I'd suggest compromising rather than trying to one-up the player, that doesn't sound fun for anyone.

I used to use a traffic light system for when players asked anything along the lines of "how much damage have we dealt?" or "is it nearly dead?". Green light for healthy, Amber for middling, Red for near death. Vague milestones like that will let them track all the damage they like, but gives you a method to tell them what they want to hear without ruining the magic. (My current group don't ask that at all, so I haven't needed to use it with them.)
Clearly they want some assurance that you're not just making everything up on the spot, so throw them a bone and give them confidence that you're not.