Yes, that's what that ridiculously small pocket on your right side is for. You're welcome.
The beauty of basic watches is that they're quiet. One can't accidentally ring. You don't forget to turn your watch off. It simply tells you the time whenever you ask. And that's all it does.
I would say that one problem with my mechanical watch is that it tends to run a little fast. However, I don't mind having extra time. I am rarely late for important things, but it never hurts to be prepared.
Still, if you desire the utmost accuracy in your timepieces, you might want to covet with me an atomic pocket watch that we don't seem to be able to buy. It receives its time through radio signal and displays it on an analogue face, with a tiny digital readout for the seconds and the date.
Gaze longingly at this no-longer-available watch over at Hammacher Schlemmer.