LII (52). Still visible inscription above the entrance to Colosseum . Sekcja(52). Author: WarpFlyght | License Creative Commons 3.0.

Roman system uses the Etruscan numerals which the Romans borrowed and modified in c. 500 BCE. It useful for writing the numbers, but not in arithmetical operations or writing fractions. Those inconveniences do not exists in the more precise, Arabic numeral system.

Roman numerals are consisting of seven basic signs, i.e. I, V, X, L, C, D and M which allow to create any number. I put a few combinations in the table below:

Writing more complex numbers was not difficult. The easiest way was to write them in decreasing order, from left to right. Then it is necessary to total them up. Eg. 127 is CXXVII, so C+X+X+V+I+I (100+10+10+5+1+1=127).

However not always everything was so simple. Smaller numbers were written with the smaller numeral put before the higher one in aim to subtract it and thus get the needed number, eg. XIV – 14, so X+V-1 (10+5-1), so XC (100-10) – 90, so C-X.

One of the rules is putting signs I, X, C before the higher number, eg. IX or CD. In case of the higher and more complex numbers they were being written as separate numerals, so for instance, number 499 was not written as ID, but CDXCIX, so 400+90+9. Thus we can find a rule saying that I can be placed only before V and X, X only before C and L and C only before D and M.

I 1 IX 9 LXXX 80 DCC 700 II 2 X 10 XC 90 DCCC 800 III 3 XX 20 C 100 CM 900 IV 4 XXX 30 CC 200 M 1000 V 5 XL 40 CCC 300 MM 2000 VI 6 L 50 CD 400 MMC 2100 VII 7 LX 60 D 500 MMD 2500 VIII 8 LXX 70 DC 600 MMM 3000

It is easy to notice that using numerals from the table above allows to write 4999 (MMMMCMXCIX) as the biggest number. But also this obstacle was easily eliminated – the form VIII.M (8000) was common. Dot separating those two parts was crucial thus the numeral on the left is a multiplier and the one on the right is a multiplicand.

There are no symbols for the numbers bigger than 1000, but it is possible to write a bigger number by using a 100 times smaller numeral and putting it between “|“, for instance:

|MD| = 1500 x 100 = 150 000

|XL| = 40 x 100 = 4000 (instead of MMMM)

Another symbol with a similar function is a line drawn across the top of the numeral to multiply it by 1000, for example:

XL = 40 x 1000 = 40 000

In order to make the number it is necessary to put certain symbols together, from the one representing the highest number to the smallest one.

If the element of the number we are writing is a multiple of a nominal number then it should be written with a few following symbols, but also remembering about the principle not to write four the same symbols in a row (however it used to be this way in the past), but to write one symbol along with another one being higher in order of magnitude.

There were forms contradicting some general rules. Sometimes 4 was being written as either IV or IIII. The same thing concerns the numeral 40 which was written either XL or XXXX.

Romans, except from the seven numerals which have survived to date, used also additional numerals for 5000 and 10000.

= 1000 = 5000 = 10 000

Number 2014 written with Roman numerals.

Roman numeral system was not working with the accounting. That is why there were used abacuses – calculating tools on which an actuary was moving counters on a small table. In the Empire there was invented a pocket abacus with movable metal beads – an ancestor of modern abacus. The ability to use abacus required many hours of practice and thus the actuaries were estimated in the society – we can find reminiscence of that nowadays as we highly respect mathematicians and IT specialists.

Romans knew the fractions although they were a little bit different from the ones we know nowadays. The most common fraction was uncia, a twelfth. They did not develop any particular rules concerning their writing but one of the most popular methods was to represent uncia with a dot and therefore 2/12 was written as •• and 1/3 (4/12) as ••••. 1/2 (6/12) was marked with the letter S (from semis – half). Fractions bigger than 1/2 were written with S and dots so 8/12 was written as S•• and 11/12 as S•••••.