Iñupiaq numerals
The Iñupiaq language has a vigesimal (base-20) numeral system, with words for numerals up to 2012 (a bit over 4 quadrillion). Numerals are built from a small number of root words and a number of compounding suffixes. The following list are the various numerals of the language, omitting only the higher derivatives ending in the suffix -utaiḷaq, which subtracts one from the value of the stem. (See Iñupiaq language#Numerals.) They are transcribed both in the vigesimal Kaktovik digits that were designed for Iñupiaq and in the decimal Hindu-Arabic digits. Apart from the subtractive suffix -utaiḷaq, which has no counterpart in Kaktovik notation, and the idiosyncratic root word itchaksrat 'six', Iñupiaq numerals are closely represented by the Kaktovik digits.
| Numeral | Morphological pattern |
Kaktovik notation |
Hindu-Arabic notation |
|---|---|---|---|
| kisitchisaġvik | 0 | ||
| atausiq | 1 | 1 | |
| malġuk | 2 | 2 | |
| piŋasut | 3 | 3 | |
| sisamat | 4 | 4 | |
| tallimat | 5 | 5 | |
| itchaksrat | 6 | 6 | |
| tallimat malġuk | 5 + 2 | 7 | |
| tallimat piŋasut | 5 + 3 | 8 | |
| quliŋŋuġutaiḷaq | 10 − 1 | 9 | |
| qulit | 10 | 10 | |
| qulit atausiq | 10 + 1 | 11 | |
| qulit malġuk | 10 + 2 | 12 | |
| qulit piŋasut | 10 + 3 | 13 | |
| akimiaġutaiḷaq | 15 − 1 | 14 | |
| akimiaq | 15 | 15 | |
| akimiaq atausiq | 15 + 1 | 16 | |
| akimiaq malġuk | 15 + 2 | 17 | |
| akimiaq piŋasut | 15 + 3 | 18 | |
| iñuiññaġutaiḷaq | 20 − 1 | 19 | |
| iñuiññaq | 20 | 20 | |
| iḷagiññaq | 400 | 400 |
- A deverbal noun. Outside of mathematics, suitchuq "none" or suitchuq X "no X" is normally used.
| malġukipiaq | 2×20 | 40 | |
| piŋasukipiaq | 3×20 | 60 | |
| sisamakipiaq | 4×20 | 80 | |
| tallimakipiaq | 5×20 | 100 | |
| tallimakipiaq iñuiññaq | 5×20 + 20 | 120 | |
| tallimakipiaq malġukipiaq | 5×20 + 2×20 | 140 | |
| tallimakipiaq piŋasukipiaq | 5×20 + 3×20 | 160 | |
| tallimakipiaq sisamakipiaq | 5×20 + 4×20 | 180 | |
| qulikipiaq | 10×20 | 200 | |
| qulikipiaq iñuiññaq | 10×20 + 20 | 220 | |
| qulikipiaq malġukipiaq | 10×20 + 2×20 | 240 | |
| qulikipiaq piŋasukipiaq | 10×20 + 3×20 | 260 | |
| qulikipiaq sisamakipiaq | 10×20 + 4×20 | 280 | |
| akimiakipiaq | 15×20 | 300 | |
| akimiakipiaq iñuiññaq | 15×20 + 20 | 320 | |
| akimiakipiaq malġukipiaq | 15×20 + 2×20 | 340 | |
| akimiakipiaq piŋasukipiaq | 15×20 + 3×20 | 360 | |
| akimiakipiaq sisamakipiaq | 15×20 + 4×20 | 380 | |
| iñuiññakipiaq (= iḷagiññaq above) |
20×20 [= 202] |
400 |
| malġuagliaq | 2×202 | 800 | |
| piŋasuagliaq | 3×202 | 1,200 | |
| sisamaagliaq | 4×202 | 1,600 | |
| tallimaagliaq | 5×202 | 2,000 | |
| quliagliaq | 10×202 | 4,000 | |
| akimiagliaq | 15×202 | 6,000 |
| atausiqpak | 1×203 [= 203] | , | 8,000 |
| malġuqpak | 2×203 | , | 16,000 |
| piŋasuqpak | 3×203 | , | 24,000 |
| sisamaqpak | 4×203 | , | 32,000 |
| tallimaqpak | 5×203 | , | 40,000 |
| quliqpak | 10×203 | , | 80,000 |
| akimiaqpak | 15×203 | , | 120,000 |
| iñuiññaqpak | 20×203 [= 204] | , | 160,000 |
| malġukipiaqpak | 2×20×203 | , | 320,000 |
| piŋasukipiaqpak | 3×20×203 | , | 480,000 |
| sisamakipiaqpak | 4×20×203 | , | 640,000 |
| tallimakipiaqpak | 5×20×203 | , | 800,000 |
| qulikipiaqpak | 10×20×203 | , | 1,600,000 |
