inexakt, but ungenau. Is this pure convention or are there any rules of thumb what prefix to choose when building an inversion of an adjective (for example pronunciation)?
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A pretty good rule of thumb is whether the word to be negated is a Fremdwort or not. Latin words are inverted with in-, Greek words are negated with a-, while typical German words are inverted with un-.
As usual, this is not a 100% rule. For example "Natur" is latin as well, but natürlich is negated to unnatürlich, because of the -lich suffix, which is typical for a German word.
Also note that you should avoid the un-prefix where possbile, for stylistic reasons. Almost all un-words can be expressed by an alternative word, without changing the rest of the sentence.
in- is used in Latin. Roughly: if the adjective has a Latin origin, we use in-, if not, we use un-.