Welsh numerals

The traditional counting system used in the Welsh language is vigesimal, i.e. based on twenties where numbers from 11 to 14 are "1-4 on ten", 16-19 are "1-4 on fifteen" (though 18 is more commonly "two nines"); numbers from 21 to 39 are "1-19 on twenty", 40 is "two twenty", 60 is "three twenty", etc.

There is also a decimal counting system, where numbers are "x ten y" unit(s), e.g. thirty-five (35) in decimal is tri deg pump (three ten five) while in vigesimal it is pymtheg ar hugain (fifteen - itself "five-ten" - on twenty).

Number Vigesimal system Decimal system 0 sero/dim 1 un 2 dau (m), dwy (f) 3 tri (m), tair (f) 4 pedwar (m), pedair (f) 5 pum(p) 6 chwe(ch) 7 saith 8 wyth 9 naw 10 deg/un deg, deng 11 un ar ddeg("one on ten") un deg un 12 deuddeg, deuddeng un deg dau/dwy 13 tri/tair ar ddeg un deg tri/tair 14 pedwar/pedair ar ddeg un deg pedwar/pedair 15 pymtheg, pymtheng un deg pump 16 un ar bymtheg("one on fifteen") un deg chwech 17 dau/dwy ar bymtheg un deg saith 18 deunaw/tri/tair ar bymtheg("two nines"/"three on fifteen") un deg wyth 19 pedwar/pedair ar bymtheg un deg naw 20 ugain dau ddeg 21 un ar hugain("one on twenty") dau ddeg un 22 dau/dwy ar hugain dau ddeg dau/dwy 23 tri/tair ar hugain dau ddeg tri/tair 24 pedwar/pedair ar hugain dau ddeg pedwar/pedair 25 pump ar hugain dau ddeg pump 26 chwech ar hugain dau ddeg chwech 27 saith ar hugain dau ddeg saith 28 wyth ar hugain dau ddeg wyth 29 naw ar hugain dau ddeg naw 30 deg ar hugain("ten on twenty") tri deg 31 un ar ddeg ar hugain tri deg un 32 deuddeg ar hugain tri deg dau/dwy etc. 40 deugain("two twenty") pedwar deg 41 deugain ac un("two twenty and one") pedwar deg un 50 deg a deugain pum deghanner cant ("half a hundred") 51 un ar ddeg a deugain pum deg unhanner cant ac un 60 trigain("three twenty") chwe deg 61 trigain ac un chwe deg un 70 deg a thrigain("ten and three twenty") saith deg 71 un ar ddeg a thrigain("one on ten and three twenty") saith deg un 80 pedwar ugain("four twenty") wyth deg 81 pedwar ugain ac un wyth deg un 90 deg a phedwar ugain("ten and four twenty") naw deg 91 un ar ddeg a phedwar ugain("one on ten and four twenty") naw deg un 100 can(t) 200 dau gant 300 tri chant 400 pedwar cant 500 pum cant 600 chwe chant 700 saith cant 800 wyth cant 900 naw cant 1000 mil 2000 dau fil/dwy fil 1,000,000 miliwn 1,000,000,000 biliwn 1,000,000,000,000 triliwn

There is some syntactically and phonologically triggered variation in the form of numerals. There are, for example, masculine and feminine forms of the numbers "two" (dau and dwy), "three" (tri and tair) and "four" (pedwar and pedair), which must agree with the grammatical gender of the objects being counted. The numerals for "five", "six" and "hundred" (pump, chwech and cant) also have reduced forms (pum, chwe, can) when they precede the object they are counting. The words for "ten", "twelve", and "fifteen" (deg, un deg dau/deuddeg, un deg pump/pymtheg) have the alternative forms deng, deuddeng, pymtheng used before nasals (which may be the result of mutation) and, occasionally, vowels; these forms are becoming less common.[1] Numerals change as expected according to normal rules of consonant mutation; some also trigger mutation in some following words (see below for details).[1]

The decimal system is widely used, but is rather uncommon for dates and ages. Larger numbers, however, tend to be expressed in this system e.g. 1,965 mil, naw cant chwe deg pump. In referring to years, on the other hand, the number of thousands is stated, followed by the individual digits, e.g. 1965 mil naw chwe(ch) pump. This system appears to have broken down for years after 2000, e.g. whereas 1905 is mil naw dim pump, 2005 is dwy fil a phump.

The Welsh decimal counting system was devised by 19th-century Patagonian Welsh businessmen in Argentina for accountancy purposes. It was recommended to teachers for use in the first Welsh language schools in Patagonia by Richard Jones Berwyn in a book published in 1878. The system was later adopted in Wales in the late 1940s with the beginning of Welsh-medium education.[2]

The singular form of the noun is used with numbers, but for larger numbers an alternative form is permitted, where o ("of") with the plural noun follows the number. Except where using this plural form, the noun is placed directly after the number but before any parts of the number that are added using ar ("on") in the traditional system.

Nouns are also mutated following many numbers. Un triggers the soft mutation (treiglad meddal) of feminine nouns, other than those beginning with "ll" and "rh", but not masculine nouns. Dau and dwy both trigger the soft mutation (ll and rh included). Tri (but not tair) and chwe trigger the aspirate mutation. Several higher numbers (pum, saith, wyth, deng, deuddeng, and pymtheng) trigger the nasal mutation when used with blynedd ("year(s)"). The part of the number immediately preceding the noun will determine any mutation of the noun. In the plural form with o, the soft mutation is used as is normal after o.

The following example illustrates several of these points:

English Thirty-six dogs Traditionalsystem Decimalsystem