Thanks to Ecce for letting me have the Metric Clock app for testing. The iTunes price is $0.99. If anybody else wants to provide me with an app, or to post about anything else relating to decimal time, or anything at all, just use the email link in my profile. (I just fixed it.)
It's certainly the prettiest decimal time app I've used. It comes with a nice background image, or you can use any image from your photo library. If you get tired of metric, it will also display a standard 12-hour clock. The clock itself is a typical round, analog dial, which can be resized and repositioned anywhere on the screen. You can also select from eleven different colors and the level of transparency, although the numbers are always black, so if you make the clock face black and set transparency to minimum, you won't be able to see it! Or you can view a digital display in the form h.mm.ss. Seconds are optional for both analog and digital.
There is an optional progress bar that displays the time as a percentage, so one hour and eighty minutes past midnight is displayed simply as 18, and increments every 10 decimal minutes, or 14.4 standard minutes, just like Rey-Pailhade's cés. There is also a progress bar for the year, which increments every 3.65 days, and one for your life, which displays the percentage of years from your birth to your life expectancy, which you can set.
One slight drawback is that you cannot turn off auto-lock from inside the app, so you have to exit and go into your iPhone settings to turn it off and on, or else the display will turn off after a minute or so. It does switch automatically from portrait to landscape mode, however.