# Roman numerals

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The numbers that we know so well (1, 2, 3 and so on) have their roots in the Hindu-Arabic numbering system. However, there is another numbering system which is often used to show the publication dates of books. These are Roman numerals which assign numerical values to letters of the alphabet which are then used in combination to express bigger numbers.
The basis of the system is:

 Value Letter 1 I 5 V 10 X 50 L 100 C 500 D 1,000 M

That’s fine as far as it goes, but the key to deciphering numbers shown using Roman numerals is to understand how these letters are combined to make up different values.

This is how it works:

 Anything below 4 is represented by the appropriate times the letter I is used. So: 2 is shown as II 3 is shown as III The same system works for some of the other core numbers XX is 10 + 10 or 20 CCC is 100 + 100 + 100 or 300

Obviously this approach isn’t necessary with V (5) or L (50) or D (500) because we have separate letters for double any of those values.

That’s the easy bit. The next step is to understand how you can represent other numbers using Roman numerals.

 Suppose you wanted to show 25. How would that be done? It’s very simple because it is, in effect, addition You have 10 + 10 + 5 or XXV

Similarly, if you wanted to show 130, you would have 100 plus three 10s or CXXX.

The same approach works with other numbers too:
For example, 550 is 500 + 50 or DL
555 is 500 + 50 + 5 or DLV
515 is 500 + 10 + 5 or DXV.

It gets more complicated now…
The Romans seem to have decided that more than three of the same letter together such as IIII was difficult to decipher quickly so they took a different approach for numbers such as 4 and 400. (It's worth making the point here that some clock faces use IIII but that has nothing to do with the Romans.)

 The basic principle here is that, if a lower value figure is to the left of a number, it is deducted from that number. Suppose you want to write 4. You write this as 1 taken away from 5 which appears as IV. The same applies with 9: it’s 1 taken away from 10 or IX.

It might sound complicated but again, it’s a simple rule: Roman numerals start with the biggest value on the left and go down in value as you move to the right.

So 515 is shown as DXV (500, 10, 5).

However, if that descending order is interrupted, for example in XIV you have 10, 1, 5, then the 1 is deducted from the 5 to give you 4 so XIV is 14.

It’s the same with CCIX which deciphers as 100, 100, 1, 10 so the 1 is deducted from the 10 which gives you 209.

## Applying the rules to dates:

When we come to dates it’s important to understand that we need to see them as plain numbers rather than dates. So 1642, for example, is easier to express as a Roman numeral if it’s thought of as one thousand six hundred and forty two ( 1,642).

 Now you can start to build the date up: Use M for the 1,000. Add the D for 500 Add C for 100 to get to 600. So far, then, you’ve got MDC meaning 1,600. Now you need 40 which is XL (50 minus 10). Finally you need 2 which is II. When these are put together you get MDCXLII.

So how is this applied to reading Roman numerals, especially as dates? Suppose you have a book published in MDCXXII.

It’s a question of breaking it down. It works like this:

M = 1,000
D = 500
C = 100
XX = 10+10 or 20
II = 1+1 or 2

The total is 1,622 or 1622
And that's how Roman numerals work.