Electronic digital calipers have gotten so cheap, that they are an essential tool for any scale machine shop. These are my notes on buying the correct replacement button cells for the common Chinese-manufactured units such as the $20 version sold by Harbor Freight.
Digital calipers use a silver oxide button cell, typically the SR44 size, aka 357, 11.6mm diameter by 5.4mm high. A genuine SR44 or 357 cell is hard to find, and the alkaline LR44, which is the same size button, and same nominal voltage, is very common and easy to find. This alkaline LR44 cell is put into toys, laser pointers, etc., and has gotten very cheap because of the large quantities made in China. However, alkaline buttons have much less mAh capacity, and have a critical weakness when used in devices like digital calipers that quit working when battery voltage falls. Alkaline cells quickly "droop" their voltage (they have a non-flat discharge curve), compared to silver oxide, and thus don't run calipers for very long before the display fades or blinks from low voltage.
Understand that these calipers are always running, and draining the battery. The on/off button simply blanks the display. So you'll typically get less than a year of service out of the correct button cell, and much less from the incorrect one.
Be careful: most retailers don't know the difference between LR44 (alkaline) and SR44 (silver oxide) and act like they are interchangeable, when they aren't. They are the same size, and the same nominal voltage, and it won't damage your calipers to run them on an LR44, but you'll only get hours of runtime from an LR44 instead of days and days from an SR44.
Notorious for this confusion is Radio Shack. Radio Shack sells an alkaline version of the silver oxide 357, which they call 357A. Ugh! No, it isn't the same thing, and a waste of money in calipers!
You can buy Chinese button cells cheap on eBay, at flea markets, and at the dollar stores, but the sellers typically are ignorant of alkaline vs silver-oxide non-interchangeability. Don't believe claims that alkaline cells are replacements for silver oxide, or that LR44 is just a cross-referenced equivalent to SR44 or 357.
For more technical details, see the excellent tutorials at http://data.energizer.com.
One ready source of these batteries is McMaster-Carr. See part number 7604K117.
The Energizer EPX76 is a valid substitute for 357. The EPX76 provides a slightly higher capacity of 200 mAh versus the 175 mAh of the 357.