Dzongkha numerals

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.


1ciː 11༡༡cu-ci
2ˈɲiː 12༡༢cu-ɲi
3sum 13༡༣cu-sum
4ʑi 14༡༤cu-ʑi
5ˈŋa 15༡༥ce-ŋa
6ɖʱuː 16༡༦cu-ɖu
7dyn 17༡༧cup-dỹ
8ɡeː 18༡༨cop-ɡe
9ɡuː 19༡༩cy-ɡu
10༡༠cu-tʰãm* 20༢༠kʰe 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':

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


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.


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