My new apartment has no 3 prong plugs with ground

Just moved, my new apartment has no three-pronged plugs within any distance of my living room. Only old 2 prong plugs with no ground.
I have been using a 3-pronged converter for now.

Anyone think this will effect my system?
Danger in damaging something?
Should I chase new wires up and put in a new outlet?
As a firefighter and part time electrician... i would not use anything that will draw a good deal of current on those old plugs.... old plugs= old wires... ask the owner to upgrade the electrical.
It is no big deal.Just make sure the cheater plug is screwed on to the outlet screw. If your equipment draws too much you will trip the circuit breaker before anything else. If you do trip the breaker then you know that you have to upgrade circuit.
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You have an advantage over the rest of us. The screw in fuses are better quality than the cheap metal they use in the circuit breakers and by floating the ground on your equipment you will most likely get better sound. The real challenge will be the room itself.
..just replace the wall outlests (easy to do). The 3rd (ground) might or might not be grounded...usually the box itself is grounded and therefore the plug will be grounded even if the 3rd wire isn't connected. Cheaters are no good..they ruin the sound.
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The house is a duplex, our floor has 100 amps: 2 X 30 and 2 X 20, people below us have 140 for some reason. Maybe its their new kitchen. Looks like the dryer is on its own 30amp wring which is good.

I screwed the cheater into the center screw of the faceplate. Not going to mess with anything for now, the wiring is a nightmare in the basement.
Speak to landlord to go with the building CODE and to replace/rewire them ALL at once. Calling building inspector once in a while will stimulate the landlord's speed of action.
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Ejs811, Look at your electrical panel. Sometimes it will state the capacity of your electrical service. Or, you can set up your gear and not worry about it. The only thing possibly drawing a lot of current is your amplifier and it depends on the load presented by your speakers and the volume you listen at. I would not count on your landlord rewiring any time soon.
There will be two mains fuses, at the top of your electrical panel. Read the sizes on those, to determine how much amperage is available, per phase. Outlet boxes in older homes ARE NOT USUALLY grounded. Especially if the wiring is knob and tube. Unless the wires were run through metal conduit(EMT), metallic liquid-tite, Bx cabling or have a third ground conductor to the box; it is NOT grounded. Grounding(running a pigtail) to the new outlet to an ungrounded box would be a waste of time/effort. Besides; the ground terminal on grounded outlets, is already grounded to the box through the mounting tabs/screws.
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Call an electrician (maybe the owner will split the cost). I live in a 90 year old house and had a dedicated line installed for the HiFi and most of the recepticals replaced.
When the electician found some outlets with pre-war wiring, I said dont bother running new lines as they are not used for high current items. (it would have been expensive). Most of my oulets are now 3-prong and up to code.
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@Mr J- I should have prefaced/qualified that statement with, "In most older homes:" OOPS!
Pre-war 2-prong wireing imposes a danger of setting building on fire and needs to be rewired new. Any tenant ringing a bell should not be neglected weather landlord loves or hates such. No matter how many amps you've got you may only use it OK for small appliances and microwaves, iron, corded drills may easily set these old wires on fire.
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EJS, you can easily determine whether or not the screw that holds the wall plate over the outlet is grounded, by using a multimeter or a cheap neon bulb AC tester to see if 120 volts or so exists between that screw and one of the two slots in the receptacle (the smaller one if they are unequal in size).

Obviously, if you do that don't touch the metal tips at the end of the test leads while they are in contact with the outlet.

According to this Wikipedia article, knob and tube wiring was in common use in North America "from about 1880 to the 1930s."

-- Al
If your house is not up to code, it doesn't matter...houses are "Grandfathered" without needing updates. I owned older houses for rentals, and that is what I was told by the township.
"If your house is not up to code, it doesn't matter...houses are "Grandfathered" without needing updates. I owned older houses for rentals, and that is what I was told by the township."

Stringreen is 100% correct. There is no rule or law that says an owner has to conform to code changes as they happen. They change frequently.
You can not replace an ungrounded two prong outlet with a 3 prong outlet without running a new 3 wire grounded cable. This would not meet electrical code and is a potential hazard .
My parents' house was built in 1948. It had no grounded outlets and used fuses. It stayed that way until 1996 when my mother died and the house was sold. We never had any problems.