupied or not occupied (energy = 0 or energy = E). The "fractional occupation" is then defined as the Gibbs factor for that particular energy over the grand partition function. The text is very vauge as to the meaning of this fractional occupation. Does it mean that if you have N occupation sites, the fractional occuption is how many of those sites will be occupied? The text seemed to only be dealing with one occupation site.