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Dzongkha , the national language of Bhutan
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 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

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Links: ------ /wiki/Dzongkha_language /wiki/Bhutan /wiki/Vigesimal /wiki/Decimal

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