The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Roman Numerals

Date: 06/05/97 at 09:08:16
From: e eddy
Subject: Roman numerals

Is there a reference table for writing Roman numerals? If so, what is 
it? If not, how does one write one million and ten thousand in Roman 

I have looked in math books, the dictionary, and searched the 
Internet. Most of the Internet search has turned up information on 
clocks and timepieces. The downloading is slow and this has taken a 
lot of time.

A student asked me this question. I am using this search as a teaching 
tool to show students how to get information on the internet. This is 
a great web site. I plan to share it with others at my school.

Date: 06/05/97 at 15:12:16
From: Doctor Jodi
Subject: Re: Roman numerals

Hi there! 

This is a great question. Here's what I found at the AskERIC site:   

Roman numerals were developed around 500 B.C. at least partially from 
primitive Greek alphabet symbols which were not incorporated into 
Latin. Using predominantly addition, they are read from left to right.
The symbol "I" for 1 was derived from one finger. Five fingers held up 
indicated five of whatever was being counted.  The "V" then was the 
hand outstretched vertically with the space between the thumb and 
first finger forming the "V".
Originally the Greek letter "X", or "chi", meant 50, but in monument 
transcriptions it is easy to trace the original symbol's change to 
"L", and "X" came to mean 10.  Another theory for "X" is that ten 1's 
were written in a row, and then crossed out with an "X" to simplify 
counting.  Then the "X" alone became a shorthand version of 10.  Yet 
another idea is that "V" looks like the top half of "X", as 5 is half 
of 10. Other scholars think that "V" doubled with an upside-down "V" 
meant 5 times 2, or "X".  "C", indicating 100, came from the Latin 
word "centum", a hundred. (Also century, centennial, etc.)  "M" is 
from "mille", a thousand. Larger numbers, like 5,000, are shown by 
putting a small bar called a "vinculum" above the "V" symbol, 
indicating multiplication by 1,000.
Until fairly recently a commonly used Roman numeral for 1,000 was "CI 
backwards C", derived from the Greek "phi", or "I" superimposed on 
"O". Half of this symbol, "I backwards C", led to "D" for 500, half
of 1,000.
Generally, decoding Roman numerals is very straightforward.  The 
largest numeral is at the left, with descending numerals moving to the 
right.  Numbers are added as you go, as seen in these examples: 

CCLXVII: 200 + 50 + 10 + 5 + 1 + 1 = 267 

MMMCCLXXXI: 1,000 + 1,000 + 1,000 + 100 + 100 + 50 + 10 + 10 + 10 + 1 
            = 3,281

DCCXVII: 500 + 100 + 100 + 10 + 5 + 1 + 1 = 717
Rather than continuing to add 1's to make 4 ("IIII") or 9 ("VIIII"), 
subtraction was included in the computation of the numerals to 
simplify and shorten the resulting numbers.  Therefore, 4 is shown 
"IV", or 5 minus 1.  The smaller numeral BEFORE the larger one means 
subtract.  "IX" is 9, or 10 minus 1.  40 is "XL", 50 minus 10; 90 is 
"XC", 100 minus 10; "CD" is 400, or 500 minus 100; and "CM" is 900, or 
1,000 minus 100. Students can follow the principle that subtraction
takes place ONLY when the smaller numeral is before the larger one, 
and involves 4 and 9 in various place values.
Obviously, the cumbersome aspect of Roman numerals is one of the main 
reasons that they have been replaced by the Arabic system in our daily 
mathematical lives. Roman numerals remain important as a part of the
world's cultural past, and a unique way to express numbers.


Most encyclopedias have at least some information on Roman numerals, 
and several books on Roman numerals are appropriate for students. 
Three suggestions:
_Number Art - Thirteen 1 2 3's from around the world_, by Leonard 
Everett Fisher, published by Four Winds Press, NY, is a fairly 
sophisticated overview of world numerical systems.

_Signs and Symbols Around the World_, by Elizabeth Helfman, published 
by Lothrop, Lee and Shepard Co, NY, has a chapter on numerals of many 
cultures. There is a very short section on Roman numerals, but a great 
deal of general information about counting and mathematics 
applications throughout the world.

_Roman Numerals_, by David A.Adler, published by Thomas Y.Crowell Co, 
NY, is a much simpler book, but suitable for younger students.

-Doctor Jodi,  The Math Forum
 Check out our web site!   
Associated Topics:
Elementary Math History/Biography
Middle School History/Biography

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.