Rules for Formation of Roman Numerals
For beginners, Roman numerals might seem like a whole different language that has nothing to do with mathematics. However if you learn the basic Roman numerals rules, it is very easy to understand how they work and to ‘decipher’ even the largest Roman numbers. Here are the basics for forming numbers with Roman numerals:
How Many Roman Numerals Are There?
There are only seven Roman numerals: I, V, X, L, C, D and M.
In the Roman system, numbers are formed with only these symbols and these seven letters are used to make up thousands of other numbers.
The values are as follows:
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000
Note that the number 0 is not existent in the Roman system.
Rule 1: Repetition Means Addition
In many numbers formed with Roman numerals, you will notice that symbols are usually repeated. The rule is that if a symbol is repeated, the values are added.
I = 1
II= 1 + 1 = 2
III = 1 + 1 + 1 = 3
XX = 10 + 10 = 20
XXX = 10 + 10 + 10 = 30
C = 100
CC = 100 + 100 = 200
CCC = 100 + 100 + 100 = 300
Rule 2: Some Symbols Are Never Repeated
The symbols V, L, D are never repeated in a Roman number. This is because ‘VV’ would give you the value of 10 which is already represented by the symbol X. In the same fashion, ‘LL’ would already be equal to C and ‘DD’ to M.
Rule 3: When Should I Add?
In any given Roman number, if a symbol is placed after a larger (or equal) one, you add the values. In other words, when you see a smaller number is on the right of a larger one, you add.
VI = V + I = 5 + 1 = 6
VII = V + I + I = 5 + 1 + 1 = 7
XI = X + I = 10 + 1 = 11
XII = X + I + I = 10 + 1 + 1 = 12
DLXII = D + L + X + I + I = 500 + 50 + 10 + 1 + 1 = 562
Rule 4: When Should I Subtract?
In any given Roman number, if a symbol is placed before a larger one, you subtract. In other words, when you see a smaller number is on the left of a larger one, you subtract.
A note to remember here is that while you can add more than two values, you cannot subtract more than one value (symbol) from a Roman numeral.
IV = V − I = 5 − 1 = 4
IX = X − I = 10 − 1 = 9
XL = L - X = 50 - 10 = 40
XC = C - X = 100 - 10 = 90
Rule 5: Don’t Repeat More Than Three Times
In the Roman numbering system, symbols cannot be repeated more than three times in a row. The reasoning behind this is similar to the symbols V, L, D never being repeated at all.
It is because if you were to repeat I four times to get the value 4, you would not write the number as ‘IIII’ but as ‘IV’. Similarly, 40 would be represented as ‘XL’ rather than ‘XXXX’.
Rule 6: How to Write Really Large Numbers With Roman Numerals
The largest Roman numeral being M (1000), the above rules mean that the largest number that could be formed with Roman numerals is 3,999, which is MMMCMXCIX.
However, the Romans have developed a system of drawing bars above the symbols to represent greater numbers. In the Roman system, numbers greater than 1000 (M) are formed by placing a line/dash over the symbol. The bar placed over a given number multiplies its value by 1000.
V̅ = 5 * 1000 = 5000
X̅ = 10 * 1000 = 10,000
X̅X̅V̅ = 25 * 1000 = 25,000
D̅ = 500 * 1000 = 500,000
M̅ = 1000 * 1000 = 1,000,000
How to Convert Roman Numerals to Decimals
The above rules mean that when trying to convert a number formed with Roman numerals, one has to subgroup the Roman number in thousands, hundreds, tens and ones. This will help determine whether you need to add or subtract.
An important note to remember is to start grouping from the right and working your way to the left. This way you see which numbers come before or after a larger one and thus, if you need to add or subtract.
Here are some examples:
XXXVIII = X + X + X + V + I + I + I = 38
XLIV = XL + IV = (50 -10) + (5-1) = 40 + 4 = 44
CXLII = C + XL + I + I = 100 + 40 + 2 = 142
MCMLXXIV = M + CM + + L + XX + IV = 1000 + 900 + 50 + 20 + 4 = 1974
MMCMXCIX = MM + CM + XC + IX = 2000 + 900 + 90 + 9 = 2,999
MMMDCCCXCIX = MMM + D + CCC + XC + IX = 3000 + 500 + 300 + 90 + 9 = 3899.
Check this our online tool to convert Roman Numerals to Numbers easily.
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