Klingon originally had a ternary number system; that is, one based on three. Counting proceeded as follows: 1, 2, 3; 3+1, 3+2, 3+3; 2*3+1, 2*3+2, 2*3+3; 3*3+1, 3*3+2, 3*3+3; and then it got complicated. In accordance with the more accepted practice, the Klingon Empire sometime back adopted a decimal number system, one based on ten. Though no one knows for sure, it is likely that this change was made more out of concern for understanding the scientific data of other civilizations than out of a spirit of cooperation.
The Klingon numbers are:
Higher numbers are formed by adding special number- forming elements to the basic set of numbers (1--9). Thus, wa'maH ten consists of wa' one plus the number-forming element for ten, maH. Counting continues as follows:
|11||wa'maH wa'||(that is, ten and one)|
|12||wa'maH cha'||(that is, ten and two)|
Higher numbers are based on maH ten, vatlh hundred, and SaD or SanID thousand. Both SaD and SanID are equally correct for thousand, and both are used with roughly equal frequency. It is not known why this number alone has two variants.
|20||cha'maH||(that is, two tens)|
|30||wejmaH||(that is, three tens)|
|100||wa'vatlh||(that is, one hundred)|
|200||cha'vatlh||(that is, two hundreds)|
|1,000||wa'SaD or wa'SanID||(that is, one thousand)|
|2,000||cha'SaD or cha'SanID||(that is, two thousands)|
Numbers are combined as in English:
5,347 vaghSaD wejvatlh loSmaH Soch or vaghSanID wejvatlh loSmaH Soch
604 javvatlh loS
31 wejmaH wa'
Some of the number-forming elements for higher numbers are:
ten thousand netlh
hundred thousand bIp
Zero is pagh.
Numbers are used as nouns. As such, they may stand alone as subjects or objects or they may modify another noun.
mulegh cha' Two (of them) see me.
(mulegh they see me, cha' two)
wa' yIHoH Kill one (of them)!
(wa' one, yIHoH kill him/her!)
The preceding sentence is grammatically correct even without the wa' because the prefix yI- indicates a singular object. The wa', therefore, is used for emphasis only.
Numbers used as modifiers precede the noun they modify.
loS puqpu' or loS puq four children
vaghmaH yuQmey or vaghmaH yuQ fifty planets
The plural suffixes (-pu', -mey) are not necessary when a number is used.
When a number is used for numbering, as opposed to counting, it follows the noun. Compare:
DuS wa' torpedo tube number 1
wa' DuS one torpedo tube
Ordinal numbers (first, second, etc.) are formed by adding -DIch to the numbers.
Ordinal numbers follow the noun.
meb cha'DIch second guest
Adding -logh to a number gives the notion of repetitions.
Hutlogh nine times
These numbers function in the sentence as adverbials (section 5.4).
"many times" or "time and time again"
Use pIj "often". One way to express this if being emphatic is periphrastically: V 'ej V-qa' ('ej V-qa'…) (where V is the repeated action):
qagh vISoppu' 'ej vISopqa'pu' 'ej vISopqa'pu'
I've eaten gagh many times.
"4 + 3 = 7" would be wej boq loS; chen Soch (literally, "four allies with three; seven forms"). It is also possible to reverse the two numbers being added: loS boq wej; chen Soch.
Note that in these mathematical constructions, the numbers, even those higher than "one," are considered singular from a grammatical point of view. One says wa' boq cha'; chen wej "2 + 1 = 3" (two allies with one, three forms"), not wa' luboq cha'... That is, the prefix lu-, indicating a third person plural subject and third person singular object, is not used. The subject ("two" in the example) is considered singular.
For subtraction, the suffix -Ha' "undo" is attached to boq producing boqHa', literally "dis-ally" or "dissociate from." Thus "4 - 3 = 1" would be loS boqHa' wej; chen wa' (literally, "three dissociates from four, one forms").
When subtracting, the subject and object cannot be reversed without changing the equation. wej boqHa' loS would be "3 - 4" and the answer would be a negative number (a concept Maltz wanted to postpone for another time).
In Klingon, multiplication involves a number allying with itself. Thus, the suffix -'egh "oneself" is used: boq'egh "ally with oneself." It is the necessary to specify how many times this alliance occurs.
For example, "2 x 3 = 6" would be cha'logh boq'egh wej; chen jav ("twice, three allies with itself, six forms"). The multiplier and multiplicand may be reversed: wejlogh boq'egh cha' ("3 x 2," "three times, two allies with itself").
Paralleling multiplication, division in Klingon involves a number dissociating from itself a specific number of times. The verb used is boqHa''egh "dis-ally from oneself, dissociate from oneself," containing both -Ha' "undo" and -'egh "oneself."
For example, "6 / 3 = 2" is wejlogh boqHa''egh jav; chen cha' ("three times, six dissociates from itself, two forms"). Reversing the dividend and the divisor changes the equation. javlogh boqHa''egh wej would be "3 / 6" and the answer would be a fraction (another topic Maltz didn't want to get into).
For exponents, there is a noun qovDa' for the name of the operation, however the idea of raising a number to the power of something is generally expressed by using the verb Sep. For example "2^3=8" is wejlogh Sep’egh cha'; chen chorgh (" 3 times, 2 breeds with itself, eight forms").
wej loch cha' 2/3 (two thirds)
vagh loch wej 3/5 (three fifths)
loS loch jav 6/4 (six quarters)
In theory, if appropriate in a mathematical discussion, one could say wa' loch wej "three one–ths". (Though perhaps a little grammatically aberrant, this would not be wa' luloch wej.))
Fractions can be used in sentences as if they are numbers.
wej loch cha' vIleghpu' I have seen two thirds
vagh loch wej wISoptaH we are eating three fifths
Use Dop to create negative numbers. wej Dop "minus three" or "negative three". Compare this to 'u' Dop "mirror universe".
For random numbers, as when throwing dice, use the verb 'al "float" instead of Haw be random.
mI' al' (a) random number
'al mI' the number is random
There is also a slang expression Du'Hom mI' "random number" (literally "garden number").)
The traditional/old Klingon way of keeping score involves cutting oneself (pe''egh), and this is the term still in use.
A "tally" or "(total) score" follows the same tradition. They say mIvwa'mey, literally "scars" (even though, in traditional scorekeeping, the cuts turn to scabs and eventually go away). This term is also used for "census" or "headcount."
"Out of" is awkward.
loSlogh pe''egh; vaghlogh nID
cut oneself four times; tried five times.
This is the construction even if the person stopped after four and didn’t really attempt the fifth.
Maltz wasn’t sure how "statistics" would be distinguished from "tally" in this context, but maybe mIvwa'mey poj "tally analysis" or mI' poj "number analysis" would work.