Iñupiaq numerals

The Iñupiaq language has a vigesimal (base-20) numeral system. 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)
NumeralMorphological
pattern
Kaktovik
notation
Hindu-Arabic
notation
kisitchisaġvik[2] 𝋀 0
atausiq1 𝋁 1
malġuk2 𝋂 2
piŋasut3 𝋃 3
sisamat4 𝋄 4
tallimat5 𝋅 5
itchaksrat6 𝋆 6
tallimat malġuk5 + 2 𝋇 7
tallimat piŋasut5 + 3 𝋈 8
quliŋŋuġutaiḷaq10 − 1 𝋉 9
qulit10 𝋊 10
qulit atausiq10 + 1 𝋋 11
qulit malġuk10 + 2 𝋌 12
qulit piŋasut10 + 3 𝋍 13
akimiaġutaiḷaq15 − 1 𝋎 14
akimiaq15 𝋏 15
akimiaq atausiq15 + 1 𝋐 16
akimiaq malġuk15 + 2 𝋑 17
akimiaq piŋasut15 + 3 𝋒 18
iñuiññaġutaiḷaq20 − 1 𝋓 19
iñuiññaq20 𝋁𝋀 20
iḷagiññaq400 𝋁𝋀𝋀 400
n-kipiaq (n × 201)
malġukipiaq2×20 𝋂𝋀 40
piŋasukipiaq3×20 𝋃𝋀 60
sisamakipiaq4×20 𝋄𝋀 80
tallimakipiaq5×20 𝋅𝋀 100
tallimakipiaq iñuiññaq5×20 + 20 𝋆𝋀 120
tallimakipiaq malġukipiaq5×20 + 2×20 𝋇𝋀 140
tallimakipiaq piŋasukipiaq5×20 + 3×20 𝋈𝋀 160
tallimakipiaq sisamakipiaq5×20 + 4×20 𝋉𝋀 180
qulikipiaq10×20 𝋊𝋀 200
qulikipiaq iñuiññaq10×20 + 20 𝋋𝋀 220
qulikipiaq malġukipiaq10×20 + 2×20 𝋌𝋀 240
qulikipiaq piŋasukipiaq10×20 + 3×20 𝋍𝋀 260
qulikipiaq sisamakipiaq10×20 + 4×20 𝋎𝋀 280
akimiakipiaq15×20 𝋏𝋀 300
akimiakipiaq iñuiññaq15×20 + 20 𝋐𝋀 320
akimiakipiaq malġukipiaq15×20 + 2×20 𝋑𝋀 340
akimiakipiaq piŋasukipiaq15×20 + 3×20 𝋒𝋀 360
akimiakipiaq sisamakipiaq15×20 + 4×20 𝋓𝋀 380
iñuiññakipiaq
(= iḷagiññaq above)
20×20
[= 202]
𝋁𝋀𝋀 400
n-agliaq (n × 202)
malġuagliaq2×202 𝋂𝋀𝋀 800
piŋasuagliaq3×202 𝋃𝋀𝋀 1,200
sisamaagliaq4×202 𝋄𝋀𝋀 1,600
tallimaagliaq5×202 𝋅𝋀𝋀 2,000
quliagliaq10×202 𝋊𝋀𝋀 4,000
akimiagliaq15×202 𝋏𝋀𝋀 6,000
n-pak (n × 203)
atausiqpak1×203 [= 203] 𝋁,𝋀𝋀𝋀 8,000
malġuqpak2×203 𝋂,𝋀𝋀𝋀 16,000
piŋasuqpak3×203 𝋃,𝋀𝋀𝋀 24,000
sisamaqpak4×203 𝋄,𝋀𝋀𝋀 32,000
tallimaqpak5×203 𝋅,𝋀𝋀𝋀 40,000
quliqpak10×203 𝋊,𝋀𝋀𝋀 80,000
akimiaqpak15×203 𝋏,𝋀𝋀𝋀 120,000
iñuiññaqpak20×203 [= 204] 𝋁𝋀,𝋀𝋀𝋀 160,000
n-kipiaq-pak (n × 204)
malġukipiaqpak2×20×203 𝋂𝋀,𝋀𝋀𝋀 320,000
piŋasukipiaqpak3×20×203 𝋃𝋀,𝋀𝋀𝋀 480,000
sisamakipiaqpak4×20×203 𝋄𝋀,𝋀𝋀𝋀 640,000
tallimakipiaqpak5×20×203 𝋅𝋀,𝋀𝋀𝋀 800,000
qulikipiaqpak10×20×203 𝋊𝋀,𝋀𝋀𝋀 1,600,000
akimiakipiaqpak15×20×203 𝋏𝋀,𝋀𝋀𝋀 2,400,000
n-pak (n × 203)
iḷagiññaqpak400×203 [= 205] 𝋁𝋀𝋀,𝋀𝋀𝋀 3,200,000
n-agliaq-pak (n × 205)
malġuagliaqpak2×202×203 𝋂𝋀𝋀,𝋀𝋀𝋀 6,400,000
piŋasuagliaqpak3×202×203 𝋃𝋀𝋀,𝋀𝋀𝋀 9,600,000
sisamaagliaqpak4×202×203 𝋄𝋀𝋀,𝋀𝋀𝋀 12,800,000
tallimaagliaqpak5×202×203 𝋅𝋀𝋀,𝋀𝋀𝋀 16,000,000
quliagliaqpak10×202×203 𝋊𝋀𝋀,𝋀𝋀𝋀 32,000,000
akimiagliaqpak15×202×203 𝋏𝋀𝋀,𝋀𝋀𝋀 48,000,000
n-pakaippaq (n × 206)
atausiqpakaippaq1×(203)2 [= 206] 𝋁,𝋀𝋀𝋀,𝋀𝋀𝋀 64,000,000
malġuqpakaippaq2×(203)2 𝋂,𝋀𝋀𝋀,𝋀𝋀𝋀 128,000,000
piŋasuqpakaippaq3×(203)2 𝋃,𝋀𝋀𝋀,𝋀𝋀𝋀 192,000,000
sisamaqpakaippaq4×(203)2 𝋄,𝋀𝋀𝋀,𝋀𝋀𝋀 256,000,000
tallimaqpakaippaq5×(203)2 𝋅,𝋀𝋀𝋀,𝋀𝋀𝋀 320,000,000
quliqpakaippaq10×(203)2 𝋊,𝋀𝋀𝋀,𝋀𝋀𝋀 640,000,000
akimiaqpakaippaq15×(203)2 𝋏,𝋀𝋀𝋀,𝋀𝋀𝋀 960,000,000
iñuiññaqpakaippaq20×(203)2 [= 207] 𝋁𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 1,280,000,000
n-kipiaq-pakaippaq (n × 207)
malġukipiaqpakaippaq2×20×(203)2 𝋂𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 2,560,000,000
piŋasukipiaqpakaippaq3×20×(203)2 𝋃𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 3,840,000,000
sisamakipiaqpakaippaq4×20×(203)2 𝋄𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 5,120,000,000
tallimakipiaqpakaippaq5×20×(203)2 𝋅𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 6,400,000,000
qulikipiaqpakaippaq10×20×(203)2 𝋊𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 12,800,000,000
akimiakipiaqpakaippaq15×20×(203)2 𝋏𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 19,200,000,000
