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### 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?
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```
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

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

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