Greek Numbers and Numerals (Ancient and Modern)

The present page is part of the author’s set of pages on the Greek language

This page attempts to explain the following topics:

• How numbers are written and pronounced in Modern Greek
• How numbers used to be written and pronounced in Ancient Greek

First, let us make one observation that is crucial for understanding both the ancient and modern counting system:

Greeks, throughout recorded history, have used the decimal system

Notice that by “decimal system” I mean a system that uses the number 10 as its so-called “base”; I do not mean one that uses our familiar Arabic numerals 1, 2, 3, etc. Not all ancient peoples used decimal systems. The Romans, for example, used a system that resembles more a base-5 system; the Babylonians used a system that is nearly base-60; some cultures have been known that use the binary system (base-2, like modern computers). The majority of ancient peoples, however, including the Chinese, the Greeks, and the Egyptians, used the decimal system. (The reason for this preference is obvious: we have 10 fingers.)

Although for Greeks the base of the system has always been 10, the writing system has been changed between ancient and modern times.

• In Modern Greek, the familiar Arabic numerals are used for writing numbers
• In Ancient Greek, a system based on the Greek alphabet was used for writing numbers

Therefore, nothing needs to be explained in Modern Greek regarding the writing of numbers; the latter needs explanation only in the case of Ancient Greek.

Note, for readers of Biblical Koine Greek: In reading the New Testament in the original Greek (the “koine” dialect), as well as the Old Testament in the Septuagint (the “official” ancient translation of the Hebrew original), you will encounter Arabic numerals (for example: 15:27, etc.) You may think that this contradicts the above statements. It should be understood that Arabic numerals appear only in our modern printing of the ancient texts. Ancient handwritten texts of the Bible certainly employed the ancient (alphabetic) style of writing numbers. You may also wonder how to read such numbers. No matter what writing notation was used, numbers were pronounced as numbers. For example, the number 12 was written as ιβ in ancient Greek (you will learn why, below); but it was not pronounced as /ib/, but through the word for number “twelve” (δυοκαίδεκα, in ancient Greek). You may choose to use either the Ancient, or the Modern way of pronouncing numbers in the Bible whichever seems most convenient to you.

With the above in mind, let us now proceed to the two cases, Modern and Ancient, separately.

Numbers in Modern Greek

Cardinal Numbers

Cardinal numbers are the ones we use for counting, in the abstract: one, two, three, etc. (as opposed to ordinal numbers: first, second, third, etc., given below). Assuming the reader is familiar with numbers in English, the corresponding system in Greek should be perceived as easy, because it is very similar to the English one. The similarity goes to such things as having special words for eleven and twelve, (and with tw- hinting at the origin of this word), having the numbers from 13 to 19 formed by a suffix (-teen; it’s a prefix in Greek), while larger 2-digit numbers are formed by the tens, followed by the digits (e.g., seventy one). All these characteristics are same in Greek as in English.

One detail that differs is the following: in Greek, the cardinal numbers for one, three, and four, have the form of adjectives; hence, they can be declined according to gender and case (but obviously not according to number, since one can be only in the singular, and three and four only in the plural). All the other numbers have just a single, undeclined form. The following table shows how to count in modern Greek, from zero to twenty.

Where an alternative form is given, it is the more colloquial one. This means that you will usually encounter the first form more often in books, or written language in general, while the second form is usually more common in speech (the emphasis on the word usually means there isn’t any hard-and-fast rule for when and where to use each form).

To understand how to use the gender-declined forms for one, three, and four, note the following: When counting in the abstract (for example, seconds of time, printed lines on a page, or any other case where you don’t care to refer to the noun being counted, but you simply want to say one, two, three, etc.), then use the neuter form: ένα, δύο, τρία, τέσσερα, etc. When you want to make reference to the counted noun, however, or (and this is mandatory) if the number appears in front of the counted noun in a sentence, then the number (one, three, or four) must agree with the noun in gender and case. For example, if you want to say: one fly, since the word for fly (the insect) in Greek is of feminine gender, you will say: μία μύγα (not ένα μύγα). If this is in the genitive case, the form will be: μίας μύγας. For three flies, the correct form is: τρεις μύγες (not τρία μύγες). The declension for the number one is identical to the indefinite article a/an in Modern Greek (i.e., the two words, one and a/an coincide).

