How come my shut off valves under the kitchen sink completely turn off the water?

Under my kitchen sink are two valves. One for hot water, one for cold water. When I turn the valves to shut off the water to work on my faucet, there is still a little bit if water seeping through. I think it is the cold water valve. How can I fix this?
I live in a condo, so I assume to fix it, water to the entire building will have to be shut off.

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