Dzongkha numerals

Numeral systems

Hindu–Arabic numeral system
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East Asian
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Former
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Positional systems by base
2 3 4 5 6 8 10 12 16 20 60
Non-standard positional numeral systems
Bijective numeration (1) Signed-digit representation (Balanced ternary) factorial negative Complex-base system (2i) Non-integer representation (φ) mixed
List of numeral systems

Dzongkha, the national language of Bhutan, has two numeral systems, one vigesimal (base 20), and a modern decimal system. The vigesimal system remains in robust use. Ten is an auxiliary base: the teens are formed with ten and the numerals 1–9.

Vigesimal

1	༡	ciː	11	༡༡	cu-ci
2	༢	ˈɲiː	12	༡༢	cu-ɲi
3	༣	sum	13	༡༣	cu-sum
4	༤	ʑi	14	༡༤	cu-ʑi
5	༥	ˈŋa	15	༡༥	ce-ŋa
6	༦	ɖʱuː	16	༡༦	cu-ɖu
7	༧	dyn	17	༡༧	cup-dỹ
8	༨	ɡeː	18	༡༨	cop-ɡe
9	༩	ɡuː	19	༡༩	cy-ɡu
10	༡༠	cu-tʰãm*	20	༢༠	kʰe ciː

*When it appears on its own, 'ten' is usually said cu-tʰãm 'a full ten'. In combinations it is simply cu.

Factors of 20 are formed from kʰe. Intermediate factors of ten are formed with pɟʱe-da 'half to':

30	kʰe pɟʱe-da ˈɲiː	(a half to two score)
40	kʰe ˈɲiː	(two score)
50	kʰe pɟʱe-da sum	(a half to three score)
100	kʰe ˈŋa	(five score)
200	kʰe cutʰãm	(ten score)
300	kʰe ceŋa	(fifteen score)

400 (20²) ɲiɕu is the next unit: ɲiɕu ciː 400, ɲiɕu ɲi 800, etc. Higher powers are 8000 (20³) kʰecʰe ('a ɡreat score') and jãːcʰe 160,000 (20⁴).

Decimal

The decimal system is the same as the vigesimal system up to 19. Then decades, however, are formed as unit–ten, as in Chinese, and the hundreds similarly. 20 is reported to be ɲiɕu, the vigesimal numeral 400; this may be lexical interference for the expected *ɲi-cu. (In any case, there is no ambiguity, because as 400 it is obligatorily ɲiɕu ciː 'one 400'.) Several of the decades have an epenthetic -p-, perhaps by analogy with 18 and 19, where the -p- presumably reflects a historical *cup 'ten':

sum-cu 30, ʑi-p-cu 40, ˈŋa-p-cu 50, ɟa-tʰampa or cik-ɟa 100 (a 'full hundred' or 'one hundred'), ɲi-ɟa 200, sum-ɟa 300, ʑi-p-ɟa 400, etc.

References

Mazaudon & Lacito, 2002, "Les principes de construction du nombre dans les langues tibeto-birmanes", in François, ed. La Pluralité, p. 6 ff

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