Is a 1.00 pt faceted diamond worth anything?

What you have is worth whatever someone will pay you for it.

If you mean .01 carat of a diamond, then its value is lower than if you mean 1.00 carat diamond. The lowest price today on Blue Nile for a 1.00 carat diamond is US$2,151. The lowest carat weight you can purchase there weighs .24 carats.