Writing Numbers To Appear In Time Format

I'm trying to write a certain number, e.g. 300355, to appear as 03:03:55 and in the time format. I've already managed to make it appear with the punctuation between by formating the cell with 00:00:00. However I need to work with the cell in a time format because I'm using stats from a program that records time spent on/off a phone. To be exact I need to sum up 4 cells and divide each one with the total to get the % of time spent on the each category, (total talking, total ready, total not ready and total working).

If I use the format I've been using (00:00:00) the % gets slightly off the true value. E.g. if the numbers are the following:

Total talking: 03:36:53Total ready: 00:55:37Total not ready: 00:52:53Total working:02:40:37

I would get 45%, 11%, 11% and 33%, accordingly, by using the values in time format but 49%, 8%, 8% and 35% by using my format.

So the question is, is there a way to write the numbers as 33653, 5537, 5253, 24037, appear as 03:36:53, 00:55:37, etc. and be in time format?