Pulled broken glass out of my tire . . .

[NbyNW]

I've suspected for a couple of days that my front tire might be slowly leaking, so when I got home tonight I gave both wheels a thorough look-see.

I found two little chips of glass embedded in my front tire, managed to coax them out with a tiny hex wrench. The glass left behind a small cut, maybe a millimeter wide and almost a quarter inch long. It looks pretty deep -- I'm not sure yet of the condition of the tube, as I'm just too tired and hungry right now to deal with it yet.

How serious is this? Can I ride my bike with this little hole in my tire, is there a product that I can use to seal it? Do I need a new tire?

Would love some advice! Thanks --