I have seen this a million times in tv and movies, that when people are negotiating the price of a car, house, etc or negotiating a salary, and instead of just saying the price or the salary, they will write the number on a paper, slide it across the table, and then the other person will react to it somehow. Does this ever actually happen in real life? I have never had this happen in any job I’ve interviewed for, and not when I bought my car. Is it just something they do in the movies? And why? Why wouldn’t they just say the number out loud?

in the movies the usefulness would be so the silent price in the plot does not distract a viewer from the plot like a spoken price could make the movie feel more dated when viewed twenty years later.
item prices change dramatically, for example 50 cent cigarette packs in 1971 compared to ten dollars a pack in 2010. and gasoline prices going up and down could date or confuse a movie by appearing on the screen needlessly.