Replacing 2-prong receptacle with 3-prong is wrong unless you properly ground it. Replacing the 2-prong outlet will use the ground prong for your protection in the event of a malfunction with an electrical appliance.
To ground a receptacle, run the properly sized wire back to fuse box and connect it to the ground terminal. This has to be done according to codes, which are usually enforced by the local building department. A permit may have to be “pulled” for this work to be done. Don’t avoid this. The cost will be minimal. It is important for your safety to have the electrical inspector check your work.
Installing grounded receptacles without grounding them is like offering a safety net that doesn’t work. If someone falls and the net fails, they could get hurt. Here is my favorite example of an accident waiting to happen.
“A carpet cleaning person comes to your house and plugs his carpet steamer into an improperly installed three-prong receptacle. During the process his machine malfunctions and he receives a shock.”
The person who installed that receptacle is at fault. If the receptacle was a two-prong, the service man could have used a plastic ground adapter to plug in his machine. He would have at least known that he was working without a ground.
A ground adapter is a small plastic plug that has three slots on one end and a two-prong plug on the other. It usually has a small terminal that can be attached to a ground or the receptacle plate screw. The problem is the electrical box (in the wall) is usually not grounded, leaving the consumer with a false sense of security.
If you want to install grounded receptacles, you will have to ground them. Sometimes older homes are wired with grounded wiring that the installer never hooked up. This isn’t very common but worth checking out before you go through the effort to run new ground wire. Many people think hooking a wire to the back of the box qualifies as grounding a receptacle. Not so. Unless the box is grounded, it is just a metal box in a wall.
Always disconnect the power when working with electricity. Shocks can be fatal. Call a licensed electrician to perform the work if the job is beyond your abilities.