Counting on the Romans
The clock face at St Lawrence's church, Winslow. Note how the '4' is shown.
Roman numerals can be seen in nearly every village and town on the church clock. Sometimes you’ll see them on milestones or you’ll have a clock at home or a watch that uses them.
Many films have their copyright notice with the year written in Roman numerals, and the BBC used to do it too. Let’s have a look at what these numerals mean, and how to read them. Unlike our Arabic numerals the value of a numeral doesn’t depend on where it is in a number. If we write 511 we know it’s 5 hundreds, 1 ten, and 1.
The Roman numerals for 5 and one are V and I. Write VII, (a 5, a 1, and a 1) a Roman will read it as 7, they’d be right.
They had no numeral for zero, so where we might note down 500 for our 5 hundreds, no tens, and no units, they couldn’t. Instead, they’d write 500 as C. This example is simpler to write, but often their system of numbers was far more difficult to use.
First let’s see what their numerals mean.

Arabic 

Roman 

1 

I 

5 

V 

10 

X 

50 

L 

100 

C 

500 

D 

1,000 

M 
But there’s a problem. Not every number we use has a Roman equivalent, so to write those numbers Roman numerals have to be combined. To make 6, a Roman would write VI; 6 + 1.
But to write 4, they would usually write IV; to put the I before the V means to subtract it, not add it.
Here are a few examples.

Arabic 
Roman 

Arabic 
Roman 

1 
I 

11 
XI 

2 
II 

12 
XII 

3 
III 

13 
XIII 

4 
IIII or IV 

14 
XIV 

5 
V 

15 
XV 

6 
VI 

16 
XVI 

7 
VII 

17 
XVII 

8 
VIII 

18 
XVIII 

9 
IX 

19 
XIX 

10 
X 

20 
XX 

Arabic 
Roman 

Arabic 
Roman 

27 
XXVII 

64 
CXIV 

29 
XXIX 

111 
CXI 

34 
XXIV 

511 
DXI 

39 
XXIX 

1969 
MCMLXIX 

40 
XC 

2023 
MMXXIII 
Counting on Time
One oddity is that there are two ways to write 4, because clock and watch faces nearly always have IIII for 4 o’clock instead of IV.
There are various theories about this, but my favourite is that it’s because it means there are four hours marked with an I, four with a V, and four with an X; it just looks better.
Films and television can often be seen with a copyright date in Roman numerals. For 20th Century works, the year number will always start with MCM; 1,900. For a 21st Century production it will always start with MM.
One other modern use of Roman numerals is in the naming of monarchs and popes, which is why today is the Coronation of Charles III, not Charles 3.
This sundial on the porch of Mentmore's St Mary's church follows the convention of having 4 o'clock written as IIII, not IV. The church does not have a clock.
Maths Rules
There are a few rules for using Roman numerals, though these were only really standardised in Medieval times. Originally things would be more variable, like the way ancient spelling varies according to who wrote it or even what mood they were in.
Numerals are written left to right, largest to smallest, and added together. Almost the same as we do.
A numeral can only be written three times in a row. I, X, C, and M can be repeated. V, L, and D cannot.
As I said above, when a smaller numeral is to the left of a bigger one it is subtracted, not added. Only I, X, C and M can be placed to the left of the next biggest numeral along; I can only go to the left of X, X only to the left of L, and so on.
Using the rules with these numerals mean that the biggest number the Romans could write is MMMCMXCIX; MMM=3,000, CM=900, XC=90, and IX=9, which add up to 3,999.
To get over this they used a vinculum; a line over a numeral which meant it was 1,000 times bigger. So while M is 1,000, M̄ is 1,000,000.
4,000 can then be written as MV̅. But under the third rule 3,999 cannot be written as IV̅M.
This strangely positioned milestone in the village of Stone once read XLIV miles to London, as far as I could make out. Now XLI... miles... London is only just visible.
Doing Sums
How do you add two numbers together? Let’s say you want to add XVIII and XXI, or 18 and 21. First write all the numerals from both numbers out in order, all together.
That gives you XXXVIIII or 39, but nine (VIIII) is written with four ‘I’s in a row. Change that to IX and the full total is XXXIX.
To subtract one number for another is similar. Let’s subtract XXVI from XLVIII, or 26 from 48. Just for the sum, you can change XLVIII to XXXXVIII. You subtract all the numerals that are in XXVI (the ones in red) to leave XXII, or 22.
Conquering Division
Multiplication and division is more difficult, especially division. To multiply, you can at least add the same number to itself several times, but how do you divide?
Let’s give it a go with a fairly easy one, LXXXIV divided by VI, or as we say, 84 divided by 6.
I suppose you could take a guess that VI will go into LXXX at least ten times to make LX, leaving XXIV; then take another guess at how many times VI will go into XXIV.
This isn’t too different from what you do today, but this was a simple example. Something like DCCLXVII divided by XIV would be a different matter.
The clock on Holy Trinity church, Old Wolverton has only one hand, but the usual arrangement of Roman numerals.
Sum Help
There’s at least one shortcut. To multiply or divide a number by ten, all you have to do is change a numeral for the second one along in either direction. So X for 10 can quickly be changed to C, or I.
In practise the Romans used multiplication and division tables for sums with large numbers, and a form of abacus with the beads in grooves, not on wires.
The numerals are partly based on counting on fingers. I is a finger, V is a parted finger and thumb, X is two ‘V’s together. C is the first letter of the Roman word centum; meaning a hundred. M is the first letter of the Roman word mille, meaning a thousand.
Next time you go to the pub you can now order a round like a Roman Centurion. It’s easy; just hold up a finger and thumb and say, “five beers, please!”.
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