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:

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.

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.

0 zero μηδέν
1 one ένα (m: ένας, f: μία, n: ένα)
2 two δύο
3 three τρία (m: τρεις, f: τρεις, n: τρία)
4 four τέσσερα (m: τέσσερις, f: τέσσερις, n: τέσσερα)
5 five πέντε
6 six έξι
7 seven επτά or εφτά
8 eight οκτώ or οχτώ
9 nine εννέα or εννιά
10 ten δέκα
11 eleven έντεκα
12 twelve δώδεκα
13 thirteen δεκατρία
14 fourteen δεκατέσσερα
15 fifteen δεκαπέντε
16 sixteen δεκαέξι or δεκάξι
17 seventeen δεκαεπτά or δεκαεφτά
18 eighteen δεκαοκτώ or δεκαοχτώ
19 nineteen δεκαεννέα or δεκαεννιά
20 twenty είκοσι

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:

21 twenty one είκοσι ένα
22 twenty two είκοσι δύο
23 twenty three είκοσι τρία
... ... ...
30 thirty τριάντα
40 forty σαράντα
50 fifty πενήντα
60 sixty εξήντα
70 seventy εβδομήντα
80 eighty ογδόντα
90 ninety ενενήντα
100 one hundred εκατό

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,

101 one hundred and one εκατόν ένα
102 one hundred and two εκατόν δύο
103 one hundred and three εκατόν τρία
... ... ...
110 one hundred and ten εκατόν δέκα
111 one hundred and eleven εκατόν έντεκα
... ... ...
120 one hundred and twenty εκατόν είκοσι
121 one hundred and twenty one εκατόν είκοσι ένα
... ... ...
198 one hundred and ninety eight εκατόν ενενήντα οκτώ
199 one hundred and ninety nine εκατόν ενενήντα εννέα

(This difference occurs because the original (ancient) word for 100 was εκατόν, 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:

200 two hundred διακόσια (m: διακόσιοι, f: διακόσιες, n: διακόσια)
300 three hundred τριακόσια (m: τριακόσιοι, f: τριακόσιες, n: τριακόσια)
400 four hundred τετρακόσια (m: τετρακόσιοι, f: τετρακόσιες, n: τετρακόσια)
500 five hundred πεντακόσια (m: πεντακόσιοι, f: πεντακόσιες, n: πεντακόσια)
600 six hundred εξακόσια (m: εξακόσιοι, εξακόσιες, f: n: εξακόσια)
700 seven hundred επτακόσια (m: επτακόσιοι, f: επτακόσιες, n: επτακόσια)
800 eight hundred οκτακόσια (m: οκτακόσιοι, f: οκτακόσιες, n: οκτακόσια)
900 nine hundred εννιακόσια (m: εννιακόσιοι, f: εννιακόσιες, n: εννιακόσια)
1000 one thousand χίλια (m: χίλιοι, f: χίλιες, n: χίλια)

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

528 five hundred and twenty eight πεντακόσια είκοσι οκτώ
1001 one thousand and one χίλια ένα
1934 one thousand nine hundred and thirty four χίλια εννιακόσια τριάντα τέσσερα

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:

2000 two thousand δύο χιλιάδες
3000 three thousand τρεις χιλιάδες
4000 four thousand τέσσερις χιλιάδες
5000 five thousand πέντε χιλιάδες
6000 six thousand έξι χιλιάδες
7000 seven thousand επτά χιλιάδες
8000 eight thousand οκτώ χιλιάδες
9000 nine thousand εννέα χιλιάδες
10000 ten thousand δέκα χιλιάδες
11000 eleven thousand έντεκα χιλιάδες
... ... ...

Now let us make some random tests:

4305 τέσσερις χιλιάδες τριακόσια πέντε
10719 δέκα χιλιάδες επτακόσια δεκαεννέα
52860 πενήντα δύο χιλιάδες οκτακόσια εξήντα
844844 οκτακόσιες σαράντα τέσσερις χιλιάδες οκτακόσια σαράντα τέσσερα

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:

1.000.000 one million ένα εκατομμύριο
2.000.000 two million δύο εκατομμύρια
3.000.000 three million τρία εκατομμύρια
... ... ...
10.000.000 ten million δέκα εκατομμύρια
20.000.000 twenty million είκοσι εκατομμύρια
... ... ...
100.000.000 one hundred million εκατό εκατομμύρια
...    
900.000.000 nine hundred million εννιακόσια εκατομμύρια

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.

