Ultimately, the householder is responsible for counting those individuals who live in their home, and their relation to those individuals. The 2000 Census was the first decennial Census to identify children in foster care specifically. The 2010 Census did not identify foster care children specifically (reasons why the question were dropped are in the article below).

The person who completes the Census (usually the homeowner or renter) is designated as the householder. Then, all other household members were categorized in terms of their relationship to the householder, where foster child was an option in the 2000 Decennial. This allowed people to view characteristics of foster children specifically, rather than only counting foster children with all children.

Foster children (and other children in temporary or complicated living situations) are more likely to be missed on the Census form, potentially because respondents are unsure of whether to include the child as a household resident (e.g. Usual Place of Residence). Source:

According to the latest Census Bureau research on Census self-response, married couple households have higher Census self-response rates than single-parent households, especially single female-headed households. In other words, households headed by single parents are less likely to answer the Census questionnaire on their own, and therefore need to be counted in person by Census enumerators, which heightens the risk that these households will be counted inaccurately or missed entirely.

Source

Source

It is important to know for a few reasons, one of those reasons being the ability to view changing demographics in America overtime. The changes in the number of children in single parent households might be an indicator of shifts in social norms, the economy, or other social institutions.

Federal funds, grants, and supports to counties and communities are based on population totals and different breakdowns by demographics like sex, age, race, etc. Single parents tend to be a disadvantaged group, with many single parent families struggling to make an adequate income. Data on household composition helps to inform federal agencies for their planning and funding of government programs that provide services, supports, or funds to people raising children alone (e.g. SNAP, WIC, Section 8, Head Start, SCHIP, and other grants).