Learn French: Le chat dort sur le tapis chez mes parents. - The cat is sleeping on the rug at my parents' house.

The preposition chez is the most natural way to say "at someone's house" or "at someone's place" in French. You just use chez followed by a pronoun or a person, like chez mes parents (at my parents' house) or chez moi (at my place).

How do we know chez means "my parents' house" and not their workplace?

When chez is used with friends or family members, it almost always refers to their home. If it is used with a profession, like chez le dentiste (at the dentist), it refers to their workplace or clinic instead.

Is the word tapis plural here because it ends in an "s"?

No, it is singular! The word tapis naturally ends in "s" even in its singular form. You can tell it is singular here because it is paired with the singular article le instead of the plural les.

Why is the verb just dort instead of something like "est dormant" for "is sleeping"?

French does not have a direct equivalent to the English "-ing" continuous tense. The present tense verb dort (from the irregular verb dormir) translates to both "sleeps" and "is sleeping" depending on the context of the sentence.