The above remarks hold for every composite number that uses these three simple numbers as a component, such as 13, 14, 21, 1001, etc.

To count beyond twenty in Greek we follow the same pattern as in English:

Now, to count beyond 100, one should notice this: although the word for one hundred is εκατό, every number between 101 and 199 uses the form εκατόν, with that extra nu (ν) at the end. Thus,

(This difference occurs because the original (ancient) word for 100 was ἑκατόν, but the final ν (nu) was dropped out of use by “erosion”; the other numbers between 101 and 199 were never used as commonly as 100, so they retained their final consonant.)

Another observation is that, contrary to English, we do not insert the word and between εκατόν and the number that follows.

The numbers for multiples of 100 up to 1000 all have genders, and are as follows:

Now, let us practice with some “random” numbers:

Continuing beyond 1999, the plural of the word for thousand is used, i.e., χιλιάδες (instead of χίλια). Therefore, the numbers for three and four thousand have to match in gender (feminine) and case with χιλιάδες:

Now let us make some random tests:

Did you notice the tricky part in the last example? Although the word for 800 is οκτακόσια (in the abstract, or neuter gender), when we want to say eight hundred thousand we have to match the gender of οκτακόσια with χιλιάδες (feminine), hence: οκτακόσιες χιλιάδες.

We continue with the words for one million, two million, etc. Notice that, in Greek numerals, the mark that separates the thousands is the period, not the comma:

Continuing beyond that, the Greek system uses the American English convention for billion, trillion, etc., i.e., a billion is a thousand million, a trillion is a million million, etc. The words beyond those (quadrillion, etc.) are seldom used in practice, except in some areas of science.

Note: the word for billion, δισεκατομμύριο, is often seen in its abbreviated form: δισ., and even δις, as if the abbreviation is the word. Likewise, the word for trillion, τρισεκατομμύριο, is often abbreviated as τρισ., and even τρις. People often use these abbreviations in speech, too.

...You get the picture. Even in science, such numbers are almost never spelled out, but written as numerals with the exponential notation instead. The last number included in the table above is close to the total number of elementary particles in the universe (at last count, ca. 2000 CE).

Let us make one last practice, with a number considerably “smaller” than the ones of the last rows (its parts are shown on separate lines, for ease of identification):

Just for the fun of it, let us finally proceed to the limits of the Modern Greek counting system. (Boy, do I love this trivia!)

The repetitive pattern in the linguistic system in relation to the denotational system becomes evident: whenever 6 zeros are “inserted” in the exponent after the first digit (i.e., whenever the exponent is multiplied by nearly one million it would be exactly 1 million if we ignored the last 3), then the word εκατομμυριάκις (“million-fold”) is inserted in the linguistic expression after the word ένα.

For those of you who have native level of command of Greek, here is the continuation of the idea of marching to infinity (in Greek only).

Ordinal Numbers

Ordinal numbers are the ones we use for ordering objects: first, second, third, etc. In Greek, ordinal numbers have always the form of an adjective; thus, they are declined by gender, case, and number. (Yes! Such numbers are declined by number, i.e., singular or plural: one can say first, if the object, person, etc., is one, and something like firsts, if they are many.) The table below gives an idea for what the words for these numbers look like. The genders appear with the masculine first, the feminine second, and the neuter third in sequence.

The continuation of the pattern should be evident from the above, as well as from the way larger cardinal numbers are formed (see cardinal numbers, above).

Reading Math Symbols

Negative numbers: The symbol - (minus) is read: μείον in Greek. For example: -12 is read: μείον δώδεκα.

Percent: The symbol % is used in Greek, as in English. It is read: “τοις εκατό”. So, 23% is read: εικοσιτρία τοις εκατό.

Occasionally, the symbol ‰ is used for “per thousand” (percent times 10, if the numbers are too low). It is read: “τοις χιλίοις”. (Strange-looking endings such as -οις are relics of the obsolete dative case).

