Metric Time, as is oh so cleverly softlinked to this node, will never happen. That said, let's run through a brief explanation of it.

Metric Time (abbreviated MT) is the Base 10 alternative to plain, old, Base 60 Anglo-Babylonian timekeeping that we all *know* and love. (abbreviated ABT)
LMT is short for Local Metric Time, which is offset for whichever time zone you happen to be in.
UMT is short for Universal Metric Time, equivalent to what would be GMT in ABT time.

Here's the most common system of Metric Time, first used during the French Revolution:
10 days in a metric week
100 metric seconds in a metric minute
100 metric minutes in a metric hour
10 metric hours in a day

Sounds pretty simple and metricky, huh? Well this has a big problem. Dividing the metric day into 10 different slices makes a metric hour last about 2.5 ABT hours. You can't make metric hour-long TV programs or schedule a metric hour-long appointment. You'll only fit a few of them in per day! People would have to resort to using clumsier prefixes to divide their schedules into - a centiday for example (approx. 14.4 ABT minutes)

Now, the following is a more real-world system using the day (equal to one solar day) as the base unit.

deciday(dd) = 1/10 day (Metric hour)
centiday(cd) = 1/100 day
milliday(md) = 1/1000 day (Metric minute)
microday(┬Ád) = 1/1000000 day (Metric decisecond)

How is Metric Time formatted?
00.0 LMT = 12:00 midnight ABT, local
50.0 LMT = 12:00 noon ABT, local
00.0 UMT = 12:00 noon ABT, GMT
50.0 UMT = 12:00 midnight ABT, GMT
50.000 LMT = 12:00:00 noon ABT, local
02.425 LMT = 12:34:56AM ABT, local
Note that the trailing zeros are never dropped.

How do I convert from ABT to Metric time?
MT = ((s/86400)+(m/1440)+(h/ 24))*10x
Where X is what unit you are solving for:
Days x=0
Decidays x=1
Centidays x=2
Millidays x=3
Quintoday x=5
Microdays x=6

How do I convert from Metric time to ABT?
h = abs(d * 24)
m = abs(((d * 24) - h) * 60)
s = abs(((((d * 24) - h) * 60) - m) * 60)

Then, ABT = h : m : s

How do I convice my friends, relatives, and coworkers to start using Metric Time?
You don't.

I pine for the day (Metric of course) when my watch will display atomic, binary, metric time. :)