Hadn't seen those before! Yeah I suppose they are, although could you call Roman numerals decimal? I don't know enough about the technical definition to say. I'm assuming "decimal" and "base 10" are synonymous. And the base is the number of distinct digits you have to work with. Roman numerals don't really work that way though. Man, I remember when I first learned about different bases, it took me a bit to wrap my head around the idea that base 10 is completely arbitrary. It doesn't make more sense than the other bases, it's just what we standardized on. Now I'm realizing that maybe the idea of bases themselves aren't some rule of the universe.
It's not a decimal system, no. The decimal system is a positional system (just like binary, hexadecimal, sexagesimal ...). In a positional system, part of the information of a symbol is in its position in the whole string, and it always represents an 1-to-(base-1) part of its base. That's why every base is base-10 when represented in itself.
However, most human languages encode numbers as an algebraic expression: "one {times} thousand {plus} three {times} {one} hundred {plus} thirty {plus} eight" = 1338. Some languages are more strict/consistent in this than others. English has its quirky unique words for 11 and 12 (instead of one-ten and two-ten), Danish and French enjoy adding multiplications and divisions to the mix (due to retaining more of their 20-based origin): "quatre-vingt-dix-sept" = 4 * 20 + 10 + 7 = 97, "halvtreds" = halvtredsindstyve = (3 - 0.5) * 20 = 50.
The Roman numeral system works likewise, it's just a shortened form of saying the number. Which means you need a symbol for every word for a magnitude, and your expression range is limited to the words your language has for ever greater quantities. But for most humans, in our daily lives we rarely need to precisely number more than, say, a few ten-thousand things. Beyond that "myriad"/"a lot"/"uncountable" suffices.
The simple form of the Roman system is just additive: MDCLXVI. You could add subtraction: XC instead of LXXXX to make it faster to write. But then you're already on the path to a positional system.
Romans used a device called a "calculator" which was a flat plate with vertical channels cut or pressed into it. It resembles what we would now call an "abacus".
get rid of the subtractive rule, and roman numerals are just a way of writing the state of a calculator, with each letter representing a calculi, and the value of the letter representing which column it is in.
most abacuses are base 10, with a special segment in each column for a stone that represents "5" in that position.
Thus, each roman numeral is either a power of 10, or half a power of 10.
with that context in place, the method of writing it isn't a positional system, exactly, but it's a way of serialising a positional system by capturing positions by naming them explicitly.
edit:
here's an image of a replica calculator, note how the columns are labeled.
edit2: it’s also easy to see in this context how this relates to our system of money, and coin values and names such as “cent”, if roman numerals aren’t decimal then neither are coins.
> English has its quirky unique words for 11 and 12 (instead of one-ten and two-ten)
Of course, consistency with other number names above 20 would lead to "ten-one" and "ten-two", not "one-ten" and "two-ten"; or consistency with other number names below 20 would lead to "oneteen" and "twoteen", or some variant (as with "thirteen" in place of "threeteen").
OK, valid point of about whether it's fair to call Roman numerals decimal. They're similar because all the symbols (except I) are multiples of 5 and 10, but it's not really the same thing as true base 10.
