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In some games, the amount of damage you inflict on an enemy is an ever changing number, based on a combination of things such as the weapon used, the character's abilities, and the strength of the enemy. Often in games like this, a specific number will briefly appear above the enemy that indicates the exact amount of damage an attack has taken away from their total hit points. These numbers can also appear when a character is healed, showing the exact number of hit points that have been restored.
This particular visual representation of damage inflicted first began appearing in early role playing games (RPGs), but has since made its way into virtually every other genre of games, including first person shooters, real time strategy, fighting games, side-scrollers, etc.
Sometimes also shown alongside an enemy health bar.