Xbox 360 games are not that cheap. That is why we have to take utmost care of the games we buy so that we can enjoy it a long time. Your most common enemy in an xbox 360 game is a scratch. Normally, you can get away with a scratch with a CD or a DVD but the xbox gaming disc is so compact with information that a single tiny scratch can make the game worthless.
If you want to avoid this kind of incident what you need to do is backup your gaming disc. Do not worry, this is perfectly legal as long as you bought your game legally. Once you have made a backup of your game you can play using your backup thereby insuring that your original xbox 360 gaming disc is safely intact. If you scratch the backup game then you can just make another backup and your problem is solved.