Is it safe to measure AAA battery current with a multimeter directly?
No, it is not safe.  An ideal current meter is a dead short.  An ideal battery has zero internal resistance.  So, in an ideal world measuring a battery by directly connecting it to a current meter will create an infinite amount of current.

In the real world, there is some resistance in just about everything.  So the current will be limited.  But most of the time this will either blow a fuse in the meter or damage the meter.  In some rare cases the battery may destroy it's self.  Which, for some battery chemistries, would be very bad.

That said, let's look at the multimeter's settings and what is displayed by the multimeter.

Read the instructions.  That should the the last word.  But an interpretation of the picture of the setup shows you have plugged in the probes to the 10A socket.  And the dial is set to 10A.  Guessing, the alternative label 20m is for when the probe is connected to the mA port.

The display is showing 5.38. Guessing, this is based on a 10A scale and is telling us that the battery is producing 5.38A.  That is really good for a 1.5 volt cell.  This is good news as we see on the multimeter's labeling next to the 10A port that the multimeter's fuse should blow when exposed to 10A for 15 seconds.  Good thing you were only testing a small battery!

Even though what you did is not recommended, let's not let the information go to wast!

We assume the battery chemistry is designed to produce 1.5 volts.  And you measured 5.4 amps.  We can then calculate the total resistance the current is running through.

V = I x R
1.5 = 5.38 x R
R = 0.28 ohms


So now we know the resistance of your 10A current meter plus the internal resistance of the battery.  If you used a second meter to measure the resistance of the 10A current meter, we could subtract that from 0.28 ohms and find the internal resistance of the battery.

Internal battery resistance is a whole other (interesting) area with respect to your question which indicates how efficient your battery will perform.



(Edit: Added text about shunt resistors and testing a power source.)

As stated earlier, an ideal current meter has zero ohms of resistance.  As a current meter is really a voltage meter (ideally infinite resistance) in parallel with a shunt resistor, we pick the shunt resistor to be a small as practical.


This arrangement makes for a good current meter.  But is a bad way to test a power source.

When testing a power source we use a "load".  Generally a resistor which has the capacity to dissipate the power we are about to put into it from the power source.  We chose the resistance of the load to be the equivalent of  what we normally use the power source for.  For example, a 1.5 volt incandescent light might be 100 ohms.  So we can pick a 100 ohm "load" or "shunt" resistor to test a 1.5 volt battery.  And we expect to see about 1.5 volts for a good battery.  So we create a graphic for our voltage meter such that when it is deflected by a 1.5 volt potential the needle is over the color green.

Here is where the above diagram came from.  You can learn more about voltage meters and shunt resistors by clicking the link.