In English, we have numbers. These numbers can be represented multiple ways. For example, "1,2,3" "one,two,three" "once, twice, thrice" and "first, second, third". Here we will go over how Sumerian handles numbers.

In English, we are base 10. So, we go "8,9,10,11,12". That is, once we hit 10, we add a digit then roll over our numbers and start again. In Sumerian, it alternates between base 10 and base 6. When counting to 10 initially, it rolls over at 10. After that, it rolls over at 60 until reaching 600 (60 x 10) and then rolls over. This continues in an alternating pattern but with 6 afterwards. Essentially rolling over at 10,6,10,6,... So, it will roll over at 3600 (60 x 6). Then at 36000 (3600 x 10). Then at 216000 (3600 x 60 or 36000 x 6). This may seem nonsensical, but if you look at the number signs, I promise that you will notice a pattern. A multiplication pattern. Because the Sumerians usually just represented their numbers with numeral signs (so "1" instead of "one") the actual names of the numbers can be difficult to find. However, the following numbers have been found:

Number sign Name Translation
𒁹 diΕ‘ 1
π’ˆ« min 2
𒁹𒁹𒁹 eΕ‘ 3
𒐼 or π’‡Ή limmu 4
π’Š ya (or "ia") 5
𒐋 aΕ‘ 6
π’…“ imin 7
𒐍 ussu 8
𒑆 ilimmu 9
π’Œ‹ u 10
π’Œ‹π’Ή, π’Œ‹π’ˆ«,... π’Œ‹π’‘† ? 11,12,...19
π’Œ‹π’Œ‹ niΕ‘ 20
π’Œ‹π’Œ‹π’Ή,...π’Œ‹π’Œ‹π’‘† ? 21....29
π’Œ‹π’Œ‹π’Œ‹ (or π’Œ) uΕ‘u 30
π’Œ‹π’Œ‹π’Œ‹π’Ή,...π’Œ‹π’Œ‹π’Œ‹π’‘† ? 31....39
𒐏 nimin 40
𒐏𒁹,...𒐏𒑆 ? 41....49
𒐐 ninnu 50
𒐐𒁹,...𒐐𒑆 ? 51....59
𒐕(bigger than 𒁹) ĝeΕ‘ (or ĝeΕ‘d) 60
𒐕𒁹,...*9𒐕*𒐐𒑆 ? 61....599
π’ž (NOT π’•π’Œ‹, 70) ĝeΕ‘u (lit. 60x10=600) 600
π’žπ’Ή,...*5π’ž**9𒐕*𒐐𒑆 ? 601....3599
π’ŠΉ (or π’„­**) Ε‘ar 3600 (It also means an uncountably large number such as "a bazillion")
π’ŠΉπ’Ή,...*9π’ŠΉ**5π’ž**9𒐕*𒐐𒑆 ? 3601....3599
𒐬 Ε‘aru (lit. 3600x10) 36000
𒐬𒁹,...*5𒐬**9π’ŠΉ**5π’ž**9𒐕*𒐐𒑆 ? 36001....215999
𒐲 or π’„± or π’ŠΉπ’ƒ² Ε‘argal (or Ε‘argaldiΕ‘) (lit. great Ε‘ar or great Ε‘ar one) 216000
𒐲𒁹,...*9𒐲**5𒐬**9π’ŠΉ**5π’ž**9𒐕*𒐐𒑆 ? 216001....2159999

*_*=Unicode doesn't exist for these numbers, follow the pattern. For example, 9𒐕 would look like 𒑆 but with 𒐕 instead of 𒁹. Or 5π’ž would be π’Š but with π’ž instead of 𒁹.

**=π’„­ is when things get interesting. From this point on, the next new sign is simply π’„­, with new numbers rolling over INSIDE of it. 𒐬 (3600x10) is just π’„­(3600) with π’Œ‹(10) written inside for example. Take note that it seems to skip π’„­(3600) with 𒁹(1), since 3600x1=3600. After this, we get to Ε‘argal. 𒐲 is quite literally π’„­(3600) with 𒁹(1) and 𒃲(great) in it. Note how 3600x60=216000. So, one could also interpret the 𒁹 as a 𒐕(60). The scribes were clever however, since they knew that writing that small would make 𒁹 and 𒐕 difficult to tell apart. So, with the 𒃲(great), it tells you that it's 3600x60.

