Decanates get a little into hard-core astrology.  Using this system, one breaks up each sign into three equal parts of 10 degrees each.  The first 10 degrees is the strongest application of a particular sign (say, Aries of Aries).  The second 10 degrees is the next sign of the particular element of Aries (Fire).  The next sign is Leo, therefore, the second decanate of Aries is Leo of Aries.  The third decanate is the third fire sign, Sagittarius or Sagittarius of Aries.

Sign Element Rules/Exalted
Aries Fire Mars/Sun
Taurus Earth Venus/Moon
Gemini Air Mercury/NorthNode
Cancer Water Moon/Jupiter, Neptune
Leo Fire Sun/Pluto
Virgo Earth Mercury/
Libra Air Venus/Saturn
Scorpio Water Mars, Pluto/
Sagittarius Fire Jupiter/SouthNode
Capricorn Earth Saturn/Mars
Aquarius Air Uranus, Saturn//Sun
Pisces Water Neptune, Jupiter/Venus
First 10 Degrees 2nd 10 Degrees 3rd 10 Degrees
Aries of Aries Leo of Aries Sagittarius of Aries
Taurus of Taurus Virgo of Taurus Capricorn of Taurus
Gemini of Gemini Libra of Gemini Aquarius of Gemini
Cancer of Cancer Scorpio of Cancer Pisces of Cancer
Leo of Leo Sagittarius of Leo Aries of Leo
Virgo of Virgo Capricorn of Virgo Taurus of Virgo
Libra of Libra Aquarius of Libra Gemini of Libra
Scorpio of Scorpio Pisces of Scorpio Cancer of Scorpio
Sagittarius of Sagittarius Aries of Sagittarius Leo of Sagittarius
Capricorn of Capricorn Taurus of Capricorn Virgo of Capricorn
Aquarius of Aquarius Gemini of Aquarius Libra of Aquarius
Pisces of Pisces Cancer of Pisces Scorpio of Pisces