Water shut off valves...should they stop all flow

Sorry - know this is a pretty basic plumbing question - but I really don't want to make a mess.

I am trying to replace my 10 year old kitchen faucet with a new faucet.

When I turn the water supply valves off under the sink - the kitchen faucet continues to drip slowly - and I can hear a slight sound (of running water) in one of the pipes to the faucet. So I think one of the water supply valves is not completely shutting off the water supply.

Can I go ahead and disconnect the old faucet - and try to change the faucet myself? Or should I call a plumber?

your stop has most likely got a little trash on the seat.

go outside and turn off the water meter.
then turn on a outside fauset, bleed the pressure

after you fix the faucet, switch out the stop that is leaking with a new one

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