Daily Scrum Meeting (Burndown chart)

Question

Here is an example: early in the morning of the second day of the Sprint (during the stand up) I go to the board and see that the story I worked the previous day (first day of Sprint) contains a big "1 IDEAL DAY" written on it (estimate). Right now (early in the second day of Sprint) the story is not completed and I guesstimate it will take half a "REAL DAY" to complete it.

Question: so to track progress and update the burndown right now, shouldn't I update that "1 IDEAL DAY" on the card with something else (recap.: original estimate in 1 ideal day, remaining work in 1/2 real day)? What would be that something else in this particular example?