Post Office Precision

The United States post office must use the most sensitive scale in the world.

I thought that a package I mailed weighed 13 pounds. I was mistaken. It only weighed 10 pounds and 4.960000000000008 ounces.

Does that equal eight trillionth of an ounce, or 800 quadrillionth? A pico ounce or a femto ounce?