As to why, it's simple. Why does a high percentage of the world use metric? It's a modern system. Metric time makes it easy to measure large and small amounts of time. Just imagine when you are measuring time in Mega Days.
As to how... Convert to 24 hour first and then use this equation:
Centidays = (hours / 0.24) + (min / 14.4) + (sec / 864)
This will give you the time in centidays, to convert to days just divide by 100. The idea is to express the day as a fraction as power crazy said. As you may see from the equation there are 24 hours in a day, 1440 minutes, and 86400 seconds. These are adjusted to be on the same level (centi) by dividing each by 100.
We didn't include this at first since most teenagers aren't keen of doing math outside of school

This is no joke by the way.