1.000.000.000 or 109 one billion ένα δισεκατομμύριο
1.000.000.000.000 or 1012 one trillion ένα τρισεκατομμύριο
1.000.000.000.000.000 or 1015 one quadrillion ένα τετράκις εκατομμύριο
1018 one quintillion ένα πεντάκις εκατομμύριο
1021 one sextillion ένα εξάκις εκατομμύριο
1024 one septillion ένα επτάκις εκατομμύριο
1027 one octillion ένα οκτάκις εκατομμύριο
1030 one nonillion ένα εννεάκις εκατομμύριο
1033 one decillion ένα δεκάκις εκατομμύριο
1036 one undecillion ένα ενδεκάκις εκατομμύριο
1039 one duodecillion ένα δωδεκάκις εκατομμύριο
1042 one tredecillion ένα δεκατριάκις εκατομμύριο
1045 one quattuordecillion ένα δεκατετράκις εκατομμύριο
1048 one quindecillion ένα δεκαπεντάκις εκατομμύριο
1051 one sexdecillion ένα δεκαεξάκις εκατομμύριο
1054 one septendecillion ένα δεκαεπτάκις εκατομμύριο
1057 one octodecillion ένα δεκαοκτάκις εκατομμύριο
1060 one novemdecillion ένα δεκαεννεάκις εκατομμύριο
1063 one vigintillion ένα εικοσάκις εκατομμύριο
1066 one unvigintillion ένα εικοσιάπαξ εκατομμύριο
1069 one duovigintillion ένα εικοσιδίς εκατομμύριο
1072 one trevigintillion ένα εικοσιτρίς εκατομμύριο
1075 one quattuorvigintillion ένα εικοσιτετράκις εκατομμύριο
... ... ...

...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):

5.577.345.001.724.230.294 πέντε πεντάκις εκατομμύρια
πεντακόσια εβδομήντα επτά τετράκις εκατομμύρια
τριακόσια σαράντα πέντε τρισεκατομμύρια
ένα δισεκατομμύριο
επτακόσια είκοσι τέσσερα εκατομμύρια
διακόσιες τριάντα χιλιάδες
διακόσια εννενήντα τέσσερα

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!)

1093 one trigintillion ένα τριακοντάκις εκατομμύριο
1096 one untrigintillion ένα τριακοντάπαξ εκατομμύριο
1099 one duotrigintillion ένα τρακονταδίς εκατομμύριο
10100 ten duotrigintillion, or
one googol
δέκα τριακονταδίς εκατομμύρια
... ... ...
10123 one quadragintillion ένα τεσσαρακοντάκις εκατομμύριο
10153 one quinquagintillion ένα πεντηκοντάκις εκατομμύριο
10183 one sexagintillion ένα εξηκοντάκις εκατομμύριο
10213 one septuagintillion ένα εβδομηκοντάκις εκατομμύριο
10243 one octogintillion ένα ογδοηκοντάκις εκατομμύριο
10273 one nonagintillion ένα εννενηκοντάκις εκατομμύριο
10303 one centillion ένα εκατοντάκις εκατομμύριο
10603   ένα διακοσάκις εκατομμύριο
10903   ένα τριακοσάκις εκατομμύριο
101203   ένα τετρακοσάκις εκατομμύριο
101503   ένα πεντακοσάκις εκατομμύριο
101803   ένα εξακοσάκις εκατομμύριο
