It is often typed as "arigatou" amongst the many anime fanatics I've come across.
You will often see me type it as "ありがとう" as this is the, more or less, "spelling" way that any Japanese person would usually write/type down. It is also a great way to get away tricking people (that is the average-Joe-in-the-U.S.-with-next-to-no-Japanese-background) into thinking you know Japanese :p
A rule of thumb: the longer you say "thank you" the more polite you are.
This can apply to any Japanese sentence. On the top of my head, there are 5 ways to say "thank you" (1 being informal to 5 being the most polite)
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1. domo (not something you would use on a professor or a superior in the workplace; more-so to someone you're close to)
2. arigatou (more general)
3. doumo-arigatou (general)
4. arigatou-gozaimasu (more to a stranger)
5. doumo-arigatou-gozaimasu (to someone of high status than yourself or just want to be extra polite)
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You can also use "sumimasen" as a sort of thank-you but it's more geared to an apology or "excuse me" sort of translation.
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