If your tap water reads ammonia then you will likely never get the ammonia to read 0. One thing you could do is to buy a jug of drinking water from the grocery store. It costs about 30 cents a gallon after you put a deposit on the 5 gallon jug but at least you will know that the water is good. You also could look into a reverse osmosis water system for a cheaper source of water, makes great drinking water as a side benefit.
I don't know the exact science behind the ammonia in your water but there is a form of ammonia that is not free in the water, it is captured by some means and therefore is not able to be processed by the bacteria. It is always present but evidently is not in a toxic form. Like I said, I am no expert so you may want to start a new thread asking about ammonia in tap water.
It is my opinion that your tank is probably cycled now even though the ammonia still shows on the test. For you, that .5 of ammonia may mean 0 if you continue to use that water source. During the summer months your tap water may not contain ammonia, many cities water changes during the winter.
