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Why are there zero weights in the 1990 Census?
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.