Fuji A205 DigiCam False Battery Low Indicator

I assume you meant you took 15 to 20 pictures rather than frames?  Your
experience is entirely normal.  It is well known with this camera that you
must use Ni-MH batteries and a good charger for respectable results.  And
you should put the camera in power save mode so that the use of the LCD is
minimized for it constitutes the greatest drain on batteries of all the
camera functions, save perhaps the flash.   The camera may demand 1 amp
drain from the batteries which taxes alkalines to their limit.  The walkman
on the other hand is very easy on batteries, requiring perhaps an estimated
1/20 of an ampere.  So it is no surprise that batteries that no longer work
in a digicam, work fine in a walkman.  They would also be able to power a
small clock for six months to a year as well.   Get yourself a good set of
Ni-MH batteries with a charger that takes at least 2 hours to charge (4
preferable) and enjoy the camera.  Do not get a fast charger as it is hard
on batteries.

I should ask you how you test batteries using a multi-meter?   I
suspect you
are just checking no-load voltage.  A multi-meter is not the
appropriate
instrument to check primary cells unless you are just looking to see
if they
are live or dead.  You need a load for those cells:  One make of
battery
tester checks AA batteries with a 36 ohm load and expects to see
upwards of
1.05 volts under that load.  Batteries in that state would not power a
digicam however.  If you want a good indication, and only have a
multimeter
without a load resistor, check the batteries in a high current
setting,
perhaps a 12 amp setting if you have it.  The batteries should be able
to
put out a number of amps momentarily.  You will find that under the
same
conditions Ni-MH batteries that are fully charged will be able to put
out
more amps than alkalines under such short circuit testing.  Be careful
not
to short circuit test for more than  2 to 5 seconds at a crack because
considerable heat will develop and sparks may fly.

Well I used a mutil-meter with settings set to 1.5V. There is a scale
which measures the battery charge. The settings are replace/?/good.
I'm not a muti-meter expert and really don't know anything about
testing electrical devices. But I do believe the test was under any
load.

I should ask you how you test batteries using a multi-meter?   I suspect you
are just checking no-load voltage.  A multi-meter is not the appropriate
instrument to check primary cells unless you are just looking to see if they
are live or dead.  You need a load for those cells:  One make of battery
tester checks AA batteries with a 36 ohm load and expects to see upwards of
1.05 volts under that load.  Batteries in that state would not power a
digicam however.  If you want a good indication, and only have a multimeter
without a load resistor, check the batteries in a high current setting,
perhaps a 12 amp setting if you have it.  The batteries should be able to
put out a number of amps momentarily.  You will find that under the same
conditions Ni-MH batteries that are fully charged will be able to put out
more amps than alkalines under such short circuit testing.  Be careful not
to short circuit test for more than  2 to 5 seconds at a crack because
considerable heat will develop and sparks may fly.