Large parts of the data in GPW do have values of less than one. Basically, the algorithm that creates the grids takes the total population of administrative units and spreads it equally over the cells that fall within that administrative unit. So, if an administrative unit with a population of 100 was comprised of 200 grid cells, each of the cell would be assigned a population value of 0.5.
Rounded integer versions of the grids are available if you would prefer to work with whole nubmers, these grids also process much faster and take up less storage space. v2glp95agi.zip would be the rounded version of the file you downloaded. The suffix ‘i’ indicates that the grid has been rounded to the nearest whole number.