Is paying an expiation (kaffarah) for an oath considered valid for someone who swore to fast for a week but was unable to fulfill it?

If one swears to perform a supererogatory act of obedience, it is commendable for him to do what he swore to do, and it is disliked to break the oath. If he breaks the oath, then he must pay expiation for an oath, which is feeding ten needy persons, or clothing them, or freeing a slave. If he cannot find any of these, then he must fast for three days. Once he has paid the expiation, he has fulfilled his obligation.