The 'inverter' in our motorhomes are quite 'efficient'; efficiency is listed in the mfg specs and inverters are about 98% 'efficient'. What Fred is getting at is better explained by the term watts, a measure of work. Ohms law; volts x amps = watts (of 'work' or 'power'). For our microwave example, 120 volts x 12 amps = 1440 watts. Or, 12v x 120 amps = 1440 watts. So to do the same amount of 'work', you have to draw 10x the amps from a 12v battery as compared to a 120v source. Its the same amount of work, no matter the voltage. Simplified I know, but I hope it helps.
Happy Holidays to one and all!!