It's a bit tricky because "price" isn't directly part of "precious", but the history of the word shows how it evolved:
* Price (Old French "prix") originally meant "value, worth, cost".
* Over time, "price" evolved to also mean "esteem, importance".
* "Precious" emerged from "price" with a slightly different meaning: "highly valued, costly, esteemed".
So while "price" isn't embedded within the spelling of "precious", it's the root word from which it developed.