Hi, welcome to the forum.
The "MKR" series have a connector for a battery.
The basic model is the MKR Zero: https://store.arduino.cc/products/arduino-mkr-zero-i2s-bus-sd-for-sound-music-digital-audio-data.
A cheap 8 MHz Arduino Pro Mini will run with three AAA batteries.
Some use a Arduino Uno with a 9V battery, but don't do that. That battery can not give enough power.
A normal multimeter is designed to last a long time on a battery. The Arduino boards are not designed for that. When you use a LCD screen, then the backlight needs current, so you need a bigger battery for that.
If you use an Arduino board to measure a voltage, then you need a good voltage reference. A Arduino has a internal voltage reference, but then you probably need a voltage divider (a voltage divider is two resistors).