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Roman Numerals

Writing Numbers using Letters

The Romans used letters to write their numbers, each letter standing for a different value. The values of all the letters were then added together to make the number. The letters (usually written in CAPITALS but they can also be lower case) they used were:

M
m
D
d
C
c
L
l
X
x
V
v
I
i
1000 500 100 50 10 5 1

The order of the letters was usually from the largest down to the smallest (left to right) and now that is a fixed rule for writing Roman numbers. For instance:

13 would be written as XIII
2003 would be MMIII
99 would be LXXXXVIIII
1998 is MDCCCCLXXXXVIII
2000 is MM

The Subtraction Rules

Instead of just adding the values, subtraction is nowadays used too (and was occasionally used by the Romans too). The rule is:

if a smaller tens value (I, X or C) appears before one of the next two larger ones:
I before V or X
X before L or C
C before D or M
it was to be subtracted not added.

So I could appear before V or X to make IV for 4 and IX represents 9 but VI is 6 and XI is 11 by the normal (addition) rule. I could not appear before any of the other letters so it is incorrect to write IL to mean one less than 50 for 49 and IC is not correct for 99 nor is IM for 1999.

Similarly, X could appear before L or C to give XL for 40 and XC for 90 (but not before any other letter). Also C could be written before D or M for 400(CD) and 900 (CM).

Can you...
  1. Write out all the Roman Numbers from 1 to 50
    1. Convert these numbers to Roman numerals:
    2. 49 (hint: it is 40 + 9)
    3. 99 (hint: it is 90 + 9)
    4. 199
    5. 299
    6. 399
    7. 499

Why don't we use Roman Numerals today?

We use a system of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to write our numbers, not the Roman system. Why?

Try writing the following in Roman numbers:

  • the speed of light: 300,000,000 metres per second (or 300,000 km per sec)
  • the mass of the Sun: 1989 1030 kg
  • the diameter of the Sun: 1,390,000 km
  • the distance of the Earth from the Sun: 149,600,000 km

Also, try multiplying two numbers using only Roman numerals!

Can you...find examples of Roman Numerals in each of the following places:
  1. on the foundation stone of an old building or bridge
  2. on a plaque commemorating the opening of a building or bridge
  3. on the final part of the credits after some TV programmes, showing when the film or programme was made
  4. as page numbers of the preface in a book, which is the initial pages before the actual text of the book starts.
  5. as a way of numbering lists (like this one!)
  6. on some clocks (e.g. Big Ben in London).

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