Numbers and Mathematics

These are the words that all numbers in Kokanu are built from:

ɕ̄ - wan "one, 1"

ɵ - ha "two, 2"

ɤ̄ - san "three, 3"

ƨ̄xſ - nanku "four, 4"

ʋıɞ - lima "five, 5"

ʋʃxſ - loku "six, 6"

ɤȷʌ̄ - setan "seven, 7"

oȷʌſ - etu "eight, 8"

ɤx - saka "nine, 9"

ʌıɂſ - tiju "ten, 10"

ɤıɂ̄ȷ - sijen "(one) hundred, 100"

ɛ̄ʃ - con "(one) thousand, 1000"

When building phrases to express numbers, number words that follow ʌıɂſ tiju don't act as modifiers, as would normally be the case in Kokanu, they simply add a unit number on.

ʌıɂſ ɵ - tiju ha "ten and two, 12"

Number words preceding ʌıɂſ tiju give the number of instances of it, as with any noun.

oȷʌſ ʌıɂſ - etu tiju "eight tens, 80"

Placing unit numbers before and after ʌıɂſ tiju allows the expression of any number up to 99.

ɤ̄ ʌıɂſ ɵ - san tiju ha "three tens and two, 32"

The number ɤıɂ̄ȷ sijen acts exactly like ʌıɂſ tiju. Placing unit numbers before and after ɤıɂ̄ȷ sijen allows the expression of any number up to 999.

ʋıɞ ɤıɂ̄ȷ ʋʃxſ - lima sijen loku "five hundreds and six, 506"

ɤȷʌ̄ ɤıɂ̄ȷ ɵ ʌıɂſ ɤx - setan sijen ha tiju saka "seven hundreds and two tens and nine, 729"

The number ɛ̄ʃ con acts similarly. Placing unit numbers before and after ɛ̄ʃ con allows the expression of any number up to 9999.

ɵ ɛ̄ʃ ʋıɞ - ha con lima "two thousands and five, 2005"

ƨ̄xſ ɛ̄ʃ ɵ ɤıɂ̄ȷ ɤx ʌıɂſ ɤȷʌſ - nanku con ha sijen saka tiju etu "four thousands and two hundreds and nine tens and eight, 4298"

The number ƨſʋ nula is used for "zero", though, like in English, it doesn't appear in compound whole number words.

Forming Numbers 10000 and larger

Powers of a 10 can also be expressed with hen, followed by an exponent. For example,

ɵ̄ȷ ɵ - hen ha "10², one hundred" (Note: the number wan does not have to precede hen)

ɵ̄ȷ ʋıɞ - hen lima "10⁵, one hundred thousand"

ɵ̄ȷ ʋʃxſ - hen loku "10⁶, one million"

ɵ̄ȷ ɤx - hen saka "10⁹, one billion"

It’s important to think of hen as “ten to the power of...” rather than just “10” (which is ʌıɂſ tiju). If hen is used multiple times or other digits follow it, each hen exponent is followed by hu. But in all instances, hu can be replaced by a verbal pause or a written comma.

ʋıɞ ɵ̄ȷ ʋıɞ ɵſ ､ ɵ ɵ̄ȷ ƨ̄xſ ɵſ ､ ʋıɞ ɛ̄ʃ ʋʃxſ ɤıɂ̄ȷ - lima hen lima hu, ha hen nanku hu, lima con loku sijen "525,600"

ɤ̄ ɵ̄ȷ ʋʃxſ ､ ƨ̄xſ ɵ̄ȷ ʋıɞ ､ ƨ̄xſ ɵ̄ȷ ƨ̄xſ ､ ʋʃxſ ɛ̄ʃ ɤȷʌ̄ ʌıɂſ oȷʌſ - san hen loku, nanku hen lima, nanku hen nanku, loku con setan tiju etu "3,446,078"

oȷʌſ ɵ̄ȷ ʌıɂſ ɵ - etu hen tiju ha "8,000,000,000,000, 8 trillion"

oȷʌſ ɵ̄ȷ ʌıɂſ ､ ɵ - etu hen tiju, ha "80,000,000,002, eighty billion two"

Grouping the digits in groups of three like this is the standard Western way of doing it, but it is not the only one. Since simple numbers can be formed with one to four digits, the number of digits grouped together can also range from one to four.

