This is absolutely normal
I'm sorry but, to be precise in the vocabulary, this may be usual (at Sony?) but not normal.
Quickly draining batteries when being OFF is neither a normal nor an acceptable behaviour for an electronic device.
This may be acceptable for a standby mode but then a full OFF mode is required.
This is especially not acceptable since SONY is now sending out unsollicited modifications to the firmware of their TV's to show an intrusive and recurrent warning about energy consumption each time the user is raising up brightness (!) using new European energy consumption guidelines as an excuse...but is still draining up energy from other devices without even the user being aware...!
This behaviour will also put useless tear on the battery itself, shortening up the life of the battery and ultimately (as Sony does not guarantee the availability of the spare parts beyond the duration of the warranty) of the device itself. And repeating removing the battery is not acceptable either, and will put unwanted tear as well on the mechanical door of the battery space.
About the RX100, the problem is of course known by SONY and even documented on this page (but without real solution).
If you do a quick search on the Internet about "RX100 battery drain", you will see that it is also a widely known problem. Or you can read the section "Known problems" in the corresponding section of the E:62:10 website.
The following are a few examples :
You may find herein some possible hints & tips to reduce the energy consumption of your device, but basically it's a known problem with this model.
