Amplitude Decibel conversion problem

Hi,
this question might be very trivial, but I haven't found good explanation
anywhere else.

I have an audio signal - some sine. Use a wavelabl to look at the
waveform, and its maximum is at about 0.6. When I change the display into
dB it shows about -5dB at that level. 
But this does not make sense - the formula is 10*log10(amplitude). So it
should be -2.5dB. I have found, that this is because we use squares for
comparison :
10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)

They say it is often used in electronics to compare voltages, but why is
it used in digital audio? Yeah I know that the digital values are
equivalent to resulting electrical power, but we are not comparing
anything
to anything. So why should we square?

And if so, then when should we NOT square?

Thanks a lot.
dmnc