worthless, worth less

Worthless or worthless ( one word ) means having no value at all, or not useful in any way--
The vase is broken in dozens of pieces; it's worthless now.
The author admitted the fraud, and now all of the research based on his work is worthless.

Worth less or worth less ( two words ) means having a value not as great as, comparatively--
The vase on TV sold for thousands, but ours has a crack in it, and it's worth less.
This model is worth less than the more popular one--you can check the used car ads if you don't believe me.

Now that you know that, you can say--
"I knew this antique would be worth less after being refinished, but a dealer just told me that it's worthless now."