Examples:

etu sijen saka tiju setan hen loku hu lima sijen loku tiju nanku hen san hu ha sijen san tiju wan ('897,564,231'; analogous to the Western system)

etu hen etu hu saka con setan sijen lima tiju loku hen nanku hu nanku con ha sijen san tiju wan ('8,9756,4231'; analogous to the Eastern system)

The groups don’t even have to be uniform:

etu tiju saka hen setan hu setan tiju lima hen lima hu loku tiju nanku hen san hu ha sijen san tiju wan ('89,75,64,231'; analogous to the Indian system)

Scientific notation is also possible:

etu pintu hu saka setan lima loku nanku tu san wan hen etu (8,97564231*10^8)

Cardinals and Ordinal Numbers

Cardinal numbers are placed before a noun. These are used for counting how many or how much of something there is.

ɞı ʋȷ ɵ̄ ōı ɤ̄ ʜɕʃ - mi le han in san pawo "I have three dogs"

ɞı ʋȷ ʌ̄ſ ʌıɂſ oȷʌſ oʃɤ ɞʌ̄ı - mi le tun tiju etu osa matin "I have been working for eighteen hours

Ordinal numbers are placed after the noun These are used to specify the position of an item in a series, like "fourth" or "seventeenth".

ʜɕʃ ɵ ʋȷ ʌʃʜȷ oƨı - pawo ha le tope ani "The second dog is the best"

ɤ̄ ʌ̄ȷ ɞȷʋ̄ʃ ɂȷ oʃɤ ʌıɂſ oȷʌſ ʋȷ ɛ̄ʃɛ - san ten melon je osa tiju etu le conca "It is 18:03" (literally "three minutes after the eighteenth hour have passed")

Therefore, when telling time, ɤ̄ oʃɤ san osa is used to mean "three hours", and oʃɤ ɤ̄ "osa san" to mean "three o'clock", literally "third hour".

Fractions, Decimals, and Percents

Numbers with fractional components tend to be more complex to express in Kokanu than whole numbers.

In fractions, the numerator is expressed as a number of oʃɤ osa, "parts", which are described by the denominator with ɂȷ je.

ɤ̄ oʃɤ ɂȷ ʋıɞ - san osa je lima "three parts of five, three five-parts, 3/5"

ɵ ʌıɂſ ƨ̄xſ oʃɤ ɂȷ ɵ ɤıɂ̄ȷ ɤ̄ ʌıɂſ ɕ̄ - ha tiju nanku osa je ha sijen san tiju wan "24/231"

For decimals the whole number is simply followed by ʜ̄ıʌſ pintu, "point", and the decimal numbers follow consecutively, with no regard for hundreds or thousands places.

ɵ ʜ̄ıʌſ ɤ̄ ɵ ƨ̄xſ ƨ̄xſ - ha pintu san ha nanku nanku "12.3244"

ɤ̄ ʜ̄ıʌſ ɕ̄ ƨ̄xſ ɕ̄ ʋıɞ ɤx ɵ ::: - san pintu wan nanku wan lima saka ha... "3.141592..."

For percentages the phrase oʃɤ ɂȷ ɤıɂ̄ȷ osa je sijen is added to the end of the number. This can be combined with decimal notation to specify decimal percentages.

