# Ancient Roman Numbers

Roman numerals came originally from Etruscan numerals, but they changed the symbols. The Roman system came into use from the 4th century BC, but the symbols we know today were not fixed until about the 1st century AD.

### Count with Roman numbers

In our number system (called Arabic numbers), we have ten digits (from 0-9) and we can make as big a number as we want with these. We use all ten digits to count to nine, then we combine them to make bigger numbers. So we never run out of numbers, as long as there is room to write them down! The more digits there are, the longer the number is. The ancient Romans didn't think this. They repeated symbols, so one was I and 2 was II. For larger numbers, they invented new symbols, so five was V, ten was X, and so on. But they didn't have a symbol for zero. They didn't need it.

Click in the first box and type in a whole positive number less than 4000. The Roman number will appear in the other box. Try different numbers, and see how the Romans would write them. If you have a Roman number and you want to find out what it is, click on the Roman box and type it in. Click on Count to watch the numbers change. If you put in a number, you can see a Roman times table in action!

Arabic number:             Roman number:

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### How Roman numbers worked

The Romans had different symbols for numbers as they got bigger:

 Arabic 1 5 10 50 100 500 1000 Roman I V X L C D M

These were the normal symbols, but they could only describe numbers up to 3999. The Romans combined their symbols, so VII meant 5+1+1 or seven. This is called a unary system. However, they found that IIII and VIIII were too confusing (for four and nine), so they introduced another idea. If the I comes after the V then you add it (VI is 6). But if the I comes before the V then you subtract it (IV is four). The rule is that you are allowed to add up to three (VIII is eight), but only subtract one (IX is nine). This means that you have to be very careful what order Roman digits are in. XI is a different number from IX.

You can also do this for larger numbers.

MDCCCLXXXVIII = 1000 + 500 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 1888

MCMXCIX = M CM XC IX or 1000 + (1000 - 100) + (100 - 10) + (10 - 1) = 1999

You have to be good at adding and subtracting for Roman numbers! Also, you can't tell from the length of the number, how big it is (MM is 2000).

### How to remember the symbols

How can we remember what these letters are? The easy letters are I, C and M. I is probably a finger. Most people start off by counting on their fingers! The Romans spoke a language called Latin, and the Latin for hundred is Centum. So C was an obvious letter for 100. We still use cent in English words to mean a hundred, so it's easy to remember. Think of a hundred centimetres in a metre, a hundred years in a century or a a hundred cents in a dollar. The Latin for thousand is Mille. So M is the letter for thousand. Think of a thousand years in a millennium or a thousand millimetres in a metre.

 Here is a way to remember that V is five. I or II or III are different numbers of fingers held up. So what are five fingers? A whole hand, of course! If you look at a hand (see left), you can see that the thumb and little finger make a V, and it's a lot easier than to draw the whole hand. Perhaps the hand can also explain why the number 4 is written as IV. It is a hand with the thumb turned down. This is a lot easier to do than turning down a couple of fingers, so it could be that's why we only subtract one, not two or three. Ten fingers are both hands, so the two V's make an X (see right).
 Now for fifty. Fifty is half of a hundred. If you take the symbol for hundred, C, and cut it in half, it looks like an L, which is the letter for fifty. Five hundred is half of a thousand. If you take the symbol for thousand, M, and cut it in half, it looks like a D (sort of), which is five hundred.

### Roman numbers greater than 4000

At the top of this page, when using the convertor, I tell you to type a number in which is less than 4000. Why? When we use Roman numbers today, we don't use them for big numbers, so you never see the Roman number for 5000 (and if you don't have that, then you can't write 4000). The Romans agreed on symbols for 1, 5, 10, 50, 100, 500, and 1000, but there were different symbols for 5000 and also for the bigger numbers. Here is one way the Romans wrote these bigger numbers.

So you would write 924,587 like this:

As you can see, it's getting quite messy!

### Modern use of Roman numbers

We still use Roman numbers today. One place where you often see Roman numbers is on a clock face. The hours are marked as I to XII. However, there is something odd about these Roman numbers. If you look at four, it is IIII instead of IV. I think that this is because half of the numbers are upside down, since they follow the edge of the clock face round. You can get IV and VI muddled up when they're the right way up. It is even worse when they're upside down! IX and XI are not such a problem, since they are more or less the right way up. In fact, the Romans never had clocks like this, since this type of clock was invented centuries afterwards.

Another place where you see Roman numbers is in the copyright year shown at the end of British TV programmes. Perhaps they do this because most people don't know their Roman numbers very well, so they can't work out how old the programme is!

This is the accepted modern way to count with Roman numbers. The Romans themselves were not so fussy. There is a Roman tombstone in York, England, of Lucius Duccius Rufinius, who was the standard bearer of the VIIII legion (9th), and was XXIIX years old (or 28).