Just to clarify since quite a few on here are geeks, the sensing device operates at less than a volt. The sensing voltage swing isn't much, usually less than .2 volts. The Radio Shack digital uses three AA batteries - big sucker at 7.5volt. The device most likely regulates to (uses) 3 volts giving it a great battery life.
My other two both use a single 1.5 volt button battery. I'd guess I have reasonable accuracy down till the battery drops below a volt. As the batter declines further, the display will look just like it does with a fresh battery, but will show a lower RH reading. I feel ok with replacing those button batteries about every quarter.