Decimals: The roles of period and comma are switched in Greek relative to English: the period is used for separating thousands, and the comma is the decimal point.

How to read numbers with decimals: simply pronounce the “comma” between the two parts:

Fractions: Exactly the same system as in English is used: the numerator is a cardinal number (one, two, three,...), and the denominator is an ordinal number (third, fourth, fifth,..., in the neuter gender). Here are some examples:

Numbers in Ancient Greek

Ancient Greeks used the letters of the Greek alphabet in order to denote numbers. But how can one represent large numbers with only 24 letters available in the Greek alphabet?

Simple: the letters from alpha to theta, plus one extra symbol at the 6th position (α, β, γ, δ, ε, ϛ, ζ, η, θ) played the role of the nine digits, 1,2,3,...,9. (The role of the accent-mark, , will be explained in a moment.) The next letter, iota (ι), stood for 10. Now, ια was 11, ιβ was 12, and so on, up to ιθ which was 19. Then, the next letter in order, kappa (κ) was used to denote 20. Likewise, lambda (λ) was 30. And so on, up to pi (π) which was 80; and then an extra symbol, the qoppa (ϙ), was used for 90. Then, the next letter, rho (ρ), was used to denote 100; sigma (σ) was 200; and so on, up to the last letter of the alphabet, omega (ω), which stood for 800. One final extra-alphabetic symbol, the sampi (ϡ) was used to denote 900. From there on... well, you already noticed the accent-mark at the upper-right of each Greek letter, right? This mark was used to mean “this is to be read as a number, not a word of the Greek language.” Now, when this mark was placed at the lower-left corner of the letter, it meant that the number was to be multiplied by 1000. Thus, α denoted 1000. (Note: there have been other notations, too, such as placing a horizontal bar over the letters of a number. In fact, this was the original practice; the one with the is a more recent one. There have also been different symbols for the numbers 6 and 90; a good description of the development of symbols for Greek numerals can be found here.)

The table that follows explains all this, and also shows the words ancient Greeks used for speaking numbers out loud. As before, wherever genders appear, the masculine gender is shown first, next is the feminine, and third in row is the neuter.

Arabic numeral	Greek numeral	How the number was pronounced:
0		οὐδείς, οὐδεμία, οὐδέν or μηδείς, μηδεμία, μηδέν
1	α	εἷς, μία, ἕν
2	β	δύο
3	γ	τρεῖς, τρεῖς, τρία
4	δ	τέτταρες, τέτταρες, τέτταρα or τέσσαρες, τέσσαρες, τέσσαρα
5	ε	πέντε
6	ϛ	ἕξ
7	ζ	ἑπτά
8	η	ὀκτώ
9	θ	ἐννέα
10	ι	δέκα
11	ια	ἕνδεκα
12	ιβ	δώδεκα or δυοκαίδεκα
13	ιγ	τρεισκαίδεκα, τρεισκαίδεκα, τριακαίδεκα or τρεῖς καὶ δέκα, τρεῖς καὶ δέκα, τρία καὶ δέκα
14	ιδ	τέτταρες καὶ δέκα, τέτταρες καὶ δέκα, τέτταρα καὶ δέκα
15	ιε	πεντεκαίδεκα
16	ιϛ	ἑκκαίδεκα
17	ιζ	ἑπτακαίδεκα
18	ιη	ὀκτωκαίδεκα
19	ιθ	ἐννεακαίδεκα
20	κ	εἴκοσι(ν)
21	κα	εἷς καὶ εἴκοσι, μία καὶ εἴκοσι, ἓν καὶ εἴκοσι
...
30	λ	τριάκοντα
31	λα	εἷς καὶ τριάκοντα, μία καὶ τριάκοντα, ἓν καὶ τριάκοντα
...

As suggested by the top row, ancient Greeks had no symbol for zero, nor was zero considered a number. Their words for zero, ουδείς and μηδείς, meant “not even one”.  The modern symbol for zero (0) originated from the first letter of the word ουδείς (source), whereas the Modern Greek word for zero (μηδέν) comes from the neuter form of the ancient word.

