How to Read Roman Numerals
You have to hand it to those Romans; for an empire that crumbled away at least 1,500 years ago they've left us with a heck of a legacy. And one of 'the things that the Romans have done for us' is to leave us a numbering system that, though occasionally mystifying, is still proving remarkably useful.
Let's take a look at Roman numerals; where they came from and how to use them.
The roman numbering system
The whole Roman numbering system uses seven basic symbols:
Note the absence of any symbol for zero. This is partly because the numeral zero is already built into the existing symbols and also for the Romans, numerals were for counting, rather than calculation. In the Roman mind, anything that had a 'zero' value was by definition not a number, and therefore could be expressed by the Latin words nihil or nulla, meaning 'nothing'.
Origins of roman numerals
It's easy to believe, mistakenly, that Roman numbers were abbreviations of the Latin words like centum (hundred) or mille (thousand) but these were the only overlaps with the language. It's more likely that the words came from the symbols and that those came from somewhere else. But where?
Most historians and archaeologists are agreed that the Romans derived their numbering system, like so much else, from their Etruscan forebears.
The Etruscan numbering system had five symbols, three of them shared with Roman.
As to how these symbols evolved, there are three main theories.
Theory One: Tally System
The first theory is that the whole numbering system derives from notches on tally sticks, with a single notch (I) representing a single event and every fifth notch double cut (V) and every tenth one cross cut (X). This would have produced the positional system seen in Roman numbering. As for the more advanced symbols, these could have evolved later, being fitted with letters of the Latin alphabet.
Theory Two: Counting on fingersAn alternative hypothesis is that the small numbers in the Roman system are related to hand signals with I, II, III, IIII corresponding to the number of fingers held up for another to see and V representing the whole hand with fingers together and thumb apart. Numbers 6–9 represented one hand held up as a V and the other showing fingers for the additional units and finally a 10 represented by two Vs, crossing the thumbs, or holding both hands up in a cross.
Theory Three: Blending symbols
The third theory is that the basic ciphers were I, X, C and Φ for 1, 10, 100 and 1000 and that the ones in between (5, 50, 500) were derived from cutting the basic symbols in half. Thus half an X is a V, half a C is L and half a Φ is D).
Using roman numbers
These symbols could be used to express any given value, by combining them. Combinations are defined by a set of rules.
Basic rules of roman numbering
There are three basic rules for constructing Roman numbers.
- Always start with the biggest symbol possible in any number (so XV, not VVV, to make 15) and use symbols left to right in decreasing value. Thus 1,666 is written MDCLXVI.
- No symbol should be repeated four or more times, so IV not IIII (but see 'Exceptions' below!).
- To avoid breaching Rule II or to use the lowest number of symbols, a value can be adjusted downwards by placing one lower value symbol (never more than one) in front of it. This is called subtractive notation.
Thus 40 cannot be XXXX but must be XL (50 – 10).
You can see the basic rules in operation in the progressions from one to ten and from ten to a hundred.
|Ⅱ||1+1 = 2|
|Ⅲ||1+1+1 = 3|
|Ⅳ||5-1 = 4|
|Ⅵ||5+1 = 6|
|Ⅶ||5+1+1 = 7|
|Ⅷ||5+1+1+1 = 8|
|Ⅸ||10-1 = 9|
|ⅩⅩ||10+10 = 20|
|ⅩⅩⅩ||10+10+10 = 30|
|ⅩⅬ||50-10 = 40|
|ⅬⅩ||50+10 = 60|
|ⅬⅩⅩ||50+10+10 = 70|
|ⅬⅩⅩⅩ||50+10+10+10 = 80|
|ⅩⅭ||100 - 10 = 90|
Advanced rules and exceptions
The subtractive notation rule (placing a small number in front of a large one to decrease overall value) is itself subject to three sub-rules:
- The subtractive numeral to the left can only be one of the principal numbers, I, X, or C, never one of the 'five' numerals V, L, and D. Of course M, being the biggest numeral, can't be subtracted either.
- You can only use one subtractive number to the left. So 27 must be XXVII, rather than IIIXXX.
- The subtracted number must at least one tenth of the value of the number it is subtracted from. So you can place X to the left of L or C to make 40 or 90 but you can't use X to the left of a D or M to make 490 or 990. In effect, each power of ten has its own group in the total number. So 999 is made up of CM (900) plus XC (90) plus IX (9).
This is, frankly, a severe pain. It means, for example, that 1999 has to be written MCMXCIX rather than MIM. These are the theoretical rules, developed for modern use of Roman numerals. However, over the course of more than two centuries right across Europe, these rules have frequently been cheerfully ignored.
For example, the number eight is frequently expressed IIX on a number of Roman tombs and monuments and in modern dates, such as the 1928 on a Kew Gardens statue expressed MCMXXIIX, rather than the correct MCMXXVIII. Similarly many clocks and some coins use IIII to represent four, rather than the correct IV.
Large numbers and fractions
So how on earth could the Roman numbering system with no zero and no single value above one thousand be used to express a really large number, such as a million? Well, the world was a much smaller place in those days and there would have been less need for really large values. Nevertheless one would expect an ingenious and supremely practical people like the Romans to have developed systems to crack that problem and in fact they had two.
Large numbers: apostrophus
One was to use the apostrophus, a system based on brackets. C|Ɔ represented 1,000 while |Ɔ was 500. Each extra set raised that by a factor of ten. Thus CCC|ƆƆƆ was 100,000 and CCCC|ƆƆƆƆ was a million. Meanwhile |ƆƆƆ represented 50,000 and |ƆƆƆƆ was 500,000.
Therefore to express 15,230 using apostrophi, one would write CC|ƆƆ|ƆƆCCXXX. This breaks down as CC|ƆƆ (10,000) plus |ƆƆ (5,000) plus CC (200) plus XXX (30).
Large numbers: vinculum
The other large number system was the vinculum, adding lines above and to the sides of conventional Roman numbers, each one multiplying it by 1,000 by adding an overline. Thus V was 5,000, D would be 500,000 while M would be 1,000,000.
If you want to convert roman numerals from the apostrophes system to vinculum system, or vice-versa, you can use this converter from ConvertUnits.com.
Rather confusingly, while the Romans counted in tens (decimal system) for whole numbers but counted in twelves (duodecimal) for fractions, probably because 12 is divisible by both three and four. The basic unit for tractions was the twelfth or uncia, from which we get our "inch" and "ounce", represented by a dot or dash following the whole number. One dot was 1/12, two dots were two twelfths (one sixth) and so on up to 5/12. Six twelfths were abbreviated as S for semis ("half") and then more uncia dots were added to the S for the remaining fractions up to eleven twelfths.
Converting Roman numerals
Should you wish to convert to or from roman numerals, or check your own conversion results, why not use our much loved roman numerals converter tool?
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