Power a multimeter from a 9V adaptor
You should NOT power the multimeter with the same power supply that you are using for your project.

One reason is that the negative lead of the meter is probably NOT tied to the battery (-) connection.  That means that you may damage your meter if you do connect the black lead to the battery (-) lead.

Note that the most common voltage measurement that you are going to make is with the meter black lead connected to the Arduino ground buss.  But you might also be doing a high-side measurement such as measuring the voltage across a resistor in series with your power supply.



There are several other reasons that you should NOT power your multimeter from an external power supply.

1) Safety.  Does your external power supply have sufficient isolation between its' input and output?  When you connect the leads of your multimeter to the circuit under test and that circuit is sitting at a high voltage (line potential, for example), that means that the power supply output is sitting at or near that same potential.  Most inexpensive power supply adapters are not rated to have the output sitting at some potential high above earth ground.

2) Noise.  Any noise that is present on your AC Mains will be passed into your meter.  This has two consequences:  you can couple that noise into the circuit that you are measuring; and that noise can corrupt your meter readings.