How to make postgresql SUM to be more accurate on large amount of floating point data?
According to the documentation of the REAL datatype http://www.postgresql.org/docs/9.2/static/datatype-numeric.html#DATATYPE-FLOAT it has a precision of 6 decimal digits. That's what you are seeing. If you need more precision you need to use double or a number with fixed precision.

Maybe casting the reals to something more precise and summing the result will give you what you need, eg:

SELECT SUM(metric::double) FROM metrics;