As I'm sure you know, the Roman number system used the letters of alphabet to stand also for the numbers. The same system, I believe, survives in Hebrew. It is probably apparent, then, that the Romans inherited this scheme from the Ancient Greeks. The Greeks themselves used a system considerably more effecient than that of the Romans, similar in fact to the Hebrew one, although problems do arrise with it that we shall encounter in a moment.

The numbers themselves were attached to the letters as follows:

α β γ δ ε ϝ ζ η θ
1 2 3 4 5 6 7 8 9
ι κ λ μ ν ξ ο π ϙ
10 20 30 40 50 60 70 80 90
ρ σ τ υ φ χ ψ ω ϡ
100 200 300 400 500 600 700 800 900
,α ,β ,γ ,δ ,ε ,ϝ ,ζ ,η ,θ
1000 2000 3000 4000 5000 6000 7000 8000 9000

This, you will note, requires 27 characters, while the Greek alphabet has only 24. This is the problem with the system, which the Greeks worked around by restoring several letters that had become extinct from the ordinary alphabet. The first of these is digamma for 6, which does look much like an F for those of you who can't see the Unicode characters. The next is the qoph or koppa, the symbol for which looks most like a vertical magnifying glass, and which eventually evolved into our q. The final one is sampi for 900, which looks a little like this:

____
\
/ \
/ /\
/ / |
/

Although this is still a fairly vague approximation.

On with the show. Numbers are written with the largest value on the left, in a sense like our own system, eg:

5214 =
,εσιδ

This allowed the easy representation of numbers up to 9999, and in the 3rd century AD, a certain Diophantus suggested the use of '.' to multiply the previous digits by 10000, eg

13310000
=,ατλα.

In this way the Greek system could cope up to 99999999 (10

^{8} - 1), and thus was comfortablely large enough for all their practical needs. It should be noted that most of their needs were indeed practical, as

mathematics in Greek times was mainly concerned with

geometry.

*Adapted from The Book of Numbers, Conway & Guy 1995*

Thanks also to evilrooster for his moment of grammatical clarity, and Cletus_the_Foetus for all the Unicode feedback and also a little background on koppa.