From this point on, only the numbers that are multiples of 10 will be shown, assuming the pattern is understood from the above.

Arabic numeral	Greek numeral	How the number was pronounced:
40	μ	τετταράκοντα or τεσσαράκοντα
50	ν	πεντήκοντα
60	ξ	ἑξήκοντα
70	ο	ἑβδομήκοντα
80	π	ὀγδοήκοντα
90	ϙ	ἐννενήκοντα
100	ρ	ἑκατόν
110	ρι	δέκα καὶ ἑκατόν
...
190	ρϙ	ἐννενήκοντα καὶ ἑκατόν
200	σ	διακόσιοι, διακόσιαι, διακόσια
...
300	τ	τριακόσιοι, τριακόσιαι, τριακόσια
400	υ	τετρακόσιοι, τετρακόσιαι, τετρακόσια
500	φ	πεντακόσιοι, πεντακόσιαι, πεντακόσια
600	χ	ἑξακόσιοι, ἑξακόσιαι, ἑξακόσια
700	ψ	ἑπτακόσιοι, ἑπτακόσιαι, ἑπτακόσια
800	ω	ὀκτακόσιοι, ὀκτακόσιαι, ὀκτακόσια
900	ϡ	ἐννεακόσιοι, ἐννεακόσιαι, ἐννεακόσια
1000		χίλιοι, χίλιαι, χίλια
1001		εἷς καὶ χίλιοι, μία καὶ χίλιαι, ἓν καὶ χίλια
...
2000		δισχίλιοι, δισχίλιαι, δισχίλια
3000		τρισχίλιοι, τρισχίλιαι, τρισχίλια
4000		τετράκις χίλιοι, τετράκις χίλιαι, τετράκις χίλια
5000		πεντάκις χίλιοι, πεντάκις χίλιαι, πεντάκις χίλια
6000		ἑξάκις χίλιοι, ἑξάκις χίλιαι, ἑξάκις χίλια
7000		ἑπτάκις χίλιοι, ἑπτάκις χίλιαι, ἑπτάκις χίλια
8000		ὀκτάκις χίλιοι, ὀκτάκις χίλιαι, ὀκτάκις χίλια
9000		ἐννεάκις χίλιοι, ἐννεάκις χίλιαι, ἐννεάκις χίλια
10000		μύριοι, μύριαι, μύρια

The ancient Greek system generally stops here: μύρια is the largest unit in counting. Nonetheless, the Greek mathematician and inventor Archimedes (287-212 BCE) was interested in even larger numbers. So he came up with a system of numbering that went way beyond the one of his contemporaries in fact, way beyond our modern system of naming numbers. The rest of the ancient Greek numbering shown below is due to Archimedes.

