Computation Using Roman Numerals
In this section I will discuss how Roman numbers were used in the daily life of the Roman people. Roman Numerals, as a topic of the Latin grammar (numeric adjectives and adverbs) is dealt with in the module of Lesson 4.
So, how were the Roman numbers used in the Latin world of those days? The numeric system that we know today was unknown then. Hence the digits 1, 2, 3, 4, etc. were not known. It was Fibonacci, in 1202, that introduced the Hindu numbers 1 to 9 into the Latin world, and even then they were not accepted till the XVI century. More of this in the section on Fibonacci. The concept of numbering and doing arithmetic with the Roman numbers was
| I | V | X | L | C | D | M |
| 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
known, but the symbols used to perform that numbering and calculations were taken from their alphabet. The basic set of numbers notation, and their equivalent modern numbers, are shown in the above table.
Method of Counting
Assumptions: I assume that you have zero knowledge of counting with Roman numerals. The term "unit" means anything, weights, miles,money, etc., e.g., one egg, three ducks for the party, two hundred asses (money not donkeys!), twenty bricks, etc.
Doubling the number I would make a count of 2, thus: II = two units.
Trebling the number I would make a count of 3, thus: III = three units.
Quadrupling the number I would make a count of 4, thus: IIII = four units.
Alternatively, four could have been written by using the two symbols I and V, and placing the smaller unit symbol, the I, to the left of the bigger symbol unit V. In this way four units, of something, could be shown as IV, instead of IIII.
From this explanation you can already imply the following rule: let's call it Rule I: When a smaller number is placed on the left hand side of a larger number, then its value is subtracted from the value of the larger number.
The opposite of this rule is also true, and let us call this opposite rule:
Rule II: If you put a smaller value number to the right of a larger value number, then the value of the smaller number is added to that of the larger number.
Thus, if you needed to write twelve units then you would write: XII
Or if you wanted to write seventeen, you would write it as XVII.
What does the number IX mean?
By Rule I, its value is nine.
What does the number XVIII mean:
By Rule II, its value is eighteen.
With this line of reasoning you can see that it is quite easy to express any number. Here are a list of examples. For the sake of speed, I will show the corresponding value using our modern numeric notation.
XX = 20
XXX= 30
XXXX=40, but this notation is wrong; use instead Rule I, XL=40
L=50
LX= 60
LXX=70
LXXX=80
XC=90
C=100
This basic pattern is now repeated for any higher numbers.
CX=110
CXX=120
CXXX=130
CXL=140
CL=150
CLX=160
CLXX=170
CLXXX=180
CXC=190
CC=200
CCC=300
CD=400
DC=600
DCC=700
DCCC=800
CM=900
M=1000
MM=2000
MMM=3000
Managing Numbers Higher than MM
You use the dash symbol "-" placed on top of a number or a set of numbers. This dash symbol represented that number multiplied by 1000. Examples:
C̅= 100 000
X̅I̅I̅I̅ = 13000
X̅I̅I̅I̅DVI= 13506
M̅ = 1000 000
A further multiplier was used, perhaps more familiar to those practising the profession of banker (argentarius) and book keeping (ratio accepti et expensi), or accountant (rationarius).
The symbol was this one: |¯| and it signified x 100 000;
hence |X̅X̅| = 20x100 000 = 2 000 000
and |X̅|X̅L̅V̅CLXVII = (10x100 000)+((45x1000)+67)= 1 045 167
A further multiplier existed. This was the symbol C written either side of a number and was derived from an alternative way of writing the number 1000. Instead of using the normal and more common M they used the C followed by the I and then by another C but written as if you were writing from right to left. I am using the Times New Roman font for writing these notes, and such inverted C is not available in the character set. The best I can use is a cyrillic character that looks like an inverted C but has a dot in the middle of it, like this: Ͽ; just ignore the dot and let's use that as the inverted C symbol.
Thus: CnumberϿ would mean 10 x number.
CCnumberϿϿ = 10x10xnumber = 100xnumber
CCCnumberϿϿϿ=10x10x10xnumber = 1000 number
Hence the alternative way of writing 1000 was CIϿ
For example: CCIϿϿ = 10 x 1000
CCCIϿϿϿ = 100 x 1000
CCCCIϿϿϿϿ = 1000 x 1000 but in this case you coould use simply M̅ = 1000 x 1000.
N.B.: If you are interested in writing Roman Numerals in your documents higher than MM, then you might like to consider referring to the page PC Fonts for Sale and purchase a font set which includes all these special characters.