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 | ciː | 11 | cu-ci |

2 | ˈɲiː | 12 | cu-ɲi |

3 | sum | 13 | cu-sum |

4 | ʑi | 14 | cu-ʑi |

5 | ˈŋa | 15 | ce-ŋa |

6 | ɖʱuː | 16 | cu-ɖu |

7 | dyn | 17 | cup-dỹ |

8 | ɡeː | 18 | cop-ɡe |

9 | ɡuː | 19 | cy-ɡu |

10 | cu-tʰãm* | 20 | 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 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.

## References

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