Roman Numerals

Using letters for numbers

The Romans depicted numbers using seven letters

of the alphabet as numerals
I=1
V=5
X = 10
L = 50
C = 100
D = 500
M = 1000
 Forming numbers
• Roman numerals are basically strung
together to create a total. However the
highest possible letter is used at any time.
For example
• VVV = 15
• But should be written
• XV = 15
 The subtractive principle
The subtractive numeral to the left must be I,
X, or C. The 'five' numerals V, L, and D
cannot be used. M cannot be used
because it is the biggest numeral
anyway.
So;
IV = 4, IX = 9, XL = 40, XC = 90, CM = 900
 What can go before what?
• The subtracted number must be no less
than a tenth of the value of the number it is
subtracted from. So an X can be placed to
the left of a C or an L but not to the left of
an M or a D. The correct way of looking at
this rule is that each power of ten is dealt
with separately. So 49 is XL IX (without the
spaces), not IL
 Exceptions to the rule
• Normally, only one smaller number can be
placed to the left. So 19 can be depicted XIX but
17 cannot be written XIIIX or IIIXX. However, this
rule is sometimes broken for number involving
an eight. On some Roman monuments and
tombs IIXX for 18 is found. And in recent times
times, a statue by Hamo Thornycroft called A
Sower in London's Kew Gardens bears an
inscription with the date MCMXXIIX meaning
1928. Such uses are not 'correct' but are found
very occasionally.
Test yourself
Test yourself 2
Test your self 3
 Going to the theatre
• The Colosseum - constructed between 70
and 80 AD and known as the Flavian
Amphitheatre - seated 55,000 people. The
audience entered through 80 arches which
were numbered 1 to 76 - the four principal
entrances were unnumbered. Each
spectator had a ticket bearing one of these
numbers and entered through the
corresponding arch. It is said they could all
enter within ten minutes.
 Going to the theatre
• Only 33 doorways remain
and they are numbered
23 to 54 with one
unnumbered entrance.
The numbers do not use
the contraction IV or IX.
Thus arch 29 is XXVIIII
and arch 54 is LIIII.
However, the contraction
for 40 - XL - is used and
so door 44 is XLIIII, as
the picture below shows.
 Go Large
Larger numbers
Once a number gets bigger than a few thousand,
Roman numerals become unwieldy.
There are no 'bigger' symbols for 5000, 10,000 or a
million.
The Romans had two ways of writing bigger numbers.
They used what I call above 'deep parentheses' to
multiply a number by 1000. They were a C and a
mirror image or upside down C and I use normal
parentheses to show them.
Thus ( I ) is 1000 and ( X ) is 10,000. ( XXIII ) is 23,000.
If you want to depict a million you can use ( M ).
Alternatively, the parentheses can be nested so ( I ) is
1,000 and ( ( I ) ) is 1,000,000. The numbers can get
a bit unwieldy as they get bigger.
 Another way to ‘Go Large’
An alternative way of depicting larger numbers
was to put a horizontal bar over the numeral,
which multiplied it by 1000. Thus
_ _
V = 5000 and X = 10,000.

On a larger scale 3,852,429 can be depicted as

___________
MMMDCCCLMMCDXXIX
.
 Write some big numbers in
‘ROMAN’
Worldometers
 Fractions 1
Fractions
The letter S was used to depict a half. Other fractions
were shown by dashes, each dash being worth one
twelfth.
So - meant 1/12, = meant two twelfths which is one
sixth, and so on.
Twenty three and a half would be written XXIIIS and
twelve and a quarter is XII-=.
The letter S and the dashes were never used
subtractively.
Other fractions could not be depicted in Roman
numerals.
Which fractions can you write?
 Fractions 2
1/12 1/2 plus 1/12th
- S- or 7/12ths
2/12 or 1/6 1/2 plus
= S= 2/12ths or 2/3
3/12ths or 1/4 1/2 plus
-= S-= 3/12ths or 3/4
4/12ths or 1/3 1/2 plus
== S== 4/12ths or 5/6
5/12ths 1/2 plus
-== S-== 5/12ths or
11/12ths
1/2
S
 Zero
Zero
The Roman numeral system did not include zero
and Romans had no concept of it in their
arithmetic. Which is one reason why Roman
numerals are so clumsy for calculation, though it
is possible.
They tended to use an abacus for arithmetic and
that device does have the concept of zero built
in - it is represented by an empty row.
 Zero 2
But it was the Indian and Arab mathematicians
after the end of the Roman empire who invented
our present system where we have the concept
of 'place' and have a distinct symbol to represent
zero or an empty column.
So when we write '10' for example the zero tells us
that the '1' is worth ten times as much as it
would be if the number was just 1.
 Telling the time
Draw and complete a clock face with
roman numerals

What is the
difference?