Belief (πιστεύω) and faith (πίστις) are key words in Romans. πιστεύω (248x in NT) occurs 21x in Romans, 7x in Rom 3:21-4:25, while πίστις (244X in NT) occurs 37x in Romans, 18x in Rom 3:21-4:25.
To "believe" is to put full trust in the God who "justifies the ungodly" (Rom 4:5) by means of the gospel--the cross and resurrection of Christ. Though intellectual assent cannot be excluded from faith, the Pauline emphasis is on surrender to God as an act of the will (Rom 4:18; 10:9).
Pauline (and NT) faith is not (primarily) agreement with a set of doctrines but trust in a person. Though not explicit in Rom 1:16, another focus of Romans is the insistence that faith is in no sense a "work" (Rom 3:20, 27-28; 4:1-8; 9:31-10:8).