ɵ ʌıɂſ ʋıɞ oʃɤ ɂȷ ɤıɂ̄ȷ - ha tiju lima osa je sijen "25%"

ƨ̄xſ ʌıɂſ ʜ̄ıʌſ oȷʌſ ɤȷʌ̄ ɕ̄ oʃɤ ɂȷ ɤıɂ̄ȷ - nanku tiju pintu etu setan wan osa je sijen "40.871%"

Negative Numbers

Negative numbers are expressed with opotu je, "opposite of..."

oʃʜʃʌſ ɂȷ ɤ̄ - opotu je san "-3"

oʃʜʃʌſ ɂȷ ƨ̄xſ oʃɤ ɂȷ ʌıɂſ - opotu je nanku osa je tiju "-4/10"

oʃʜʃʌſ ɂȷ ʋʃxſ ʜ̄ıʌſ ɤx ɤx - opotu je loku pintu saka saka "-6.99"

Mathematical Operations

While no words are specially assigned for mathematical operations such as "addition" or "multiplication", other words can be used to describe the operations and will be understood in a mathematical context.

Addition

2 + 3

ʌȷ ʌȷƨȷ ōı ɤ̄ xı ɵ - te tene in san ki ha "giving 3 to 2"

ʌȷ ʜ̄ʃ ʌ ɵ ʋȷ oſƨıʌſ x̄ ɤ̄ - te pon ta ha le unitu kan san "combining 2 with 3"

2 + 3 = 5

ɵ ōſ ɤ̄ ʋȷ ʋıɞ - ha un san le lima "2 and 3 is 5"

Subtraction

7 - 4

ʌȷ ʋ̄ſ ʋıʜƨ̄ı ƨ̄xſ ɤ̄ſ ɤȷʌ̄ - te lun lipan in nanku sun setan "to make-absent 4 from 7"

ʌȷ oʋſ ōı ƨ̄xſ ɤ̄ſ ɤȷʌ̄ - te alu in nanku sun setan "to take 4 from 7"

7 - 4 = 3

ɤȷʌ̄ ōſ oʃʜʃʌſ ɂȷ ƨ̄xſ ʋȷ ɤ̄ - setan un opotu je nanku le san "7 and -4 is 3"

Multiplication

2 * 5

ʌȷ ʌ̄ſ ōı ɵ ƨ̄ʃ ɂȷ ʋıɞ - te tun in ha non je lima - "creating 2 groups of 5"

ʌȷ ʋ̄ſ ʋ̄ ōı ɵ ɕıɂ ʋıɞ - te lun lan in ha wija lima "to make-many 2 with 5"

2 * 5 = 10

ɵ ƨ̄ʃ ɂȷ ʋıɞ ʋȷ ʌıɂſ - ha non je lima le tiju "2 groups of 5 is 10"

ʋıɞ ɞıʌ ɂȷ ɵ ʋȷ ʌıɂſ - lima mita je ha le tiju "5 amounts of 2 is 10"

Division

9 / 4

ʌȷ ʋ̄ſ ʜ̄ʋı ōı ɤx ɕıɂ ƨ̄xſ - te lun panli in saka wija nanku "to cut 9 using 4"

9 / 4 = 2.25

ʌȷ ʋ̄ſ ʜ̄ʋı ōı ɤx ɕıɂ ƨ̄xſ - nanku panli je saka le ha pintu ha lima "4 divisions of 9 is 2.25"

ɤx oʃɤ ɂȷ ƨ̄xſ ʋȷ ɵ ʜ̄ıʌſ ɵ ʋıɞ - saka osa je nanku le ha pintu ha lima - expressing 9/4 in standard fraction form directly

Exponentiation

6³

ʌȷ ʋ̄ſ ʋ̄ ōı ʋʃxſ ɕıɂ ɤ ō ɤ̄ ʌ̄ȷ - te lun lan in loku wija sa an san ten - "to make-many 6 using itself 3 times"

6³ = 216

ɤ̄ ɞıʌ ɤɞ̄ ɂȷ ʋʃxſ ʋȷ ɵ ɤıɂ̄ȷ ʌʃɂſ ʋʃxſ - san mita saman je loku le ha sijen tiju loku "3 identical bunches of 6 is 216"