If the DMV shows that the index has 11.111% fragmentation, then the index has 11.111% fragmentation. Not 5%, not 3%, 11.111%. The DMV is accurate.
If the index is small (which it very likely is) the fragmentation is meaningless and should be ignored.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability