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Roman Numerals

Image of mosaic with Roman numerals
Roman numerals in a mosaic
DCCCLXX = 870
The Roman numeral system was used by the Romans to record taxes, trade and dates. Even when the Roman Empire fell, Roman numerals were used by many places in Europe, mostly because the decimal system was too easy to forge I.e. turning a 10 into 100 or a 0 into a 9 was very easy.

The Roman numerals are I, V, X, L, C, D and M, which stand for the numbers 1, 5, 10, 50, 100, 500 and 1,000, each new numeral added in counts of 5.

5 10 50 100 500 1000
V X L C D M

Image:Patriarch's basilica, Aquileia. 4th century mosaic with Latin inscription: IANUARIU[S] DE DEI DONO V[OVIT] P[EDES] * DCCCLXX (Januarius paid for 870 square feet of mosaic as a votive offering ). Image by Wolfgang Sauber.

Counting to 10

1 2 3 4 5 6 7 8 9 10
I II III IIII OR IV
(1 less than 5) 		V VI VII VIII VIII OR IX
(1 less than 10) 		X

To count in this system you add (and subtract) the numerals to get your total.

6 11 60 110 600 1612
VI XI LX CX DC MLCXII

Subtraction - 4s and 9s

If the number is a 4 or a 9 sometimes subtraction is used. When you see a smaller numeral to the right of a bigger numeral, you need to subtract the smaller numeral.

4 9 40 90 400 900
IV IX XL XC CD CM

Counting Roman numerals as decimals

Roman Numerals Expanded value
of Decimal 		Decimal place value
1000s 100s 10s 1s
X V

X (10) + V (5)

1 5
X V I I

X (10) + V (5) + I (1) + I (1)

1 7
L X X V I

L (50) + X (10) + X (10) + V (5) + I (1)

7 6
D C L V

D (500) + C (100) + L (50) + V (5)

6 5 5
X C I X = (X (10) '''red less thanC (100)) + (I (1)red less than''' X (10)) = 9 9
M M

M (1000) + M (1000)

2 0 0 0

Drawbacks of the system

Image of clock with Roman numerals
Roman numerals in a modern clock
This system doesn't use the tidy place value columns that many counting systems use. One column doesn't go all the way up to 5 before starting another column. This means you can't tell just by looking if one number is bigger than another. To represent 76 you need to use 5 characters, LXXVI, but to represent 2000 you only need two, MM.
Every time you read the number you have to do addition and subtraction. This is fine for small numbers but what if we are trying to represent really big numbers like "3,219,876", the numerals are 18 characters long "MMMCCXIXDCCCLXXVI".

Our current decimal system with it's indo-arabic numbers gradually replaced Roman numerals. This is because, even though it was easier to forge I.e. change a 0 to a 9, decimal is also much much easier to read and use in math.

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