What about larger numbers?

They aren't known. However, scribes seem to have given us as easily repeated pattern. None of the following has any evidence written in clay, it's just my theoretical reconstruction based off of the above. Let's reiterate:

1. The numbers roll over at 10, then 60, then 600, then 3600, etc... Essentially, it rolls over at 10,6,10,6,10,6,10. Let's assume this continues to infinity.

2. Upon reaching 3600, you get π’„­. After this, adding π’Œ‹ inside multiplies it by 10 (𒐬=3600). Let's assume that placing a sign inside of π’„­ will always signify multiplication when making a new sign.

3. Upon reaching 216000, you get 𒃲 inside of π’„­, along with either𒁹(1) or 𒐕(60). 216000 is 3600x60. So, let's assume 𒃲 is used with all number signs inside of π’„­ past this point, and according to 2. they cause multiplication. Additonally, notice that π’Œ‹ has disappeared and the math is 3600x60 NOT 36000x60.

This means that 𒐲𒐲 = 216000x2 = 432000. Up until *9𒐲**5𒐬**9π’ŠΉ**5π’ž**9𒐕*𒐐𒑆 = 2159999.

For 2160000, that's 216000x10. So we follow the pattern and put π’Œ‹ inside (so 𒃲 𒁹 and π’Œ‹) of π’„­. That's base 10 added, like the pattern above.

Now to add the next base 6, following the pattern above, I'd guess we'd replace 𒁹(1) with π’ˆ«(2) and drop π’Œ‹. So, 𒃲,π’ˆ« inside π’„­ for 216000x60=12960000. Notice, like above, that π’Œ‹ is missing. So, it is NOT 2160000x60. Make sure you count the zeros in the above statement.

One could think that this continues to infinity. Alertnating 𒃲,π’ˆ« inside π’„­ then 𒃲,π’ˆ«,π’Œ‹ inside π’„­ then 𒃲,𒁹𒁹𒁹 inside π’„­. etc... As the numbers get massive, alternating 10,6,10,6,10,6

What about π’„­ inside π’„­? I don't even know what number that'd be. A large one I guess. At that point, I have no idea what comes next. Maybe you put your next sign inside the innermost π’„­, or you make space and put the next sign beside the innermost π’„­. Or, maybe there is only one π’„­ and you put TWO 𒃲. These are wild theories which have no way of being proven. There's no written remains even hinting at numbers this large.

Ordinal Numbers

This is how people say "1st" or "2nd" or "3rd". In Sumerian, you add the suffix .kamak to the end of the number. Imagine .kamak as part of the root, and attach all cases and pronouns behind it. Note that if an ordinal number is by itself (i.e. no cases or anything), .kamak will be at the end of the word with nothing behind it. In this case, you drop the last "k", making it -kam-ma . Here's some examples (I used the number instead of the name to communicate that the number is not phonetic):

ud 3-kam-ma = ud 3.kamak = third day

ud 3-kam-ma-ka = ud 3.kamak.a = on (lit. at) the third day

ud 3-kam-ak-gin7 = ud 3.kamak.gin7 = like the third day

Numbers in Sentences

There are many ways to communicate a number in a sentence:

őita ur saĝ 3.da = mace lion head 3.with = mace with 3 lion heads (numbers can use cases, since they are nouns)

ud 7-am3 = 7 days (lit. day is 7)

For systems of measurment and units, there are two ways of communicating number. The first (informal) is "item unit number-copula". The second (formal) is "number unit item". Here is one example for each:

kug = silver (item) giĝ = shekel (unit) 5 = five (number)

Informal: kug giĝ 5-am3 = 5 silver shekels (lit. silver shekel is 5)

Formal: 5 giĝ kug = 5 silver shekels (lit. 5 shekel silver)

One can also use possesive pronouns to show what the number is counting. In this manner, the noun that the number counts can be put anywhere, not just beside the number. Let me show you two examples. Note that lugal (king) is animate, and anubda (quarter) is inanimate, so their possesive pronouns (3rd person anim. and 3rd person inanim.) will be different.

lugal anubda = king of four quarters

lugal anubda 4.ane.ak = quarter of four kings

Sine "ane" is for animate things, we know that in the second example, the number 4 counts the kings, not the quarter. Do keep in mind that this is not always used. In our example with lion heads no possesive pronoun was used, and that was still allowed.