page_title: Greek numerals
section_title: Description
hierarchical_section_title: Greek numerals / Description
caption_attribution_description: English: A Greek-language map of Hibernia (Ireland) and Albion (Great Britain) derived from Ptolemy's Geography, probably in the early 14th century at Constantinople (Istanbul), held by the Vatopedi Monastery on Mount Athos prior to its theft and purchase by the British Museum. The map reflects Ptolemy's mistaken placement of Scotland at a right angle to the rest of Britain, apparently derived from his reliance on seafarer's logs.
context_page_description: Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used elsewhere in the West. For ordinary cardinal numbers, however, Greece uses Arabic numerals.
context_section_description: Greek numerals are decimal, based on powers of 10. The units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Instead of reusing these numbers to form multiples of the higher powers of ten, however, each multiple of ten from 10 to 90 was assigned its own separate letter from the next nine letters of the Ionic alphabet from iota to koppa. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well, from rho to sampi. (That this was not the traditional location of sampi in the Ionic alphabetical order has led classicists to conclude that sampi had fallen into disuse as a letter by the time the system was created.)
  This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example, 241 was represented as  (200 + 40 + 1). (It was not always the case that the numbers ran from highest to lowest: a 4th-century BC inscription at Athens placed the units to the left of the tens. This practice continued in Asia Minor well into the Roman period.) In ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars: α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ (600 + 60 + 6). (Numbers larger than 1,000 reused the same letters but included various marks to note the change.) Fractions were indicated as the denominator followed by a keraia (ʹ);  γʹ indicated one third, δʹ one fourth and so on.  As an exception, special symbol ∠ʹ indicated one half, and γ°ʹ or γoʹ was two-thirds.  These fractions were additive (also known as Egyptian fractions); for example δʹ ϛʹ indicated ​¹⁄₄ + ​¹⁄₆ = ​⁵⁄₁₂.
  Although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the former ones, especially in the case of the obscure numerals. The old Q-shaped koppa (Ϙ) began to be broken up ( and ) and simplified ( and ). The numeral for 6 changed several times. During antiquity, the original letter form of digamma (Ϝ) came to be avoided in favour of a special numerical one (). By the Byzantine era, the letter was known as episemon and written as  or . This eventually merged with the sigma-tau ligature stigma ϛ ( or ).
  In modern Greek, a number of other changes have been made. Instead of extending an over bar over an entire number, the keraia (κεραία, lit. "hornlike projection") is marked to its upper right, a development of the short marks formerly used for single numbers and fractions. The modern keraia is a symbol (´) similar to the acute accent (´), the tonos (U+0384,΄) and the prime symbol (U+02B9, ʹ), but has its own Unicode character as U+0374. Alexander the Great's father Philip II of Macedon is thus known as Φίλιππος Βʹ in modern Greek. A lower left keraia (Unicode: U+0375, "Greek Lower Numeral Sign") is now standard for distinguishing thousands: 2019 is represented as ͵ΒΙΘʹ (2 × 1,000 + 10 + 9).
  The declining use of ligatures in the 20th century also means that stigma is frequently written as the separate letters ΣΤʹ, although a single keraia is used for the group.
caption: A 14th-century Byzantine map of the British Isles from a manuscript of Ptolemy's Geography, using Greek numerals for its graticule: 52–63°N of the equator and 6–33°E from Ptolemy's Prime Meridian at the Fortunate Isles.
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