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In Australian (and British) English, dependant is the noun form, used to describe someone (such as a child) who depends on you for support, often financial. Dependent is the adjectival form. Your dependants are dependent on you.
US English has dumped the "a" variant and uses dependent in all circumstances. That is one less spelling to learn. However, in Australia you'll need the correct version if you want to find out what tax benefits you might get from having to raise your offspring. Accuracy matters.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.