According to the famous death note rules, when an owner performs a deal with a shinigami, his/her life span is cut by half, if the owner were to quit the ownership of the note, he’d loose all his related memories and his life span would not come back. While in possession of the Shinigami Eyes, the owner has the ability to see a person’s full name and remaining life span, but we wouldn’t expect to see the main character’s (or any important character in the plot for that matter) remaining life span, so instead these numbers and letters are unknown characters called “letters from the shinigami world”, illegible and and blurry scribbles with no meaning at all. These leads to a question: How did the characters who possessed the eyes at any time, managed to understand and carry out their objectives with this unknown alphabet? since it clearly makes no sense at all.
On this episode, Chief Yagami Light made a deal with the Shinigami called Ryuk, Ryuk had also performed a deal previously on Misa, which means there isn’t necessarily a limit to how many times a shinigami can perform a deal on humans. Chief Yagami died by receiving various bullets in his back, despite the bullet proof vest, one or more bullets had hit the flesh, furthermore he was burned badly (i’d say 3rd degree burns) by the explosion caused by Mello for his escape route. He died just a while after doing the deal, maybe half and hour or 15 minutes later, in his original life span, only less than an hour remained.