Fractional weight plates are great for adding incremental weight to the barbell. We often talk about progressive overload in weightlifting. In other words adding a little bit of weight each session to your lifts. Many lifters do this until they plateau. If we could keep adding weight every week forever we could all bench press cars! Sometimes taking a smaller jumps is needed depending on the exercise or workout regimen.
When you hit that plateau and may need to consider fractional plates to keep the gainz rolling. As an example maybe you can’t get the reps you want with a 340lb bench press so you do 337.5lbs to get all your reps instead using 2 of the 1.25lb plates. That’s just one possible option. The fractional plates can be used for PR attempts too.