Voltage drop measurement result doesn't match my theoretical calculation
I don't quite understand why the calculated voltage drop is 8.84V - every battery has nonzero internal resistance, so it looks like what you measured was the voltage drop on this internal resistance.

EDIT (09/01/2013): Your schematics seems to confirm that you measured the voltage drop on the internal resistance of your battery. I also suspect that your "multimeter tip's resistance" of 0.3Ω is rather irrelevant, as a decent voltmeter itself should have a much greater resistance. However, your voltage drop of 0.34V seems very low, as the internal resistance of the battery should be about 1.7Ω (http://www.alliedelec.com/images/products/datasheets/bm/DURACELL/70149225.pdf ), so the current in the circuit should be greater than, say, 2.5A, and the voltage drop on the battery should be at least 4V. Maybe I am missing something?