# Iñupiaq numerals

The Iñupiaq language has a vigesimal (base-20) numeral system, with words for numerals up to 20$^{12}$ (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.
Units (n × 20$^0$) :
| Numeral | Morphological pattern | 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 |
n-kipiaq (n × 20$^1$) :
| 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 [= 20$^2$] | 400 |
n-agliaq (n × 20$^2$) :
| malġuagliaq | 2×20$^2$ | 800 |
| piŋasuagliaq | 3×20$^2$ | 1,200 |
| sisamaagliaq | 4×20$^2$ | 1,600 |
| tallimaagliaq | 5×20$^2$ | 2,000 |
| quliagliaq | 10×20$^2$ | 4,000 |
| akimiagliaq | 15×20$^2$ | 6,000 |
n-pak (n × 20$^3$) :
| atausiqpak | 1×20$^3$ [= 20$^3$] | , | 8,000 |
| malġuqpak | 2×20$^3$ | , | 16,000 |
| piŋasuqpak | 3×20$^3$ | , | 24,000 |
| sisamaqpak | 4×20$^3$ | , | 32,000 |
| tallimaqpak | 5×20$^3$ | , | 40,000 |
| quliqpak | 10×20$^3$ | , | 80,000 |
| akimiaqpak | 15×20$^3$ | , | 120,000 |
| iñuiññaqpak | 20×20$^3$ [= 20$^4$] | , | 160,000 |
n-kipiaq-pak (n × 20$^4$) :
| malġukipiaqpak | 2×20×20$^3$ | , | 320,000 |
| piŋasukipiaqpak | 3×20×20$^3$ | , | 480,000 |
| sisamakipiaqpak | 4×20×20$^3$ | , | 640,000 |
| tallimakipiaqpak | 5×20×20$^3$ | , | 800,000 |
| qulikipiaqpak | 10×20×20$^3$ | , | 1,600,000 |
| akimiakipiaqpak | 15×20×20$^3$ | , | 2,400,000 |
n-pak (n × 20$^3$) :
| iḷagiññaqpak | 400×20$^3$ [= 20$^5$] | , | 3,200,000 |
n-agliaq-pak (n × 20$^5$) :
| malġuagliaqpak | 2×20$^2$×20$^3$ | , | 6,400,000 |
| piŋasuagliaqpak | 3×20$^2$×20$^3$ | , | 9,600,000 |
| sisamaagliaqpak | 4×20$^2$×20$^3$ | , | 12,800,000 |
| tallimaagliaqpak | 5×20$^2$×20$^3$ | , | 16,000,000 |
| quliagliaqpak | 10×20$^2$×20$^3$ | , | 32,000,000 |
| akimiagliaqpak | 15×20$^2$×20$^3$ | , | 48,000,000 |
n-pakaippaq (n × 20$^6$) :
| atausiqpakaippaq | 1×(20$^3$)$^2$ [= 20$^6$] | ,, | 64,000,000 |
| malġuqpakaippaq | 2×(20$^3$)$^2$ | ,, | 128,000,000 |
| piŋasuqpakaippaq | 3×(20$^3$)$^2$ | ,, | 192,000,000 |
| sisamaqpakaippaq | 4×(20$^3$)$^2$ | ,, | 256,000,000 |
| tallimaqpakaippaq | 5×(20$^3$)$^2$ | ,, | 320,000,000 |
| quliqpakaippaq | 10×(20$^3$)$^2$ | ,, | 640,000,000 |
| akimiaqpakaippaq | 15×(20$^3$)$^2$ | ,, | 960,000,000 |
| iñuiññaqpakaippaq | 20×(20$^3$)$^2$ [= 20$^7$] | ,, | 1,280,000,000 |
n-kipiaq-pakaippaq (n × 20$^7$) :
| malġukipiaqpakaippaq | 2×20×(20$^3$)$^2$ | ,, | 2,560,000,000 |
| piŋasukipiaqpakaippaq | 3×20×(20$^3$)$^2$ | ,, | 3,840,000,000 |
| sisamakipiaqpakaippaq | 4×20×(20$^3$)$^2$ | ,, | 5,120,000,000 |
| tallimakipiaqpakaippaq | 5×20×(20$^3$)$^2$ | ,, | 6,400,000,000 |
