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.^[1] (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 × 20⁰)
Numeral	Morphological pattern	Hindu-Arabic notation
kisitchisaġvik	^[a]	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.

n-kipiaq (n × 20¹)
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

n-agliaq (n × 20²)
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

n-pak (n × 20³)
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

n-kipiaq-pak (n × 20⁴)
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

n-pak (n × 20³)
iḷagiññaqpak	400×20³ [= 20⁵]	,	3,200,000

n-agliaq-pak (n × 20⁵)
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

n-pakaippaq (n × 20⁶)
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

n-kipiaq-pakaippaq (n × 20⁷)
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

n-pakaippaq (n × 20⁶)
iḷagiññaqpakaippaq	400×(20³)² [= 20⁸]	,,	25,600,000,000

n-agliaq-pakaippaq (n × 20⁸)
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

n-pakpiŋatchaq (n × 20⁹)
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

n-kipiaq-pakpiŋatchaq (n × 20¹⁰)
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

n-pakpiŋatchaq (n × 20⁹)
iḷagiññaqpakpiŋatchaq	400×(20³)³ [= 20¹¹]	,,,	204,800,000,000,000

n-agliaq-pakpiŋatchaq (n × 20¹¹)
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

References

^ MacLean (2014) Iñupiatun Uqaluit Taniktun Sivuninit / Iñupiaq to English Dictionary, p. 840 ff

[2] A deverbal noun. Outside of mathematics, suitchuq "none" or suitchuq X "no X" is normally used.

[1] MacLean (2014) Iñupiatun Uqaluit Taniktun Sivuninit / Iñupiaq to English Dictionary, p. 840 ff

[1]

[a]