Many of the methods to entering these numbers are very error prone:
- Laser scanners
- Cameras
- Humans
- Magnetic readers
- etc
The check digit lets the system know the error was likely misread / mistyped without needing a database or the like and also helps prevent an accidental mistyped value from also being a valid valud (The number for Book A is unlikely to be mistyped exactly to be the number for Book B because of the check digit).
It also can help to improve scanning speed to some degree since if you have two interpretations of the signal it is possible to infer which one is most likely to be correct.