All about roman numerals

By Nick Valentine| Last update: 03 November 2015
Roman numerals 1 to 10 on black background. - photo

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.

So 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 only seven basic symbols:

The system of roman numerals

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.

The Etruscan numbering system

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 fingers

An 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.

On the next page we look at the three basic rules for constructing Roman numbers and we discuss large numbers and fractions.

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