Using Margins of Error in Data Aggregation

I am working on a project in which we wish to calculate population changes over time in different types of neighborhoods. We began by classifying each census tract in the U.S. as urban, suburban, or rural. We next needed to calculate the total population living in all urban, all suburban, and all rural census tracts in 2000 (2000 Census, Table DP-1) and 2011-2015 (5-Year ACS, Table S0101 Age & Sex). To do so, we summed together the population that lived in the same neighborhood type. In other words, to calculate the total population living in urban neighborhoods, we summed together the populations living in all urban census tracts. Aggregating the data in this manner worked fine with the 2000 census data; however, we are unsure about how account for the ACS margin of error (MOE) when aggregating data from multiple census tracts as each census tract is associated with a unique MOE.

I am seeking advice on if there is a way to either create a MOE for aggregated tabular ACS data or to account for the MOE in aggregated tabular data. I recognize that another solution to handle MOE is to use IPUMS data, but I require the census tract identifier for analysis. Many thanks in advance!