For digital micrometers which I don't use regularly (It is too cold to work in the shop right now) I open the battery compartment and flip the cell upside down (so it does not feed the power to anything), and pop the cap back on. This keeps it handy with the micrometer, but also keeps it fresh. I also keep a spare cell in the box the micrometer is stored in.
Most micrometers use the 357 and 44 sized cells (easy to remember -- both numbers are magnum calibers) and they are available in either alkaline or silver oxide variants. The battery life is much better in the silver oxide (I prefer SR-357 cells) -- and I believe they are also much less likely to leak and damage the micrometer.
Yes -- I also have pure analog micrometers too. Old eyes tell me I need to wear glasses to use them.
BTW I also have one Russian 0-25mm micrometer. It is beefier than all the others which I have or have used. I think the shaft is 8mm (about 5/16" instead of the more common 1/4" shaft on the others. I guess that I would not be too upset at seeing it used as a C-clamp. :-)
Enjoy, DoN.