Digital calipers do require a battery (there are solar ones as well, with an internal backup battery) but good calipers rarely need to have the battery replaced. The pair we have is used many times a day and often isn't even turned off for a few days but has been running without issue for over 5 years. We do suggest turning them off when not in use but many people don't even bother since the battery drain is so low.
To replace the battery, just snap of the top cover, the battery is LR44/SR44 size 1.5V button battery, available in any hardware or grocery store. The Silver Oxide SR44 costs more, but will last longer.