102103   ένα επτακοσάκις εκατομμύριο
102403   ένα οκτακοσάκις εκατομμύριο
102703   ένα εννεακοσάκις εκατομμύριο
103003 one millillion ένα χιλιάκις εκατομμύριο
106003   ένα δισχιλιάκις εκατομμύριο
109003   ένα τρισχιλιάκις εκατομμύριο
1012003   ένα τετράκις χιλιάκις εκατομμύριο
1015003   ένα πεντάκις χιλιάκις εκατομμύριο
1018003   ένα εξάκις χιλιάκις εκατομμύριο
1021003   ένα επτάκις χιλιάκις εκατομμύριο
1024003   ένα οκτάκις χιλιάκις εκατομμύριο
1027003   ένα εννεάκις χιλιάκις εκατομμύριο
1030003 one decimillillion ένα δεκάκις χιλιάκις εκατομμύριο
1033003   ένα ενδεκάκις χιλιάκις εκατομμύριο
1036003   ένα δωδεκάκις χιλιάκις εκατομμύριο
1039003   ένα δεκατριάκις χιλιάκις εκατομμύριο
1042003   ένα δεκατετράκις χιλιάκις εκατομμύριο
1045003   ένα δεκαπεντάκις χιλιάκις εκατομμύριο
1048003   ένα δεκαεξάκις χιλιάκις εκατομμύριο
1051003   ένα δεκαεπτάκις χιλιάκις εκατομμύριο
1054003   ένα δεκαοκτάκις χιλιάκις εκατομμύριο
1057003   ένα δεκαεννεάκις χιλιάκις εκατομμύριο
1060003   ένα εικοσάκις χιλιάκις εκατομμύριο
1063003   ένα εικοσιάπαξ χιλιάκις εκατομμύριο
1066003   ένα εικοσιδίς χιλιάκις εκατομμύριο
1069003   ένα εικοσιτρίς χιλιάκις εκατομμύριο
1072003   ένα εικοσιτετράκις χιλιάκις εκατομμύριο
... ... ...
1090,003   ένα τριακοντάκις χιλιάκις εκατομμύριο
10120,003   ένα τεσσαρακοντάκις χιλιάκις εκατομμύριο
10150,003   ένα πεντηκοντάκις χιλιάκις εκατομμύριο
10180,003   ένα εξηκοντάκις χιλιάκις εκατομμύριο
10210,003   ένα εβδομηκοντάκις χιλιάκις εκατομμύριο
10240,003   ένα ογδοηκοντάκις χιλιάκις εκατομμύριο
10270,003   ένα εννενηκοντάκις χιλιάκις εκατομμύριο
10300,003 one centimillillion ένα εκατοντάκις χιλιάκις εκατομμύριο
10600,003   ένα διακοσάκις χιλιάκις εκατομμύριο
10900,003   ένα τριακοσάκις χιλιάκις εκατομμύριο
101,200,003   ένα τετρακοσάκις χιλιάκις εκατομμύριο
101,500,003   ένα πεντακοσάκις χιλιάκις εκατομμύριο
101,800,003   ένα εξακοσάκις χιλιάκις εκατομμύριο
102,100,003   ένα επτακοσάκις χιλιάκις εκατομμύριο
102,400,003   ένα οκτακοσάκις χιλιάκις εκατομμύριο
102,700,003   ένα εννεακοσάκις χιλιάκις εκατομμύριο
103,000,003 one millimillillion ένα εκατομμυριάκις εκατομμύριο
106,000,003   ένα δισεκατομμυριάκις εκατομμύριο
109,000,003   ένα τρισεκατομμυριάκις εκατομμύριο
1012,000,003   ένα τετράκις εκατομμυριάκις εκατομμύριο
... ... ...
103,000,000,000,003   ένα εκατομμυριάκις εκατομμυριάκις εκατομμύριο