n-pakaippaq (n × 206)
iḷagiññaqpakaippaq400×(203)2 [= 208] 𝋁𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 25,600,000,000
n-agliaq-pakaippaq (n × 208)
malġuagliaqpakaippaq2×202×(203)2 𝋂𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 51,200,000,000
piŋasuagliaqpakaippaq3×202×(203)2 𝋃𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 76,800,000,000
sisamaagliaqpakaippaq4×202×(203)2 𝋄𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 102,400,000,000
tallimaagliaqpakaippaq5×202×(203)2 𝋅𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 128,000,000,000
quliagliaqpakaippaq10×202×(203)2 𝋊𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 256,000,000,000
akimiagliaqpakaippaq15×202×(203)2 𝋏𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 384,000,000,000
n-pakpiŋatchaq (n × 209)
atausiqpakpiŋatchaq1×(203)3 [= 209] 𝋁,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 512,000,000,000
malġuqpakpiŋatchaq2×(203)3 𝋂,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 1,024,000,000,000
piŋasuqpakpiŋatchaq3×(203)3 𝋃,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 1,536,000,000,000
sisamaqpakpiŋatchaq4×(203)3 𝋄,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 2,048,000,000,000
tallimaqpakpiŋatchaq5×(203)3 𝋅,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 2,560,000,000,000
quliqpakpiŋatchaq10×(203)3 𝋊,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 5,120,000,000,000
akimiaqpakpiŋatchaq15×(203)3 𝋏,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 7,680,000,000,000
iñuiññaqpakpiŋatchaq20×(203)3 [= 2010] 𝋁𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 10,240,000,000,000
n-kipiaq-pakpiŋatchaq (n × 2010)
malġukipiaqpakpiŋatchaq2×20×(203)3 𝋂𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 20,480,000,000,000
piŋasukipiaqpakpiŋatchaq3×20×(203)3 𝋃𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 30,720,000,000,000
sisamakipiaqpakpiŋatchaq4×20×(203)3 𝋄𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 40,960,000,000,000
tallimakipiaqpakpiŋatchaq5×20×(203)3 𝋅𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 51,200,000,000,000
qulikipiaqpakpiŋatchaq10×20×(203)3 𝋊𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 102,400,000,000,000
akimiakipiaqpakpiŋatchaq15×20×(203)3 𝋏𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 153,600,000,000,000
n-pakpiŋatchaq (n × 209)
iḷagiññaqpakpiŋatchaq400×(203)3 [= 2011] 𝋁𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 204,800,000,000,000
n-agliaq-pakpiŋatchaq (n × 2011)
malġuagliaqpakpiŋatchaq2×202×(203)3 𝋂𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 409,600,000,000,000
piŋasuagliaqpakpiŋatchaq3×202×(203)3 𝋃𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 614,400,000,000,000
sisamaagliaqpakpiŋatchaq4×202×(203)3 𝋄𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 819,200,000,000,000
tallimaagliaqpakpiŋatchaq5×202×(203)3 𝋅𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 1,024,000,000,000,000
quliagliaqpakpiŋatchaq10×202×(203)3 𝋊𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 2,048,000,000,000,000
akimiagliaqpakpiŋatchaq15×202×(203)3 𝋏𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 3,072,000,000,000,000
iñuiññagliaqpakpiŋatchaq20×202×(203)3 [= 2012] 𝋁,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀,𝋀𝋀𝋀 4,096,000,000,000,000

References

  1. 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.
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