Except in the rare case of scopes designed and intended for fully floating operation (e.g. Fluke ScopeMeters), your scope was designed under the assumption that no hazardous voltages would be present on its chassis (or front panel PCB ground plane). You don't know how good the insulation is between the scope chassis or ground plane and your finger at the supposedly insulated control you are touching. e.g. conductive dirt may have built up on the sides of a button from fingerprint oils and ambient dust. If your scope isn't properly grounded, all it takes is one bad mains spike at the wrong moment i.e. while you are pushing a button, and there's a significant risk of one dead engineer.
There was absolutely no need to float your scope. If you were probing within its (and its probes) ratings, with the ground clips removed and the scope set to display the difference between two channels (with equal Y attenuator settings), your scope would have been safer properly grounded.
The matter of not having a proper ground at your workbench is another issue:
I knew the risks, and I knew that I should never float my scope....
Except that the scope is floating whether I like it or not. By doing this, I just isolated the ground from my power strip and nothing else. Houses here don't have a ground. We thought ours had ground in the kitchen only, turns out the ground wire is just connected to neutral at one of the plugs, and not behind the circuit breakers. We do have codes, but no inspections, and so wiring tends to be a complete disaster. Against all advice, my father (I am a college student, this is our summer house where I live alone for 9 months of the year) wont do anything about it, and I was 6 when we this house was built.
If you advise me to wire the ground to neutral locally at this socket only, sure, ill do that, but something tells me this is worse than just leaving the scope floating, as it has been for a year now
Personally if I was in your situation, I'd get a ground to my bench no matter what. As long as its a single occupancy dwelling, driving a ground rod, and running a 4mm
2 ground wire to your bench should be possible. A
TT earthing system is recognized as safe and is commonly used in rural areas in many countries. You can set up just the socket strips on your bench that way without having to change any wall outlet or breaker panel wiring. A RCD (GFCI) is *ESSENTIAL* especially in hot dry climates as you are likely to have difficulty getting a low enough ground resistance to reliably trip ordinary circuit breakers or fuses. *DO* *NOT* use water (or any other) pipes for the TT ground connection - if their grounding isn't as good as you thought it was, one unnoticed fault on your bench could make every water tap in the whole building lethal. All socket strips on your bench should have their grounds tied together, and you shouldn't be physically able to come into contact with any metal pipes or building metalwork while at your bench. If the floor is dirt or concrete, you'll also need a good quality rubber or plastic insulating mat for your entire work area. Don't get a black one as it may be somewhat conductive due to being carbon filled.
If its actually a multi-occupancy building (e.g. apartments etc.) and/or you cant drive a ground rod and run a ground wire, ask about reasonably safe options that don't involve having to find an honest, competent electrician to come in to rewire it properly.