| akimiakipiaqpak | 15×20×203 | , | 2,400,000 |
| iḷagiññaqpak | 400×203 [= 205] | , | 3,200,000 |
| malġuagliaqpak | 2×202×203 | , | 6,400,000 |
| piŋasuagliaqpak | 3×202×203 | , | 9,600,000 |
| sisamaagliaqpak | 4×202×203 | , | 12,800,000 |
| tallimaagliaqpak | 5×202×203 | , | 16,000,000 |
| quliagliaqpak | 10×202×203 | , | 32,000,000 |
| akimiagliaqpak | 15×202×203 | , | 48,000,000 |
| atausiqpakaippaq | 1×(203)2 [= 206] | ,, | 64,000,000 |
| malġuqpakaippaq | 2×(203)2 | ,, | 128,000,000 |
| piŋasuqpakaippaq | 3×(203)2 | ,, | 192,000,000 |
| sisamaqpakaippaq | 4×(203)2 | ,, | 256,000,000 |
| tallimaqpakaippaq | 5×(203)2 | ,, | 320,000,000 |
| quliqpakaippaq | 10×(203)2 | ,, | 640,000,000 |
| akimiaqpakaippaq | 15×(203)2 | ,, | 960,000,000 |
| iñuiññaqpakaippaq | 20×(203)2 [= 207] | ,, | 1,280,000,000 |
| malġukipiaqpakaippaq | 2×20×(203)2 | ,, | 2,560,000,000 |
| piŋasukipiaqpakaippaq | 3×20×(203)2 | ,, | 3,840,000,000 |
| sisamakipiaqpakaippaq | 4×20×(203)2 | ,, | 5,120,000,000 |
| tallimakipiaqpakaippaq | 5×20×(203)2 | ,, | 6,400,000,000 |
| qulikipiaqpakaippaq | 10×20×(203)2 | ,, | 12,800,000,000 |
| akimiakipiaqpakaippaq | 15×20×(203)2 | ,, | 19,200,000,000 |
| iḷagiññaqpakaippaq | 400×(203)2 [= 208] | ,, | 25,600,000,000 |
| malġuagliaqpakaippaq | 2×202×(203)2 | ,, | 51,200,000,000 |
| piŋasuagliaqpakaippaq | 3×202×(203)2 | ,, | 76,800,000,000 |
| sisamaagliaqpakaippaq | 4×202×(203)2 | ,, | 102,400,000,000 |
| tallimaagliaqpakaippaq | 5×202×(203)2 | ,, | 128,000,000,000 |
| quliagliaqpakaippaq | 10×202×(203)2 | ,, | 256,000,000,000 |
| akimiagliaqpakaippaq | 15×202×(203)2 | ,, | 384,000,000,000 |
| atausiqpakpiŋatchaq | 1×(203)3 [= 209] | ,,, | 512,000,000,000 |
| malġuqpakpiŋatchaq | 2×(203)3 | ,,, | 1,024,000,000,000 |
| piŋasuqpakpiŋatchaq | 3×(203)3 | ,,, | 1,536,000,000,000 |
| sisamaqpakpiŋatchaq | 4×(203)3 | ,,, | 2,048,000,000,000 |
| tallimaqpakpiŋatchaq | 5×(203)3 | ,,, | 2,560,000,000,000 |
| quliqpakpiŋatchaq | 10×(203)3 | ,,, | 5,120,000,000,000 |
| akimiaqpakpiŋatchaq | 15×(203)3 | ,,, | 7,680,000,000,000 |
| iñuiññaqpakpiŋatchaq | 20×(203)3 [= 2010] | ,,, | 10,240,000,000,000 |
| malġukipiaqpakpiŋatchaq | 2×20×(203)3 | ,,, | 20,480,000,000,000 |
| piŋasukipiaqpakpiŋatchaq | 3×20×(203)3 | ,,, | 30,720,000,000,000 |
| sisamakipiaqpakpiŋatchaq | 4×20×(203)3 | ,,, | 40,960,000,000,000 |
| tallimakipiaqpakpiŋatchaq | 5×20×(203)3 | ,,, | 51,200,000,000,000 |
| qulikipiaqpakpiŋatchaq | 10×20×(203)3 | ,,, | 102,400,000,000,000 |
| akimiakipiaqpakpiŋatchaq | 15×20×(203)3 | ,,, | 153,600,000,000,000 |
| iḷagiññaqpakpiŋatchaq | 400×(203)3 [= 2011] | ,,, | 204,800,000,000,000 |
| malġuagliaqpakpiŋatchaq | 2×202×(203)3 | ,,, | 409,600,000,000,000 |
| piŋasuagliaqpakpiŋatchaq | 3×202×(203)3 | ,,, | 614,400,000,000,000 |
| sisamaagliaqpakpiŋatchaq | 4×202×(203)3 | ,,, | 819,200,000,000,000 |
| tallimaagliaqpakpiŋatchaq | 5×202×(203)3 | ,,, | 1,024,000,000,000,000 |
| quliagliaqpakpiŋatchaq | 10×202×(203)3 | ,,, | 2,048,000,000,000,000 |
| akimiagliaqpakpiŋatchaq | 15×202×(203)3 | ,,, | 3,072,000,000,000,000 |
| iñuiññagliaqpakpiŋatchaq | 20×202×(203)3 [= 2012] | ,,,, | 4,096,000,000,000,000 |
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