In our "Ten things you should know about" series http://mcdc.missouri.edu/TenThings/urbanrural.shtml
we talk about how urban and rural portions are defined and calculated. The Missouri Census Data Center has a web application called Mable/Geocorr that can calculate "correlation lists" between geographies. One of the additional things it can do is calculate the urban/rural portion of geographies.
To calculate the urban/rural portions of Jackson County, Missouri goto http://mcdc.missouri.edu/websas/geocorr2k.html
and follow the following steps:
1. Missouri should already be selected as the state
2. Choose County(2000) as the Source Geocode
3. Choose Urban-Rural portion (2000)
4. Scroll down and press the "Run Request" button
Here is the output http://mcdc1.missouri.edu/forum/attachments/Urban_Rural_Portion_Missouri_Counties.html
, that contains the output for all Missouri Counties.
For other geographies choose that geography for the "Source Geocode".