Kaktovik Numerals

Kaktovik numbers or numerals (or Iñupiaq numerals) are a positional base 20 numeral system (with a sub-base of 5) used by Inuit/Inupiat peoples in Alaska and Canada.

Start by converting the number to base 20 (see explanations on converting to base N).

Then replace each number (from 0 to 19) with the corresponding Kaktovik symbol:

Decimal Value	Unicode	Image	Name
0	𝋀		kisitchisaġvik
1	𝋁		atausiq
2	𝋂		malġuk
3	𝋃		piŋasut
4	𝋄		sisamat
5	𝋅		tallimat
6	𝋆		itchaksrat
7	𝋇		tallimat malġuk
8	𝋈		tallimat piŋasut
9	𝋉		quliŋŋuġutaiḷaq
10	𝋊		qulit
11	𝋋		qulit atausiq
12	𝋌		qulit malġuk
13	𝋍		qulit piŋasut
14	𝋎		akimiaġutaiḷaq
15	𝋏		akimiaq
16	𝋐		akimiaq atausiq
17	𝋑		akimiaq malġuk
18	𝋒		akimiaq piŋasut
19	𝋓		iñuiññaġutaiḷaq

To write a Kaktovik number in classic decimal representation, locate each symbol and replace it with the associated number (between 0 and 19) so as to obtain a positional numeration in base 20 which will still have to be converted into base 10 (decimal).

Decimal writing uses the dot . to separate the integer part and the decimal part.

As the writing is in base 20, the first digit after the decimal has the unit $ 20^{−1} = 0.05 $, the second $ 20^{−2} = 0.0025 $ etc.

Historically, many indigenous languages, including the Iñupiat, used a vigesimal system, where base 20 often reflected counting using fingers and toes.

The Kaktovik number system reflects the cultural and linguistic values of the Iñupiat, while facilitating the understanding of modern mathematical concepts.

Current use is primarily for educational purposes, rather than historical uses such as trade or record keeping.

Kaktovik arithmetic operations in numbers follow the classic rules (while taking into account position values in base 20).

However, Kaktovik symbols are very visual and allow you to quickly and easily perform additions and subtractions (and also some divisions), see the video here

For more calculations, there is a calculator application here

The digits of the Kaktovik Iñupiaq numeral consist of 0 to 5 vertical bars/strokes on the lower part (forming W) and 0 to 3 horizontal bars on the top part (forming 𝆒)

Any references to Inuit, Iñupiats or even Inuktitut are clues.

The count was developed in 1994 in Kaktovik, a town in Alaska by a group of students.