Approach

A student is nervous about asking her professor for a letter of recommendation. She walks toward the professor’s office, hesitates, then finally knocks on the door and starts speaking. She is moving from a distance to a closer point. What is the student doing? She is approaching the professor.

Approximate (to come close to something in number, quality, or amount, but not exactly) contrasts with Approach, which means to come nearer in space, time, or a figurative sense. Approach often implies intentional movement or a direct path toward a target, while approximate is about estimation or similarity without exactness.