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The Census Bureau used integer values for weights to avoid complications in rounding for tabulated data. If the final weight of the persons in a particular group was .80, then 4/5 of them were randomly assigned to get a weight of 1 and 1/5 of them were randomly assigned to get a weight of 0. This logic applies to other weights. A weight of 5.5 for a group of persons means half of the persons in this group were randomly assigned a weight of 5 and half of the persons in this group were assigned a weight of 6.
For further discussion of this, see page 4-3 in the technical documentation to the 1990 PUMS.
Source: Census of Population and Housing, 1990: Public Use Microdata Sample U.S. Technical Documentation / prepared by the Bureau of the Census. Washington: The Bureau, 1992.