20000		δισμύριοι, δισμύριαι, δισμύρια
30000		τρισμύριοι, τρισμύριαι, τρισμύρια
40000		τετράκις μύριοι, τετράκις μύριαι, τετράκις μύρια
...
100000		δεκάκις μύριοι, δεκάκις μύριαι, δεκάκις μύρια
200000		εἰκοσάκις μύριοι, εἰκοσάκις μύριαι, εἰκοσάκις μύρια
300000		τριακοντάκις μύριοι, τριακοντάκις μύριαι, τριακοντάκις μύρια
400000		τεσσαρακοντάκις μύριοι, τεσσαρακοντάκις μύριαι, τεσσαρακοντάκις μύρια
500000		πεντηκοντάκις μύριοι, πεντηκοντάκις μύριαι, πεντηκοντάκις μύρια
600000		ἑξηκοντάκις μύριοι, ἑξηκοντάκις μύριαι, ἑξηκοντάκις μύρια
700000		ἑβδομηκοντάκις μύριοι, ἑβδομηκοντάκις μύριαι, ἑβδομηκοντάκις μύρια
800000		ὀγδοηκοντάκις μύριοι, ὀγδοηκοντάκις μύριαι, ὀγδοηκοντάκις μύρια
900000	ϡ	ἐννενηκοντάκις μύριοι, ἐννενηκοντάκις μύριαι, ἐννενηκοντάκις μύρια
1000000	(?)	ἑκατοντάκις μύριοι, ἑκατοντάκις μύριαι, ἑκατοντάκις μύρια
2000000		διακοσάκις μύριοι, διακοσάκις μύριαι, διακοσάκις μύρια
3000000		τριακοσάκις μύριοι, τριακοσάκις μύριαι, τριακοσάκις μύρια
4000000		τετρακοσάκις μύριοι, τετρακοσάκις μύριαι, τετρακοσάκις μύρια
5000000		πεντακοσάκις μύριοι, πεντακοσάκις μύριαι, πεντακοσάκις μύρια
6000000		ἑξακοσάκις μύριοι, ἑξακοσάκις μύριαι, ἑξακοσάκις μύρια
7000000		ἑπτακοσάκις μύριοι, ἑπτακοσάκις μύριαι, ἑπτακοσάκις μύρια
8000000		ὀκτακοσάκις μύριοι, ὀκτακοσάκις μύριαι, ὀκτακοσάκις μύρια
9000000		ἐννεακοσάκις μύριοι, ἐννεακοσάκις μύριαι, ἐννεακοσάκις μύρια
107		χιλιάκις μύριοι, χιλιάκις μύριαι, χιλιάκις μύρια
108		μυριάκις μύριοι, μυριάκις μύριαι, μυριάκις μύρια

Archimedes went on with his system, reaching the following number (in modern notation): 10^{80,000,000,000,000,000}, or 1 followed by 80 quadrillion zeros, a number that in the Modern Greek system would be called εκατό εικοσιεξάκις χιλιάκις εκατομμυριάκις εκατομμυριάκις εκατομμύρια (see the end of the table in the Modern system, above; Archimedes’s system named this number differently). This was Archimedes alone, however, so his system cannot be considered part of the traditional numbering system of ancient Greeks.

Some observations are in order:

• First, I put a question mark at the symbol for “one million”, because I do not have any idea of what notation would be used. The fact of the matter is, however, that such large numbers seldom needed to be referred to in the ancient world; and if there indeed was a need to refer to such numbers, the reference would be through their linguistic expression, not through the denotational system (and that is precisely what Archimedes did).

• Second, we see that ancient Greeks used a different unit (μύριοι, -αι, -α) for 10000, and all higher numbers were formed on the basis of this unit. The modern Greek word εκατομμύριο (for “one million”) actually comes from that unit, meaning “one hundred ten-thousands”. The usage of a different linguistic unit for 10000 (and basing the rest on it) is reminiscent of the Chinese numbering system (although there was no communication between the two cultures).

• And third, one might be tempted to charge the ancient Greek denotational system for inadequacy to express numbers larger than one million. This observation, although true from our modern perspective, is actually diminished in importance if seen in the proper context. The Greek denotational system was capable of expressing all numbers that would appear in the lives and the everyday dealings of ancient people. They were concerned neither with the number of atoms in a grain of sand, nor with the number of stars in the universe (and if they were, they did not have a clue about the actual numbers involved). Likewise, our “modern” denotational system has its limitations, too. We can easily express numbers that we consider “very large” from our point of view, by using the exponential (scientific) notation, such as 10¹⁰⁰, and such numbers happen to be larger than any notion of number (cardinality) that we could be concerned with today (e.g., “the number of elementary particles in the universe”), but we cannot keep on expressing larger and larger numbers with such a system, because the exponents would end lined up in an awkward up-and-right-rising tower; let alone that our system of naming such numbers (by multiples of 1000, hence increasing the exponents by 3) does not match well with the fact that the base of the exponents is 10. (We can see this anomaly in the table for the modern Greek language, above, where the symbol 10³³ is used to represent the number “one decillion”, but the prefix dec- (“ten”) does not relate straightforwardly to 33.) It is conceivable that cultures of the future will need to refer to even larger numbers than those that seem large to us today, and hence will find that our denotational system of numerals (and our language for describing them) is inadequate.