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Roman Numerals


Today most people in Britain and Europe and North America, and many other countries, use what were until recently called Arabic numerals, 1, 2, 3 etc, for both doing sums and writing down the answers. But it has not always been like that.

The Romans used (surprise!) what we call Roman numerals, I, V, X, C etc, and everywhere the Romans went they took Roman numerals with them, and this included England (but not Scotland, hence Hadrian’s Wall) and much of Europe. Most people in Europe were still using Roman numerals for most purposes a thousand years after the Romans had left.

Arabic numbers actually originated in India, about one thousand seven hundred years ago. They reached the Arab World about two hundred years later. They came into Europe from the Arab World at the time of the Crusades, which is why Europeans called them Arabic numerals, but it was another six hundred years before most people were using them regularly. Victorian children had to learn both Arabic and Roman numerals, and Roman numerals are still used for many purposes even today.

Today most people other than mathematicians do not use the words Arabic numerals, and many mathematicians prefer to refer to them as Hindu-Arabic.

Today we are used to everything being new or improved, and old-fashioned is often used as a term of abuse. It is easy to forget that until the Industrial Revolution and the coming of the railways most people, throughout the whole world, lived in small villages, where their lifestyle hardly changed from one generation to another.

There is a good reason for this. Three hundred years ago everyone, from the mightiest Emperor to the humblest peasant, was well aware that food came from farms not from supermarkets. If the farms did not produce enough food the people would go hungry. If someone came along and said “I’ve invented a new type of plough which will not need an animal to pull it” the villagers would not immediately rush out and buy it: if after they had bought it they found it kept breaking down they would not be able to plant their crops. They could not afford to change the way they did things until they were certain that the changes “ had stood the test of time” - not an expression to common use today, but then today if you buy a new smartphone and it is not as good as the salesman had claimed you have only wasted money not endangered the lives of everyone in your village.

Nevertheless things do change, however slowly: the way the Romans used Roman numerals was not the same as the way they were being used in Europe a thousand years later, any more than the way English was spoken a thousand years ago is the same as the way it is spoken today.

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Roman numerals today

When reading or writing Roman numerals today

So 3 would be III, 8 would be VIII, 15 would be XV, 38 would be XXXVIII, 70 would be LXX, 108 would be CVIII, 658 would be DCLVIII and 1666 would be MDCLXVI.

In the original Roman system four would be written IIII, forty would be written XXXX and four hundred CCCC, so 45 would be XXXXV, 89 would be LXXXVIIII and 694 would be DCLXXXXIIII, but today we usually use IV (one less than five) for 4, and similarly IX for 9, XL and XC for 40 and 90, and CD and CM for 490 and 900, so 45 would be XLV, 89 would be LXXXIX and 694 would be DCXCIV. This is more fully discussed in IIII or IV?

The Ancient Egyptians had symbols for all numbers up to a million and you can see them on my Egypt Page. When we are using Roman numerals today we quite happily use M for a thousand and MM for two thousand, for example the year 2014 is MMXIV, but this is not the way the Romans usually wrote numbers more than DCCCCLXXXXVIIII (999 if you cannot work it out yourself). But except for year numbers such as 1999 (MCMXCIX) or 2014 (MMXIV) most people today will probably never come across or use Roman numerals for numbers bigger than 999, so this Page does not explain how the Romans did do it. (If you really do want to find out how they did it an internet search on “Roman numerals + M” will throw up several explanations - but it is very heavy going.)

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Using Roman numerals today

We still use Roman numerals even today for some purposes. We can usually use either upper case, for example VI, or lower case, for example vi. Here are some common uses.

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Writing nine hundred and ninety nine as DCCCCLXXXXVIIII is quite tedious, and even in Roman times individuals were experimenting with ways of making numbers simpler to write, for example, nine is one less than ten so if one more than ten is XI why not write one less than ten as IX?

There are however several problems with doing this. For example why stop there? If twelve is XII why not write eight as IIX? But a bigger problem arises because there is no zero in Roman numerals.

If you use Xs for the tens then if you want to write three hundred and five, where there aren’t any tens, you just don’t put in any Xs, and so end up with CCCV, in exactly the same way that if you want to say three hundred and five you do not put in a silent pause in the place where the tens would be. No problems if you are just writing or saying numbers. But doing calculations, particularly subtractions, using a numbering system without a zero is a different matter, which is why people used tools such as the abacus for actually doing sums - this is much more fully discussed in the Page on Early Numbering System, while zero is more fully discussed in the zero section of the Natural Numbers page. Using an abacus, if you subtract one from a thousand you do not end up with one less than a thousand (IM), you end up with a hundred less than a thousand plus ten less than a hundred plus one less than ten, or CMXCIX. So the Romans had to have Rules about how they could simplify the way they wrote numbers. The problem is the Rules were quite complicated, so some people ignored them and made up their own, while other people could not cope with remembering them all and just went on using the old way - there was no consistent way which everyone used. In the Colosseum in Rome (built in about 80 CE) all the entrances are clearly numbered, as they are in sports arenas today. Entrance forty is numbered XL but entrance forty four is numbered XLIIII. This state of affairs continued in Europe long after the Romans had left.

In mediaeval England lords of manors could not always read or write, and in any case were usually too busy to keep the manor accounts themselves, instead they employed stewards. Writing pages and pages of Roman numerals was very tedious, so stewards used their own shorthand ways of writing them, in exactly the same way that today’s teenagers use their own shorthand for sending each other text messages. The steward would of course still need to present the accounts to his lord, which he would do by reading them aloud. This was called auditing, from the Latin word audio, meaning I hear - company accounts still have to be audited (that is, independently checked by someone else - but not by reading them aloud!) today. Other clerks often used a similar shorthand when preparing what might today be called internal memos or personal aide-memoires, documents never intended for the public to see.

Printing came to Europe in the fifteenth century: William Caxton printed his first book in England in 1476. Because of the way the type was set in those days there were very powerful reasons (explained on another Page) why printers did not wish to use DCCCCLXXXXVIIII for nine hundred and ninety nine if they could use something shorter, and so printers were soon all using a single, standardardised shorter way: IV (one less than five) for 4 and IX for 9, XL (ten less than fifty) for 40 and XC for 90, CD (a hundred less than five hundred) for 400 and CM for 900, so 999 would be CMXCIX. Since then almost all books have been printed in this way.

Initially this way applied only to printed books, most things not printed, hand-written letters, legal documents, bank accounts, clock faces etc. continued to use the old way for another three hundred years. In 1821 George the Fourth was crowned as King George IIII and all the coins for 1821, 1822 and 1823, and all legal documents for these years, carried the name George IIII. However in 1824 he started using George IV on coins and in documents, and after that the old system soon fell almost completely out of use, not only in Britain, except on clocks.

There are many different explanations for why we still use IIII on a clock, but the most satisfactory is that it looks better because the IIII balances the VIII.

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© Barry Gray January 2016