|Hindu–Arabic numeral system|
|Positional systems by base|
|Non-standard positional numeral systems|
|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.
*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).
The decimal system is the same 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 same as 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.
- Mazaudon & Lacito, 2002, "Les principes de construction du nombre dans les langues tibeto-birmanes", in François, ed. La Pluralité, p. 6 ff