decimus (tenth) + -ate (convert to verb) = decimate
decimus (tenth) + -ation (resulting state of -ate form) = decimation
Primate, secundate, tertiate, and octavate have meanings other than either "reduce by 1/Nth" or "reduce to 1/Nth". Tertiate is actually roughly equivalent to "threepeat". Those words have about as much inherent meaning as "tenthing", but some had meanings extrapolated from "decimate" as early as 200 years ago. The "reduce to 1/Nth" meanings would be more accurately encapsulated with the "an-" (to) prefix, as in "annihilate": literally "to nothing (verb)". That would give you antertiate, anquartate, anquintate, et cetera for the reciprocal-valued words.
As I said, "decimate" is the most well-known of the bunch. "Annihilate" is also well known. But every last one of them is a perfectly acceptable English combination of Latin roots, and should be understood easily enough.
I think you'll find you have an easier time communicating if you stick to terms that people have heard before, even if they're slightly less accurate than new creations.
Of course, if you're trying to get famous, you should absolutely invent new words. Take Thomas Friedman's "glocalization". That one didn't do so well. Steven Colbert's "truthiness", that was a gem.
Knowing the root words are sufficient to both guess the meaning of many of the 600k+ English words that are in the dictionary, but not typically used, and to formulate new, English-sounding words with intuitively obvious meanings. This is similar to knowing the IUPAC chemical naming rules, which allow chemists to name molecules in such a way that other chemists will know how it is structured, just by reading the name. (Z)-Hex-3-en-1-ol, for instance: hex means the longest carbon chain is 6 atoms long, 3-en means there is a double bond following the 3rd carbon, (Z) means it is in cis configuration, and 1-ol means there is an -OH alcohol group on the first carbon in place of a hydrogen. English is less formally structured, but it still has rules.
Truthiness = truth + -y (similar to) + -ness (quality of being)
Therefore, truthiness is the quality of being similar to truth, which is as Colbert's character described it. It follows the rules. It reads like an English word with unambiguous meaning, and is therefore adopted as though it already was an English word.
Glocalization = global + local + -ize (convert to verb) + -ation (state resulting from the verb action)
This smashes two dissimilar words (global, local) into one portmanteau that has ambiguous, unclear meaning (glocal), and then tries to extend it with regular English suffixes. Portmanteaus are less readily adopted without literary backup. Dodgson's frumious (furious + fuming) never would have made it without the Bandersnatch, and slithy (slimy + lithe) required a bit of explanation from Humpty Dumpty. Needless to say, Dodgson was much better at it than Friedman.
This is why I like to say that people who know English well are sesquilingual, because you need to know a little bit of several other languages to know that many of the words.
This is what school is for.