Interesting. I guess I lucked out then, because I've had the $40 iGaging Absolute Origin for a couple years and it's still on the same battery.

https://www.amazon.com/iGaging-ABSOLUTE-Digital-Electronic-Caliper/dp/B00INL0BTS/ref=sr_1_1?dchild=1&keywords=iGaging&qid=1596599064&sr=8-1

I've got these at work, they lay flat.

https://www.amazon.com/gp/aw/d/B00INL0BTS/ref=mp_s_a_1_7?ie=UTF8&qid=1517528088&sr=8-7&pi=AC_SX236_SY340_FMwebp_QL65&keywords=Digital+caliper&dpPl=1&dpID=51r2J68iW3L&ref=plSrch