Greek numerals

Greek numerals are a system of representing numbers using letters of the Greek alphabet. In modern Greece, they are still in use for ordinal numbers, and in much the same situations as Roman numerals are in the west; for ordinary numbers, arabic numerals are used.

The earliest system of numerals in Greek was 4th century BC, the acrophonic system was replaced with a quasi-decimal alphabetic system, sometimes called the Ionic numeral system. Each unit (1, 2, ..., 9) was assigned a separate letter, each tens (10, 20, ..., 90) a separate letter, and each hundreds (100, 200, ..., 900) a separate letter. This requires 27 letters, so the 24-letter Greek alphabet was extended by using three obsolete letters: digamma (ϝ, also used are ς or στ) for 6, qoppa (ϟ) for 90, and sampi (ϡ) for 900. An acute sign (´) is used to distinguish numerals from letters.

The alphabetic system operates on the additive principle in which the numeric values of the letters are added together to form the total. For example, 241 is represented as σμα´ (200 + 40 + 1).

To represent numbers from 1,000 to 999,999 the same letters are "recycled" to serve as thousands, tens of thousands, and hundreds of thousands. A comma or inverted acute is put in front of thousands to distinguish them from the standard use. For example, 2004 is represented as ,βδ´ (2000 + 4).

Letter	Value	Letter	Value	Letter	Value
α´	1	ι´	10	ρ´	100
β´	2	κ´	20	σ´	200
γ´	3	λ´	30	τ´	300
δ´	4	μ´	40	υ´	400
ε´	5	ν´	50	φ´	500
ϝ&acute or ς´ or στ´	6	ξ´	60	χ´	600
ζ´	7	ο´	70	ψ´	700
η´	8	π´	80	ω´	800
θ´	9	ϟ´	90	ϡ´	900

Hellenistic astronomers extended this into a sexagesimal positional numbering system by limiting each position to a maximum value of 59 and including a special symbol for zero, which usually looked like τ with a small circle at the bottom of its descender. However, these positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.), but were not used for their integral part. This system was used by Ptolemy (c. 140), Theon (c. 380), and Theon's daughter Hypatia (died 415). It was probably adapted from Babylonian numerals by Hipparchus c. 140 BC.

See also

Hebrew numerals: The Hebrew language has the same numeral equivalencies.