# 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.

## Vigesimal

 1 ༡ ci 11 ༡༡ 2 ༢ 'nyî 12 ༡༢ 3 ༣ sum 13 ༡༣ 4 ༤ zhi 14 ༡༤ 5 ༥ nga 15 ༡༥ 6 ༦ dru 16 ༡༦ 7 ༧ dün 17 ༡༧ 8 ༨ gä 18 ༡༨ 9 ༩ gu 19 ༡༩ 10 ༡༠ cuthâm 20 ༢༠

*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 ཁལ khä (pronounced kʰe). Intermediate factors of ten are formed with pɟʱe-da 'half to'.

 30 ཁལ་ཕྱེད་དང་གཉིས། khä pched˚â 'nyî a half to two score 40 ཁལ་གཉིས། khä yî two score 50 ཁལ་ཕྱེད ་དང་གསུམ། khä pched˚â sum a half to three score 100 ཁལ་ལྔ། khä 'nga five score 200 ཁལ་བཅུ་ཐམ། khä cutham ten score 300 ཁལ་བཅོ་ལྔ། khä cä'nga fifteen score

400 (202) ɲiɕu ci is the next unit: ཉི་ཤུ་གཅིག nyishu cî (pron. ɲiɕu ciː) 400, ཉི་ཤུ་གཉིས། nyishu 'nyî (pron. ɲiɕu ɲi) 800, etc. Higher powers are 8000 (203) ཁལ་ཆེན་གཅིག khächen (cî) (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':

སུམ་ཅུ། (sumcu) 30, བཞི་བཅུ། (zhipcu, pronounced ʑi-p-cu) 40, ལྔ་བཅུ། (ngapcu, pron. ˈŋa-p-cu) 50, བརྒྱ་ཐམ་པ། (jathamb˚a, pron. ɟa-tʰampa) or གཅིག་བརྒྱ། (cikja) 100 (a 'full hundred' or 'one hundred'), ཉིས་བརྒྱ། (nyînja, pron. ɲi-ɟa) 200, སུམ་བརྒྱ། (sumja) 300, བཞི་བརྒྱ། (zhipja, pron. ʑi-p-ɟa) 400, etc.