Subtracting Roman Numerals

Date: 03/14/99 at 15:59:31
From: Heather
Subject: Roman Numerals

What are the rules for the "subtraction components" in writing Roman 
Numerals?

Date: 03/15/99 at 08:28:42
From: Doctor Rick
Subject: Re: Roman Numerals

These are the limits on the use of the subtraction method, according 
to the modern rules of Roman numerals:

  I. You can only subtract I, X, C, etc. (powers of 10; not V, L, 
     or D).

 II. You can only subtract a single letter from a single numeral 
     (no IIX or IXX).

III. What you are subtracting cannot be any smaller than 1/10 of what 
     you are subtracting it from. You can only subtract I from V or X, 
     and X from L or C (MIM is not allowed).

Here is a positive way to look at it. When converting an Arabic numeral 
to a Roman numeral, convert it one digit at a time. Write each piece as 
a Roman numeral, then stick them all together left to right. 

For instance, 

  1999 = 1000 + 900 + 90 + 9
       = M    + CM  + XC + IX
       = MCMXCIX

The rules make for longer numerals sometimes than you might make by 
breaking the rules. But they make numerals easier to read, because you 
can read the Arabic digits off in small groups (M CM XC IX) and the 
subtractions are easy. Even in ancient Rome, though the place-value 
system of Arabic numerals (and the zero necessary to make it work) had 
not been invented, people already thought in terms of decimal groups, 
the way an abacus works: each digit made up of a collection of ones 
and fives.

In ancient times and even in the Renaissance, the rules were not very 
strict (any more than spelling rules were!). You could find examples 
that violate each of my rules. See these interesting sites:

  Roman Numerals: History and Use
  http://www.deadline.demon.co.uk/roman/intro.htm   

  Roman Numeral Date Conversion Guide
  http://www2.inetdirect.net/~charta/Roman_numerals.html   

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/