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.

0th zeroth μηδενικός, μηδενική, μηδενικό
1st first πρώτος, πρώτη, πρώτο
2nd second δεύτερος, δεύτερη, δεύτερο
3rd third τρίτος, τρίτη, τρίτο
4th fourth τέταρτος, τέταρτη, τέταρτο
5th fifth πέμπτος, πέμπτη, πέμπτο
6th sixth έκτος, έκτη, έκτο
7th seventh έβδομος, έβδομη, έβδομο
8th eighth όγδοος, όγδοη, όγδοο
9th ninth ένατος, ένατη, ένατο
10th tenth δέκατος, δέκατη, δέκατο
11th eleventh ενδέκατος, ενδέκατη, ενδέκατο
12th twelfth δωδέκατος, δωδέκατη, δωδέκατο
13th thirteenth δέκατος τρίτος, δέκατη τρίτη, δέκατο τρίτο
14th fourteenth δέκατος τέταρτος, δέκατη τέταρτη, δέκατο τέταρτο
... ... ...
20th twentieth εικοστός, εικοστή, εικοστό
21st twenty first εικοστός πρώτος, εικοστή πρώτη, εικοστό πρώτο
... ... ...
30th thirtieth τριακοστός, τριακοστή, τριακοστό
40th fortieth τεσσαρακοστός, τεσσαρακοστή, τεσσαρακοστό
50th fiftieth πεντηκοστός, πεντηκοστή, πεντηκοστό
60th sixtieth εξηκοστός, εξηκοστή, εξηκοστό
70th seventieth εβδομηκοστός, εβδομηκοστή, εβδομηκοστό
80th eightieth ογδοηκοστός, ογδοηκοστή, ογδοηκοστό
90th ninetieth εννενηκοστός, εννενηκοστή, εννενηκοστό
100th hundredth εκατοστός, εκατοστή, εκατοστό
101st hundred and first εκατοστός πρώτος, εκατοστή πρώτη, εκατοστό πρώτο
  ...  
200th two hundredth διακοσιοστός, διακοσιοστή, διακοσιοστό
300th thee hundredth τριακοσιοστός, τριακοσιοστή, τριακοσιοστό
400th four hundredth τετρακοσιοστός, τρετρακοσιοστή, τετρακοσιοστό
500th five hundredth πεντακοσιοστός, πεντακοσιοστή, πεντακοσιοστό
600th six hundredth εξακοσιοστός, εξακοσιοστή, εξακοσιοστό
700th seven hundredth επτακοσιοστός, επτακοσιοστή, επτακοσιοστό
800th eight hundredth οκτακοσιοστός, οκτακοσιοστή, οκτακοσιοστό
900th nine hundredth εννεακοσιοστός, εννεακοσιοστή, εννεακοσιοστό
1000th thousandth χιλιοστός, χιλιοστή, χιλιοστό
1001st thousand and first χιλιοστός πρώτος, χιλιοστή πρώτη, χιλιοστό πρώτο
... ... ...
2000th two thousandth δισχιλιοστός, δισχιλιοστή, δισχιλιοστό
3000th three thousandth τρισχιλιοστός, τρισχιλιοστή, τρισχιλιοστό
4000th four thousandth τετράκις χιλιοστός, τετράκις χιλιοστή, τετράκις χιλιοστό
5000th five thousandth πεντάκις χιλιοστός, πεντάκις χιλιοστή, πεντάκις χιλιοστό
6000th six thousandth εξάκις χιλιοστός, εξάκις χιλιοστή, εξάκις χιλιοστό
7000th seven thousandth επτάκις χιλιοστός, επτάκις χιλιοστή, επτάκις χιλιοστό
8000th eight thousandth οκτάκις χιλιοστός, οκτάκις χιλιοστή, οκτάκις χιλιοστό
9000th nine thousandth εννεάκις χιλιοστός, εννεάκις χιλιοστή, εννεάκις χιλιοστό
10000th ten thousandth δεκάκις χιλιοστός, δεκάκις χιλιοστή, δεκάκις χιλιοστό
20000th twenty thousandth εικοσάκις χιλιοστός, εικοσάκις χιλιοστή, εικοσάκις χιλιοστό
... ... ...
100,000th hundred thousandth εκατοντάκις χιλιοστός, εκατοντάκις χιλιοστή, εκατοντάκις χιλιοστό
200,000th two hundred thousandth διακοσάκις χιλιοστός, διακοσάκις χιλιοστή, διακοσάκις χιλιοστό
... ... ...
106th millionth εκατομμυριοστός, εκατομμυριοστή, εκατομμυριοστό
109th billionth δισεκατομμυριοστός, δισεκατομμυριοστή, δισεκατομμυριοστό
1012th trillionth τρισεκατομμυριοστός, τρισεκατομμυριοστή, τρισεκατομμυριοστό
1015th quadrillionth τετράκις εκατομμυριοστός, τετράκις εκατομμυριοστή, τετράκις εκατομμυριοστό
  ...  

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 o/oo 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:

English Greek
12.34 twelve point thirty four 12,34 δώδεκα κόμμα τριάντα τέσσερα

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:

1/2 one half ένα δεύτερο
  half (adj.) m: μισός, f: μισή, n: μισό
1/3 one third ένα τρίτο
1/4 one fourth ένα τέταρτο
  quarter (adj.) τέταρτο (neuter only)
2/3 two thirds δύο τρίτα
3/4 three fourths τρία τέταρτα
34/56 thirty four fifty sixths τριάντα τέσσερα πεντηκοστά έκτα

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 in the 6th position (α, β, γ, δ, ε, ς, ζ, η, θ) were playing 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), was standing for 10. Now, ια was 11, ιβ was 12, and so on, up to ιθwhich 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 (), 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 was standing for 800. One final extra-alphabetic symbol, the sampi ( ) was used to denote 900. From there on... well, you already noticed the small 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 was denoting 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 were using 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  
1 α
2 β
3 γ
4 δ
5 ε
6 ς
7 ζ
8 η
9 θ
10 ι
11 ια
12 ιβ
13 ιγ
14 ιδ
15 ιε
16 ις
17 ιζ
18 ιη
19 ιθ
20 κ
21 κα
...    
30 λ
31 λα
...    

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 or
50 ν
60 ξ
70 ο
80 π
90
100 ρ
110 ρι
...    
190 ρ
200 σ
...    
300 τ
400 υ
500 φ
600 χ
700 ψ
800 ω
900
1000
1001
...    
2000
3000
4000
...    
9000
10000

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
30000
40000
...    
100000
200000
...    
900000
1000000 (?)
2000000  
3000000  
...    
107  
108  

Archimedes went on with his system, reaching the following number (in modern notation): 1080,000,000,000,000,000, 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:

 


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