With miles, there are no SI prefixes, so, you just write "every 3k/10k miles".
With kilometres, there's already an SI prefix present.
What's the sane way to write, say, "5000 / 16'000 km" in a shorter form, without all the zeros?
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Yes you can apply all SI prefixes to meters. So a megameter would be one million meters or 1000 kilometers.
Gigameter is 1000 megameters.
Terameter is 1000 gigameters.
Petameter is 1000 terameters etc.
Gigameter and higher are usually only used in the context of space and astronomy because in normal contexts it is impossible to visualize or relate those distances. People don't simplify down 120,000 km to 120 Mm because of tradition and because their odometer reads in kilometres, and also because it is hard to relate to a megameter.