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:

1 | wa' |
6 | jav |

2 | cha' |
7 | Soch |

3 | wej |
8 | chorgh |

4 | loS |
9 | Hut |

5 | vagh |
10 | wa'maH |

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) |

etc. |

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) |

etc. | ||

100 | wa'vatlh |
(that is, one hundred) |

200 | cha'vatlh |
(that is, two hundreds) |

etc. | ||

1,000 | wa'SaD or wa'SanID |
(that is, one thousand) |

2,000 | cha'SaD or cha'SanID |
(that is, two thousands) |

etc. |

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**

million **'uy'**

billion **Saghan**

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.

**wa'DIch** *first*

**cha'DIch** *second*

**HutDIch** *ninth*

Ordinal numbers follow the noun.

**meb cha'DIch** *second guest*

Adding *-***logh** to a number gives the notion of repetitions.

**wa'logh** *once*

**cha'logh** *twice*

**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.*

**Addition**

"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.

**Subtraction**

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).

**Multiplication**

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*").

**Division**

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).

**Exponents**

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").

**Fractions**

**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**.))

**Negatives**

Use **Dop **to create negative numbers. **wej Dop** "*minus three*" or "*negative three*". Compare this to **'u' Dop** "*mirror universe*".

**Random**

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*").)

**Keeping Score/Tallying**

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.