Lisa,
You are correct that v$version does not show the version of database. It only shows versions numbers of product installed.
I have downloaded the patch 9.0.1.3.0 and only installed patch by using Installer and did not run Oracle scripts (catalog, catproc etc) but still v$version shows that I have 9.0.1.3.0

I don't know how you can see this information.
Originally posted by DBA_Lisa
Are you sure v$version can display the version number of the database? I heard the v$version only display the version number of the Oracle installation.

Please advise. My concern is that we have a database that is not updated to the latest version. When I use 8172 point to it, the v$version shows 8172. This is not correct because the database has not been updated.

So, if you are not sure whether the db has been updated or not, how do you know the correct version number of the db?