| qulikipiaqpakaippaq | 10×20×(20$^3$)$^2$ | ,, | 12,800,000,000 |
| akimiakipiaqpakaippaq | 15×20×(20$^3$)$^2$ | ,, | 19,200,000,000 |
n-pakaippaq (n × 20$^6$) :
| iḷagiññaqpakaippaq | 400×(20$^3$)$^2$ [= 20$^8$] | ,, | 25,600,000,000 |
n-agliaq-pakaippaq (n × 20$^8$) :
| malġuagliaqpakaippaq | 2×20$^2$×(20$^3$)$^2$ | ,, | 51,200,000,000 |
| piŋasuagliaqpakaippaq | 3×20$^2$×(20$^3$)$^2$ | ,, | 76,800,000,000 |
| sisamaagliaqpakaippaq | 4×20$^2$×(20$^3$)$^2$ | ,, | 102,400,000,000 |
| tallimaagliaqpakaippaq | 5×20$^2$×(20$^3$)$^2$ | ,, | 128,000,000,000 |
| quliagliaqpakaippaq | 10×20$^2$×(20$^3$)$^2$ | ,, | 256,000,000,000 |
| akimiagliaqpakaippaq | 15×20$^2$×(20$^3$)$^2$ | ,, | 384,000,000,000 |
n-pakpiŋatchaq (n × 20$^9$) :
| atausiqpakpiŋatchaq | 1×(20$^3$)$^3$ [= 20$^9$] | ,,, | 512,000,000,000 |
| malġuqpakpiŋatchaq | 2×(20$^3$)$^3$ | ,,, | 1,024,000,000,000 |
| piŋasuqpakpiŋatchaq | 3×(20$^3$)$^3$ | ,,, | 1,536,000,000,000 |
| sisamaqpakpiŋatchaq | 4×(20$^3$)$^3$ | ,,, | 2,048,000,000,000 |
| tallimaqpakpiŋatchaq | 5×(20$^3$)$^3$ | ,,, | 2,560,000,000,000 |
| quliqpakpiŋatchaq | 10×(20$^3$)$^3$ | ,,, | 5,120,000,000,000 |
| akimiaqpakpiŋatchaq | 15×(20$^3$)$^3$ | ,,, | 7,680,000,000,000 |
| iñuiññaqpakpiŋatchaq | 20×(20$^3$)$^3$ [= 20$^{10}$] | ,,, | 10,240,000,000,000 |
n-kipiaq-pakpiŋatchaq (n × 20$^{10}$) :
| malġukipiaqpakpiŋatchaq | 2×20×(20$^3$)$^3$ | ,,, | 20,480,000,000,000 |
| piŋasukipiaqpakpiŋatchaq | 3×20×(20$^3$)$^3$ | ,,, | 30,720,000,000,000 |
| sisamakipiaqpakpiŋatchaq | 4×20×(20$^3$)$^3$ | ,,, | 40,960,000,000,000 |
| tallimakipiaqpakpiŋatchaq | 5×20×(20$^3$)$^3$ | ,,, | 51,200,000,000,000 |
| qulikipiaqpakpiŋatchaq | 10×20×(20$^3$)$^3$ | ,,, | 102,400,000,000,000 |
| akimiakipiaqpakpiŋatchaq | 15×20×(20$^3$)$^3$ | ,,, | 153,600,000,000,000 |
n-pakpiŋatchaq (n × 20$^9$) :
| iḷagiññaqpakpiŋatchaq | 400×(20$^3$)$^3$ [= 20$^{11}$] | ,,, | 204,800,000,000,000 |
n-agliaq-pakpiŋatchaq (n × 20$^{11}$) :
| malġuagliaqpakpiŋatchaq | 2×20$^2$×(20$^3$)$^3$ | ,,, | 409,600,000,000,000 |
| piŋasuagliaqpakpiŋatchaq | 3×20$^2$×(20$^3$)$^3$ | ,,, | 614,400,000,000,000 |
| sisamaagliaqpakpiŋatchaq | 4×20$^2$×(20$^3$)$^3$ | ,,, | 819,200,000,000,000 |
| tallimaagliaqpakpiŋatchaq | 5×20$^2$×(20$^3$)$^3$ | ,,, | 1,024,000,000,000,000 |
| quliagliaqpakpiŋatchaq | 10×20$^2$×(20$^3$)$^3$ | ,,, | 2,048,000,000,000,000 |
| akimiagliaqpakpiŋatchaq | 15×20$^2$×(20$^3$)$^3$ | ,,, | 3,072,000,000,000,000 |
| iñuiññagliaqpakpiŋatchaq | 20×20$^2$×(20$^3$)$^3$ [= 20$^{12}$] | ,,,, | 4,096,000,000,000,000 |