The Question:
In a recent academic competition, the students raised a question
about Roman numerals. I immediately referred to the 1998 Information
Please Almanac, and then to several other references, and could not
find an answer for them. The rules you cite are well
accepted and representative of what I have located in the texts. But,
here are the questions the students raised that seem to be beyond the
standard rules.
- Even though 49 is typically written XLIX, is it also
acceptable to write it as IL?
- Even though 400 is typically written CD, is it acceptable to
write it as CCCC?
- Are there generally accepted rules which govern these
situations?
The Answer:
The answer to the first of these questions is a fairly definite
"no". Though a smaller numeral placed before a larger one generally
decreases it by the amount of the first, the smaller number must be a
power of ten, and cannot precede a number more than ten times its
value. In other words, V, L, and D cannot be used to modify larger
numbers; I (the numeral, not the editor) may modify only V and X, X
only L and C, and C only D and M. As tempting as it might be to
represent 1999 by MIM, common usage dictates that it be written
MCMXCIX.
As to your students' second (and third) question: the use of
Roman numerals, in both ancient and modern times, has tended not to
adhere to any rigid set of rules. Even the rules of number formation
taken to be standard today were applied somewhat haphazardly by the
ancients. CCCC, though nonstandard, is acceptable; the only question
that remains is why one would wish to write those extra two
numerals.
One possible explanation for this lack or rigor is the fact that
Roman numerals were in use throughout the ancient world. Time and
distance naturally led to significant local differences in practice.
Exacerbating this was the fact that Roman numerals were seldom, if
ever, used in formalized abstract mathematics (the absence of a symbol
for zero severely limits their usefulness in this capacity); there was
therefore no authority setting the standards of their use. Needless to
say, the same cannot be said of Arabic numerals today.
For a fascinating (and much more in-depth) discussion of Roman
numerals, see Christopher Handy's guide
to the conversion of Roman dates.
—The Editors
Information Please® Database, © 2007 Pearson Education, Inc. All rights reserved.
